text:
\section{Introduction}\label{intro}
Despite its low abundance (N(Li)/N(H) $\leq 2\times 10^{-9}$),
lithium (Li)
plays a fundamental role in different fields of astrophysics because of
how it is created and destroyed. The $^7$Li isotope is the heaviest element
produced during Big Bang nucleosynthesis
(BBN), and its primordial abundance strongly depends on $\eta$, the ratio
of baryons to photons (e.g., Steigman~\cite{steig_cast} and references therein).
At the same time, Li is easily depleted from stellar atmospheres:
$^7$Li is destroyed by proton reactions at
the relatively low temperature of $\sim 2.5$~MK, implying depletion with
respect to the initial content
whenever a mixing process is present that
is able to transport surface material down to the deeper regions in
the stellar interior where this temperature is reached.

Primordial Li abundance has been empirically estimated by means of
Li measurements in old Pop.~{\sc ii} stars and, theoretically, using
BBN calculations combined
with the baryon density derived from measurements of  the  cosmic
microwave background temperature fluctuations. The reliability of the
latter has dramatically  improved after data  from the WMAP  satellite
became available (Cyburt et al.~\cite{cyburt};
Spergel et al.~\cite{spergel}). Estimates from old
stars rely on the assumption that the hot (T$_{\rm eff}\geq$ 5800
K), metal poor, Pop.~{\sc ii} dwarfs do not deplete Li in their
atmosphere, hence represent the primordial
material from which they were born.
The confidence on this assumption is based on the near
constancy of their Li abundance with metallicity, first discovered by
Spite \& Spite (\cite{spite82})
and generally referred to as the Spite plateau.
Primordial Li abundance predicted from standard BBN calculations with
WMAP is a factor of two to three higher than that of the  Spite
plateau, which might indicate that halo stars have indeed undergone
some Li depletion, possibly due to microscopic diffusion,
as recently claimed by Korn et al. (\cite{korn},~\cite{korn1}). Only
through a full understanding of mixing inside stars and its dependence
on metallicity will we be able to reach a conclusion with complete
confidence.

To achieve that, studies in Pop.~{\sc   i} stars,  and in
particular among open cluster members, are the most suitable observation
tool. Lithium (and beryllium) measurements in Galactic
open clusters (OCs) indeed allow us to empirically trace Li depletion with age,
metallicity, and mass.
Focusing on solar-type stars, standard models of stellar
evolution (those including  convection only) predict that these stars  should
not suffer any Li depletion during the main sequence (MS), since their
convective zone does not reach the Li burning layer.  Surveys of Li in
a variety of OCs and, in particular, the comparison  of the Li
patterns of OCs of different age, have shown that, at variance
with these predictions, solar-type stars do deplete Li on the MS.
Depletion  starts at $\sim 100$~Myr and smoothly goes on up to
the Hyades age, on a timescale of $\sim 1.4$~Gyr. After that age depletion
becomes bimodal: it is very fast for a fraction of stars, like the Sun itself,
and the lower envelope of M~67 (Pasquini et al. \cite{pas97} and references
therein), while
depletion completely stops after
$\sim 1$~Gyr for a significant fraction of stars (Sestito \& Randich
\cite{sr05}; Prisinzano \& Randich~\cite{pr07})
In particular, Randich et al.
(\cite{randich_188} -RSP03
hereafter) have shown that members of the old (6--8~Gyr) OC
NGC~188 have a Li abundance only  a factor of two smaller than their
counterparts in  the factor of 10 younger Hyades; moreover, the average
value of Li in NGC~188
is surprisingly close to what is measured in Pop.~{\sc ii} stars.
This open cluster has a solar metallicity and, as discussed by RSP03, this
result might be a mere coincidence; however, the issue is obviously
worth  further  studies. It might indeed represent a link between
Pop.~{\sc i} and Pop.~{\sc ii}. Li depletion histories and provide a
clue to understand  whether the latter  have undergone Li depletion.
Investigating Li in additional very old OCs is thus very important.

It is worth mentioning that, to explain the unexpected Li
depletion during the MS,
several non-standard processes
were included in the models. The proposed mechanisms include
diffusion (Michaud~\cite{mich86}, Michaud et al.~\cite{mich04};
Chaboyer et al.~\cite{chab95}),
meridional circulation (Charbonnel \& Talon~\cite{ct99} and references
therein), angular momentum
loss and rotationally driven mixing (Eddington 1925;
Zahn 1974, 1992; Deliyannis \& Pinsonneault 1997),
gravity waves (Garc\'\i a L\'opez \& Spruit 1991; Montalb\`an \& Schatzmann
2000),
tachocline (Spergel \& Zahn 1992; Brun et al. 1999; Piau et al. 2003),
and combinations of waves and rotation (Charbonnel \& Talon~\cite{ct05};
Talon~\cite{talon}).
Each of these models makes specific predictions on the timescales of Li
depletion which can be compared with observational patterns.

We present here Li observations in a very large sample of members of
Berkeley 32. This open cluster is one of the  oldest in the Galaxy (5~Gyr
--e.g. D' Orazi et al.~\cite{dorazi}) and its metallicity is a factor of
two below
solar (Sestito et al.~\cite{sestito06}); therefore, it provides an
ideal sample to further
investigate the issue of the convergence of Li at old ages.

The paper is organized as follows. In Sect.~2 we describe the sample,
the observations, and data reduction. Data analysis and the results
are presented in Sects. 3 and 4. A discussion is provided in Sect.~5,
followed by conclusions in Sect.~6.
\section{Sample and observations}
The observations were obtained with VLT/FLAMES.
Specifically,  we used the fiber link to UVES
to acquire spectra of evolved stars (RGB and clump stars)
to be used for the determination of
the cluster chemical compositions (Sestito et al.~\cite{sestito06};
Bragaglia et al.~\cite{brag08}),
while the Giraffe spectrograph and Medusa fiber system were employed
to observe MS and/or turn-off (TO) cluster candidates as well as
a few subgiants, in order to derive
membership and information on Li.
\subsection{Targets}
Photometric surveys of Be 32 have been performed by Kaluzny \& Mazur
(\cite{km91}), Richtler \& Sagar (\cite{rs00}), Hasegawa
et al. (\cite{hase}), and D'~Orazi et al. (\cite{dorazi}). A re-analysis
of D'~Orazi et al. photometry was performed by Tosi et al.(\cite{tbc}).
All these studies agree on a cluster age of 5--6~Gyr, on a subsolar
metallicity, and on a reddening E(B--V) in the range 0.08 -- 0.16,
with a most likely value of 0.1--0.12
(see discussion in Tosi et al.). Based on UVES
spectra of nine cluster members Sestito et a.~(\cite{sestito06})
derived for the
cluster a metallicity [Fe/H]=$-0.29\pm 0.04$. So far no spectroscopic
studies of MS stars have been performed and membership is based only
on photometric criteria.
\begin{figure}
\psfig{figure=0995fig1.ps, width=8.5cm}
\caption{V vs. V--I diagram of Be~32 with FLAMES targets shown
as filled symbols.
The whole catalog was constructed using Richtler \& Sagar (\cite{rs00})
photometry. We show in the figure only stars brighter than V=21.
}\label{fig1}
\end{figure}
\begin{figure*}
\psfig{figure=0995fig2.ps, width=17cm}
\caption{Sample spectra in the Li region. The position of the Li line
is marked.}
\label{fig2}
\end{figure*}
We selected Giraffe target stars from the
catalogs of Kaluzny \& Mazur (\cite{km91}) and Richtler \& Sagar (\cite{rs00}),
since  the study of D'Orazi et al.
was still in preparation at the time of the observations.
The V -- V--I diagram of the target stars is displayed in Fig.~\ref{fig1}
which shows that the sample includes stars from the cluster subgiant branch and
turn-off (TO)
(V~$\sim 16$) down to V=18.
As mentioned, membership for these candidates so far has been based
only on photometry.
One of the purposes of this study is a more reliable
determination of membership via radial velocity measurements.
\subsection{Observations and data reduction}
Be~32 was observed with two different FLAMES configurations
(A and B) centered at
RA(2000)=06h~58m~04.2s and DEC(2000)=$-$06d~28m~21.1s and
RA(2000)=06h~58m~02.0s and DEC(2000)=$-$06d~22m~41.4s, respectively.
We obtained four and one 3600~s long exposures for configurations A and B,
respectively.
Observations were obtained in Visitor mode
on Jan. 20, 2005 (configuration A) and
Jan. 21, 2005 (configuration B).
Medusa fibers were allocated to 112 and 108 objects
in the two configurations, with 63 stars in common. In total we thus
obtained spectra of 157 cluster candidates. In both configurations 15 fibers
were put on the sky. Stars covered by configurations A and B
were observed for a total of 4 and 1~hrs, respectively, while the
63 stars in common were observed for 5 hrs.
Target stars, together with their photometry, are listed in Table~\ref{sample}.
In the table we list our running ID (Col.~1), coordinates from Kaluzny \& Mazur
(\cite{km91}) if the star is present in their catalog otherwise from
Richtler \& Sagar (\cite{rs00} --Cols.~2-3); photometry from D'~Orazi
et al. (\cite{dorazi} --Cols.~4--7);
V magnitude from Kaluzny \& Mazur
(\cite{km91}) if the star is present in their catalog otherwise from
Richtler \& Sagar (\cite{rs00} --Col.~8); B--V from Kaluzny \& Mazur
(Col.~9); V--I from Richtler \& Sagar (Col.~10); radial velocity
and membership flag (Cols.~11--12).
Giraffe was used
in conjunction with the 316 lines/mm grating and order-
sorting filter 15 (H15N)
yielding a nominal resolving power R=17000 and covering a spectral
interval from 644.2 to 681.8~nm, including the
Li~{\sc i}~670.8~nm line and several features to be used for radial velocity
measurements.

Data reduction was performed using the Giraffe BLDRS
pipeline\footnote{version 1.12 -- http://girbldrs.sourceforge.net/},
following the standard procedure and steps (Blecha et al.~\cite{blecha04}).
Sky subtraction was carried out separately;
namely, we first computed the average sky (sky$_{\rm av.}$)
of three sets of five sky spectra and then derived
the median of the three sky$_{\rm av.}$.
Radial velocities (RV) were
derived from each single spectrum (see below). Spectra of stars that were
not found to be RV~variables were then co-added.
Examples of final, sky-subtracted spectra are shown in Fig.~\ref{fig2}.
Final S/N range between 20 and 85, with an average value of $\sim 50$.
\section{Analysis}
\subsection{Radial velocities}
Radial velocities were obtained from our spectra and used
to derive membership information for the sample stars. The 645 - 682 ~nm
region contains a large number of unblended lines (mainly Fe, Ca, Ti, and Ni)
of various strengths suitable for accurate RV measurements.
The individual lines used for the RV
computation are listed in Table~\ref{lines}.
\begin{figure}
\psfig{figure=0995fig3.ps, width=8.5cm}
\caption{Density distribution of radial velocities for the 153
stars for which we could get a measurement.
The two Gaussians (solid curves) indicate the best fits for the cluster and
field, respectively. The average velocities along with $1 \sigma$ dispersion
are indicated.
}\label{fig3}
\end{figure}
\setcounter{table}{1}
\begin{table}
\caption{Individual lines suitable for RV computations.
\label{lines}}
\begin{tabular}{cc}
\hline
line \&  multiplet & $\lambda$ (\AA)\\
\hline
CaI 19	&	6449.810\\
CaI 18	&	6462.566\\
CaI 18	&	6471.660\\
FeI 206	&	6475.632\\
FeI 168	&	6494.985\\
FeI 268 + Ti 102 &6546.252\\
H$_\alpha$	&6562.808\\
FeI 268	&	6592.926\\
FeI 1197	&6633.764\\
NiI 43	&	6643.641\\
FeI 111	&	6663.446\\
FeI 268	&	6677.993\\
LiI 1	&	6707.815\\
CaI 32	&	6717.687\\
FeI 111	&	6750.152\\
NiI 57	&	6767.778\\
FeI 205	&	6783.710\\
FeI 268	&	6806.851\\
FeI 1197&	6810.280\\ \hline
\end{tabular}
\end{table}
The data analysis was performed by standard procedures within the IRAF
package\footnote{
IRAF is distributed by the National Optical
Astronomical Observatories, which  are operated by the Association of
Universities for Research in Astronomy,  under contract with the National
Science Foundation.},
fitting the strongest lines present in each spectrum by a Gaussian
profile. The resulting RVs from the individual lines were averaged, and
heliocentric corrections applied. Normally less than ten lines
per spectrum allowed us to obtain an RV value with an error of about 2 km/s;
RV values of spectra referring to the same star were then averaged for
stars in configuration A having multiple exposures.
Final radial velocities with their errors are given in Col.~9 of Table~
\ref{sample}. For stars with multiple RV measurements, the
error is the standard deviation from the average RV, while for stars in
configuration B the error is the uncertainty in the RV measurement itself.
\subsection{Li abundances}
Lithium abundances were derived by measuring the equivalent width (EW)
of the Li~{\sc I} line at 670.8~nm. Measurements were performed
by direct integration below the continuum.
For stars with detected Li, each measurement was performed
twice, meaning we determined the maximum and minimum  reasonable
values. We then
adopted the average between these two last values as EW measurement,
and we used half of the difference between
them as the error estimate on EW. In some RV members, the Li line could
not be detected and
we measured its upper limit, which was estimated
as the EW of the smallest detectable feature in the Li spectral region.
We measured the Li line in both radial velocity members and non-members.
Whereas for most radial velocity members we detected the Li line,
for six and 19 stars in fields A and B the S/N was
too low to even infer a meaningful upper limit. We mention in
passing that these stars are
not necessarily fainter than those where the Li line was measurable.
Lithium was also detected in 27 RV non-members.

Effective temperatures were determined on the basis of published
photometry (Richtler \& Sagar \cite{rs00}; D'Orazi et al. \cite
{dorazi}) and using the
color versus temperature calibrations by Alonso et al.~
(\cite{al96} --for MS stars, \cite{al99} --for evolved stars).
When available, we used the photometry of
D'Orazi et al., while we took colors from Richtler \& Sagar
for stars not included in the study of D'~Orazi et al.
As shown by Tosi et al.~(\cite{tbc}), the agreement between the two
photometries is very good for most stars in the magnitude
range considered here. More specifically,
we used B--V colors
from D' Orazi et al. (\cite{dorazi}) for 45 stars out of the 47 for which
they were available.
Stars \#364 and \#1241 have B--V colors from D'Orazi et al., but
that of the former star
is too red compared to the V--I, while B--V of the latter
is much bluer than the cluster sequence on the CM diagram; therefore
we did not use B--V from D'Orazi et al. We employed B--V of Kaluzny
\& Mazur (\cite{km91}) for two stars not included in the study
of D'Orazi et al. (\#236 and \#333) and for the aforementioned star \#364.
Finally, for star \#1241 and for eight stars
without available B--V we transformed
V--I into B--V using a linear relationship that nicely
fits the sequence of stars with both colors available.
Reddening determinations towards Be~32 vary between
E(B--V)=0.10 and 0.18~mag (see Tosi et al.~\cite{tbc});
we assumed the value E(B--V)$=0.14$, determined
by Bragaglia et al.~(\cite{brag08}) using spectroscopic temperatures, since
we regard it as
more reliable than values obtained from main sequence fitting.

To evaluate the random error that affects our temperature determinations,
we compared
effective temperatures based on the B--V colors of D'~Orazi et al. with
those estimated from B--V of
Kaluzny \& Mazur for the  32 stars studied in both referenced papers.
The average
$\Delta$T$_{\rm eff}$~=(T$_{\rm eff}$$^{\rm D'Orazi}$-T$_{\rm eff}$$^{\rm K\&M}$)
is $-50$~K with a standard deviation
equal to 116~K. We adopt this value as the typical error
on effective temperatures.

In previous studies (see Sestito\& Randich~\cite{sr05}), we derived
effective temperatures using the calibration of Soderblom et al.
(\cite{sod93a}). Since this calibration does not have a term
taking into account metallicity, we prefer to use Alonso's calibrations
for Be~32, whose metallicity is below solar.
Soderblom et al.'s calibration would have given warmer temperatures, with
a typical difference of 144~K. However, at solar metallicity
the two scales are very similar.

As is well known,
at our resolution the Li line is blended with a Fe~{\sc i} line.
To estimate the contribution of Fe to the total EW,
we cannot use the analytical approximation of Soderblom et al.
(\cite{sod93b}), which was derived using stars with solar metallicity.
We instead estimated the EW of this feature employing
MOOG (Sneden~\cite{sneden}
--Version 2000) and the driver {\it ewfind} using the appropriate
metallicity and stellar parameters. Effective temperatures
were derived as described above. The surface gravity for evolved stars
was estimated in the same fashion as in Sestito et al.~(\cite{sestito06}),
while for stars on the MS we assumed $\log$~g=4.5.
Microturbulence values $\xi=1.1$ and 1.5~km/s were used
for unevolved and evolved stars, respectively.
We found that for MS objects
EW(Fe~6707.44)=$(22.5-3.3\times 10^{-3}\times \rm T_{\rm eff}$)~\AA, while
the EW of the Fe line was computed separately for each evolved star.
The strength of this shallow Fe line has a very weak
dependence on both the microturbulence $\xi$ and $\log$~g:
a change in $\xi$ of 1 km/s
results in a change in EW below 0.2~m\AA, while a change of 0.5~dex
in $\log$~g results in a difference of $\sim 0.2$~m\AA.

The Li abundances were derived from corrected EWs using Soderblom
et al. (\cite{sod93b}) curves of growth (COGs), which assume local
thermodynamic equilibrium (LTE). A correction for non--LTE effects following
Carlsson et al. (\cite{carls}) has
also been run on our data, but it produces no significant changes.
Li for evolved stars was instead derived using MOOG, which allows changing
surface gravity and microturbulence. Using of a different code and
method to derive Li for evolved and unevolved stars introduces
a small offset between the two abundance scales. By using MOOG, we would
obtain slightly higher $\log$~n(Li)~for dwarf stars, typically by 0.05-0.1~dex.
On the one hand, this offset does not affect our results and,
in particular, our conclusions on dilution in more evolved stars
(Figs.~\ref{fig5} and \ref{fig6});
on the other hand, the use for Be~32 dwarf members of the same COGs
employed in
the literature for other OCs is critical to correctly draw
the time evolution of Li.

The final error on  the Li abundance measurement is  computed by
summing  quadratically the contributions from EW and temperature.
Errors in the Fe I contribution due to errors in T$_{\rm eff}$~are
very small, much smaller than the errors in the EW measurements
themselves: namely, $\delta$EW(Fe~I)=0.5~m\AA~for $\delta$T$_{\rm eff}$=100~K.
\section{Results}
\subsection{Radial velocities and membership} \label{memb}
In Fig.~\ref{fig3}, we show the density distribution of
radial velocities for
the 153 stars for which we were able to measure them. The figure
clearly shows a very narrow peak that indicates the presence
of the cluster. To derive the average cluster radial velocity,
we fitted the observed distribution
with two Gaussians, one for the cluster and
one for the field, and determined the best fit using a maximum
likelihood algorithm.
We obtained
RV$_{\rm cluster}=105.2$~Km/s, $\sigma_{\rm cluster}=0.86$ Km/s and
RV$_{\rm field}=62.6$~Km/s, $\sigma_{\rm field}=32.1$ Km/s, respectively.
Our measurement of the RV is in good agreement with the values of
D'~Orazi et al. (\cite{dorazi}, RV=106.7$\pm 8.5$~Km/s) from low-
resolution spectroscopy of 48 stars brighter than the turn-off,
of Sestito et al.~(\cite{sestito06}, RV=106$\pm 1.4$~Km/s), and
of Scott, Friel, \& Janes~(\cite{scott},
106$\pm 10$~Km/s) from the intermediate-resolution
spectroscopy of 10 giants. Also, three stars in our sample
have an RV measurement from D'Orazi et al.: \#74 (their \#698),
\#97 (their \#113), and \#1090 (their \#364).
The agreement in RV is excellent for all of them.
We stress that, thanks to our large
sample, we have been able to constrain the internal dispersion in
velocity much better than in previous studies, pushing it to below 1~Km/s.

We considered all stars as cluster members with RV within $3 \sigma$
from the cluster average: adopting this criterion, 59 and 24 stars
turned out to be members in fields A and B.
The total fraction of members is
83/153 stars, i.e., 54 \%.
The expected number of contaminants, or non members with RV consistent
with the cluster, is 2 stars.
Since our observations were obtained
within the same night, we have only been able to identify one possible binary
systems (star \#1090). This system has average velocity consistent
with membership, but a double-line system and larger-than-average deviation
around the mean. We have tentatively
classified it as an SB2 cluster member.
Most likely, additional unidentified binaries
might be present among
stars with RV discrepant with membership and detected Li line. Further
follow-up is needed to confirm their membership. Therefore, we regard
the fraction of members as a lower limit to the real value.
\begin{figure*}
\includegraphics[height=17cm, angle=-90]{0995fig4.ps}
\caption{``Cleaned" color-magnitude diagrams.
Open symbols represent all observed
stars, while filled symbols denote radial velocity
members. The crossed symbol denotes the possible SB2 binary. When available
we have considered photometry from D'Orazi et al.~(\cite{dorazi}), while
in the other cases we have considered B--V colors from Kaluzny \& Mazur
(\cite{km91}) and V--I colors from Richtler \& Sagar (\cite{rs00}).
}\label{fig4}
\end{figure*}
\begin{figure*}
\includegraphics[width=17cm,angle=0]{0995fig5.ps}
\caption{
Panel a) V -- V--I diagram of confirmed cluster members. Different symbol
sizes indicate different Li abundance bins; namely, from the largest
to the smallest ones: $\log$~n(Li)$\geq 2.0$,
2.0$\leq$ $\log$~n(Li)$< 1.7$, and $\log$~n(Li)$<1.7$. For 47 of the 57 stars with
a Li measurement, we have considered photometry from D'Orazi et al.
(\cite{dorazi}), while for the remaining 10 stars not included in the
D'Orazi et al. study, we used Richtler \& Sagar (\cite{rs00}) magnitudes
and colors.
Panel b): Lithium abundance --$\log$~n(Li), in the usual logarithmic scale
where n(H)=12--  as a function of V magnitude for confirmed cluster members.
}\label{fig5}
\end{figure*}
The ``cleaned" CM diagrams are shown in Fig. \ref{fig4}, where RV members
and non-members and the SB2 binary
are denoted with different symbols. Whereas
we refer to Tosi et al.~(\cite{tbc}) for a detailed
discussion of the analysis of the cluster CM diagram, we mention
here that our membership determination has allowed us to clean
the turn-off region, thus allowing a more solid derivation of cluster
parameters, as done by Tosi et al.
Among the subgiants we note the presence of two confirmed members
(one in the V vs. B--V
diagram) somewhat fainter than the cluster sequence. We do not
have any explanation for them, but suggest that they might be the
two expected contaminants.
\subsection{Lithium abundances} \label{lithium}
In Table \ref{tab_lith} we list confirmed members (from Table~\ref{sample})
for which we were able to either measure the EW of the Li
line or infer a reasonable upper limit.
In the table we provide IDs (same as in Table
~\ref{sample}), dereddened B--V colors, effective temperatures, measured
Li equivalent widths, and Li abundances. The last are in the
usual notation $\log$~n(Li)=$\log$N(Li)/N(H)+12.
In Fig.~\ref{fig5}a we
plot the V--V$-$I~diagram of cluster members with different
symbol sizes denoting stars with different Li contents, while
in Fig~\ref{fig5}b we
show Li abundances as a function of V magnitude.
The figures very well illustrate the evolution of Li along
the CM diagram. All stars on the MS and at the TO
have Li abundances larger than $\log$~n(Li)$=2$ and
their present Li abundance is the result of MS depletion;
on the other hand, cluster members slightly more evolved than TO
have started diluting their surface Li, due to the deepening of
the convective zone (e.g., Randich et. al. \cite{randich_subg}).
The transition between stars that have and that have not undergone
dilution occurs in a very narrow magnitude range (see also Pasquini
et al.~\cite{pas04}). Dilution
progressively continues along the subgiant
branch, up to a Li abundance $\sim 1$.
\begin{figure}
\psfig{figure=0995fig6.ps, width=8.5cm}
\caption{Upper panel: comparison of the distribution
of $\log$~n(Li)~as a function of T$_{\rm eff}$~for unevolved stars in Be~32 (open circles)
and the Hyades (filled circles); lower panel:
same as upper panel, but Be~32 is compared to
M67 (filled triangles) and NGC~188 (filled circles).
}\label{fig6}
\end{figure}
In Fig.~\ref{fig6} we show the usual plot of Li abundances
as a function of effective temperature for unevolved cluster stars (TO and
MS) and compare Be~32 with the much younger and more metal-rich Hyades
(upper panel) and with both the slightly younger M~67 and the
slightly older cluster NGC~188 (lower panel).
Both NGC~188 and M~67 OCs have a solar
metallicity (Randich et al.~\cite{randich_188},~\cite{randich_m67}), and thus
are a factor of $\sim 2$ more metal rich than Be~32.
Lithium abundances for the three OCs were taken from the compilation
of Sestito \& Randich (\cite{sr05}). In that paper Li abundances
had been derived using the same COGs and NLTE correction employed here.

The figure shows that, at variance with the Hyades and M~67, but
more like NGC~188, Be~32 distribution does not show any major
trend of decreasing Li abundance with decreasing T$_{\rm eff}$.
We find average Li abundance
values of $\log$~n(Li)$=2.63\pm 0.17, 2.62 \pm 0.07$, and $2.47 \pm 0.16$
for stars in the temperature ranges T$_{\rm eff}$~$>6200$ K, 6200$\geq$T$_{\rm eff}$$\geq 6000$
~K, and T$_{\rm eff}$$<$6000~K. The three average values are, within the errors,
the same. Also,
at variance with M~67, but similar to NGC~188,
the Be~32 sample is not characterized by
any significant (larger than errors) dispersion in Li.
More specifically, Figs.~\ref{fig5}b and \ref{fig6} show that the maximum
star-to-star difference for unevolved stars is on the order of 0.5~dex.
Assuming Gaussian statistics,
this corresponds to a 1$\sigma$ dispersion of $\sim 0.15$~dex,
comparable to the average error in $\log$~n(Li).
Given the large size of our sample, we regard the lack of a significant
scatter as real and
not due to low number statistics and conclude that the appearance
of the spread among open cluster stars is an exception rather than the rule,
since the majority of OCs do not show it.
Most important, whereas Hyades stars warmer than $\sim 6000$~K are somewhat
more Li-rich than their Be~32 counterparts, the Li distributions of cooler
stars are almost indistinguishable. The $\log$~n(Li)--T$_{\rm eff}$~of NGC~188
and Be~32
patterns are also very similar and close to the
upper envelope of M67. In other words, the comparison
of OCs of different ages and metallicity
shows that, with the exceptions of the severely Li-depleted stars in the
lower envelope of M~67, stars in the $\sim 6000-5700$~K T$_{\rm eff}$~range seem to
converge to a very similar value of Li abundance.
\section{Discussion}
\subsection{Pop.~{\sc i} plateau}
The present study allows us to make
firm conclusions about the empirical evolution of Li abundance during the MS
of stars with temperatures (but not necessarily masses --see next
section) similar to the Sun.
In Fig.~\ref{fig7} we show the mean Li abundance as a function
of age for stars in the 6050--5750 temperature range. The figure
was done using the data of Sestito \& Randich (\cite{sr05}), to
which we added the average Li abundance of the $\sim$1~Gyr old
NGC~3960 (from Prisinzano
\& Randich \cite{pr07}) and the average for Be~32 inferred here.
As already discussed by Sestito \& Randich, stars in this T$_{\rm eff}$~interval
undergo a smooth, but continuous Li depletion
during the first $\sim 600$~Myr on the main sequence,
on a typical timescale
of $\sim 1.4$~Gyr. As already mentioned, at
older ages depletion becomes bimodal: it continues for a fraction of stars,
while it stops for the majority
of stars and the average $\log$~n(Li)~converge to a plateau,
which is quantitatively -and surprisingly- close to the plateau
of Pop.~{\sc ii} stars. The evidence for this Pop.~{\sc i}
plateau is statistically
confirmed by the inclusion in the sample of the Be 32, for which
we derived an average abundance $\log$~n(Li)=$2.47 \pm 0.16$. This value is, slightly
higher, but within
the margins of error consistent, with that of
the intermediate age OCs ($2.33 \pm 0.17$),
the upper envelope of M~67 ($2.25 \pm 0.12$), and NGC~188 ($2.34 \pm 0.14$).
As to the Pop.~{\sc ii} plateau, values range between a minimum of
$2.10 \pm 0.09$ (Bonifacio et al.~\cite{bon07}) and a maximum of $\sim 2.4$
(Mel\'endez \& Ramirez~\cite{mel04}).
\begin{figure}
\psfig{figure=0995fig7.ps, height=8.5cm, angle=-90}
\caption{
Average Li abundance as a function of age for stars in the
5750--6050~K~interval. Open squares are OCs
from Sestito and Randich (\cite{sr05}), the open triangle
represents the average for NGC~3960 (Prisinzano
\& Randich (\cite{pr07}), while the filled circle denotes Be~32.
For M~67
the average of the upper and lower
envelopes are plotted. The Sun is also shown in the figure.
}\label{fig7}
\end{figure}
The conclusion is that
Pop.~I stars are not necessarily heavily Li-depleted, even at very old ages.
The major consequence is that
Li cannot be used as an age indicator for stars older
than $\sim 500$~Myr: a lithium abundance in the interval
$\log$~n(Li)~$\sim 2.3-2.6$ does not allow discerning whether
a star is 0.5 or 6~Gyr old.
The above points are to be kept in mind when deriving the properties, age
in particular, of stars hosting extra-solar planets.
On the other hand, the Sun represents an exception and is
not representative of Li depletion in solar--type stars, since
it has undergone a larger-than-normal depletion.
We believe that low Li (a factor greater than 30-50 depletion) should
be regarded as indicative of a peculiar, but similar-to-the Sun, evolution.
\subsection{Lithium as a function of stellar mass}
Figure~\ref{fig6} clearly shows that the amount of Li depletion at a given
T$_{\rm eff}$~does not depend
on the cluster metallicity. The lack of any Li-metallicity dependence
has already been discussed by Sestito \& Randich (\cite{sr05}) on empirical
grounds and
by Piau et al.~(\cite{piau}) on theoretical grounds.
The latter study show that metallicity variations on
the order of 0.1~dex result
in changes of both T$_{\rm eff}$~and temperature at the basis
of the convective zone (T$_{\rm BCZ}$); however, the relationship between
T$_{\rm eff}$~and T$_{\rm BCZ}$, and thus the amount of depletion at a given T$_{\rm eff}$,
remain almost unaltered. The inclusion of
Be~32 in the open cluster sample and the comparison with the Hyades shows
that this holds true for metallicity differences as large
as 0.4-0.5~dex.

As is well known, however, metallicity does affect stellar structure:
specifically, for a given mass, lower
metallicities correspond to higher T$_{\rm eff}$.
In contrast, for a given effective temperature, lower metallicity
stars have lower masses and stars with the same, close-to solar
temperature, do not have the same, solar mass, if their metal content
is different. In order to investigate Li depletion as a function
of mass, we derived masses for unevolved stars in Be~32, as well as for the
Hyades, M~67, and NGC~188 using the Padova isochrones
(Girardi et al.~\cite{girardi} --http://pleiadi.pd.astro.it/) and
the appropriate metallicities. When needed, we interpolated between different
isochrones.
\begin{figure}
\psfig{figure=0995fig8.ps, height=8.5cm, angle=-90}
\caption{
$\log$~n(Li)~as a function of mass for Be~32 (open circles),
the Hyades (asterisks),
M~67 (filled triangles), and NGC~188 (filled circles).
The horizontal lines delimits the range covered by Pop.~II stars considering
the lowest and highest values of the plateau.
}\label{fig8}
\end{figure}
In Fig.~\ref{fig8} we compare Li abundances as a function of
mass for unevolved stars
in Be~32 with the Hyades, M~67, and NGC~188 members.
The range covered by Pop.~II stars is also shown.
This figure indicates that the distributions of the different OCs
no longer overlap in the $\log$~n(Li)-- mass
diagram as it was instead the case
for the $\log$~n(Li)--T$_{\rm eff}$~plane. This is due to the fact that
Be~32 stars with temperatures close to solar are less
massive than the Sun, of their counterparts in the solar metallicity
NGC~188 and M~67, and of their metal-rich counterparts in the Hyades.
The figure proves that Be~32 members at all
masses have depleted less Li than stars with similar mass
in the other old OCs; also, focusing on star with mass close to solar,
the figure shows that NGC~188 members and the upper envelope of M~67
have depleted the same Li as their more metal-rich Hyades counterparts.
In summary, both the
timescales and the amount of Li depletion are
different for stars with the same mass and different metallicities.
This result indicates that, when looking at masses,
metallicity affects the amount of depletion at a given age. In contrast,
we stress again that
the evolution of star with the same T$_{\rm eff}$~does not depend on [Fe/H]
(at least within $\pm 0.2-0.3$~dex from the solar value), since more
metal-poor and less massive stars, have the same internal structure of
solar-metallicity, solar-mass ones.
\subsection{Comparison with model predictions}
For a formally correct
comparison of the empirical evolution of Li with model predictions at a
given mass, one should not mix data of OCs with significantly different
metallicities or, alternatively, the appropriate metallicity should
be considered.
However, we believe that the comparison between model predictions
and empirical evolution in a given temperature range can still be performed,
since, at least as far as Li is concerned, the evolution of stars with
similar temperatures, but different masses and metallicities is virtually
the same. As an example,
we show again in Fig.~\ref{fig9} the
mean Li abundance as a function of age (see Fig.~\ref{fig7}) and compare
it with the predictions
of the models by Charbonnel \& Talon (\cite{ct05}), which include both
rotational mixing and gravity waves. The figure indicates that these models
reproduce the observed distribution up
to 1~Gyr rather well. Also, the models with initial rotational velocity
50--80~km/s
are in good agreement with the datapoints corresponding to the lower envelopes
of M~67 and with the solar datapoint. However,
even the model with the lowest initial rotation is not able to
fit the plateau in Li. In conclusion, while all classes of models including
extra-mixing processes predict that, once they start causing Li depletion,
they continue being efficient throughout the permanence on the MS,
observational evidence indicates that this is not the case at all.
To our knowledge, none of the models proposed so far
predicts the convergence of Li at old ages.
We note that, when comparing model predictions with observations,
we assumed that all OCs have the same initial (meteoritic)
Li abundance. The assumption that the initial Li is instead
higher in young OCs
would imply a different normalization of theory vs. models and a better
fit of the very old OCs; still, the disagreement between the observed
convergence and the models, which keep decreasing at old ages, remains.
\begin{figure}
\psfig{figure=0995fig9.ps, height=8.5cm, angle=-90}
\caption{
Same as Fig.~\ref{fig7}, but a narrower age interval is shown.
The empirical distribution is compared with the predictions
of the models by Charbonnel \& Talon~(\cite{ct05}). The latter have been
reconstructed starting from Fig.~2 in that paper. Different curves are
for different initial rotational velocities (in km/s) as labeled. Solid curves
correspond to model including waves + rotation, while dashed lines
denote models including only waves.
}\label{fig9}
\end{figure}
\subsection{Pop.~I and Pop.~II plateaus}
In the previous sections we have definitively shown that stars
with temperatures similar to the Sun are not necessarily heavily Li-depleted
like the Sun is; instead, Li abundances of the majority of stars converge
towards a plateau, whose value, on the order of $\log$~n(Li)$=2.3-2.5$, is close
(although not identical)
to that of Pop.~II stars. However, the path/masses/timescales are
different towards virtually this same average value of Li.
The similarity of the plateau of Pop.~I stars to the plateau of the
significantly more metal-poor Pop.~{\sc ii} is indeed very intriguing
and should be investigated on theoretical grounds.
Figure~\ref{fig8} indeed suggests that there might be a sequence
between old, solar-metallicity OCs and metal--poor less
massive Pop. II stars, with Be~32 in the middle.
This sequence is purely phenomenological and it does not provide insight
into the depletion history of Pop.~II stars or into whether
they actually depleted some Li or not; nevertheless,
it is tempting to interpret it
as evidence that, whatever the initial Li abundance and whatever
the mixing mechanism, the final Li abundance is the same for metal-poor
Pop~{\sc ii} stars and more metal-rich ones.
Those stars, like the Sun,
that instead deplete a much larger amount of Li represent an exception.
\section{Conclusions}
We carried out a FLAMES/Giraffe survey of almost 160 candidate
members of the old, metal-poor open cluster Be~32, with the goals of
inferring membership
and of studying the Li abundance pattern. To this aim,
we derived radial velocities
and Li abundances. Slightly more than half of the sample stars are confirmed
as cluster members. This is a lower limit, since we may have missed some
binaries due to the too short time coverage of our observations.
The Li versus T$_{\rm eff}$~distribution of unevolved members
overlaps with that of the slightly older, more metal-rich NGC~188,
and with the upper envelope of M~67. At variance with the last, Be~32 does
not show any dispersion in Li. The average abundance of stars with solar--like
{\it temperature}
is slightly below the Hyades but, within the margins of error,
the same as for their counterparts in the intermediate
age OCs, the upper envelope of M~67, and NGC~188.
This confirms, on solid and statistically significant grounds, that,
with exception of Li--poor stars like the Sun, Li abundances
in solar-like Pop.~I stars converge towards a plateau value, implying
that Li cannot be used as an age indicator after about 0.5~Gyr. In addition,
the plateau of old OCs is close to the plateau
value of Pop.~II stars.
To our knowledge, none of the models including extra-mixing
developed so far predicts the convergence toward a plateau at old ages.

Given their lower metallicity, Be~32 stars with temperature close to the Sun
are less massive than the Sun. A comparison in a $\log$~n(Li)--mass diagram
shows that these stars have depleted much less Li than the Hyades with similar
mass.
Our conclusion is that stars with different masses
and metallicities, but very similar temperatures, converge at old ages to
the same Li abundance, though following different Li depletion histories.
This might also be true for halo stars.
\begin{acknowledgements}
We are grateful to Paolo Span\`o
for help with the maximum-likelihood analysis of radial velocities
and to Paolo Montegriffo
for providing the software to cross-correlate catalogs. We thank the referee,
Andreas Korn, for very useful suggestions.
This work has made extensive use of the
services of WEBDA, ADS, CDS, etc.
S. Randich has been supported by an INAF grant on
{\it Young clusters as probes of star formation and early stellar evolution.}
\end{acknowledgements}

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Q: Seating people around a table (elementary counting technique) Eight people, including Abigail and Bethany, are to be seated at a square table so that two people are along each edge. Two seatings are considered distinct if, and only if, the ordering of people starting with Abigail and continuing clockwise around the table in one seating is distinct from that in the other seating.  How many distinct seatings are there so that Abigail and Bethany are not next to nor across from each other?
There are 8!/8 = 7! seatings of the eight people around the table. There are 2(7!/7) = 2(6!) seatings with Abigail and Bethany next to each other, and there are 2(7!/7) = 2(6!) seatings with Abigail and Bethany across from each other. So, there
\begin{equation*}
7! - 2(6!) - 2(6!) = 2160
\end{equation*}
seatings in which Abigail and Bethany are not next to nor across from each other.
I am using the Complement Principle.  Is this correct?

A: The way I read the problem I think you are subtracting $2(6!)$ one too many times. Unrolling the argument I suppose it should look like the following.
Since you don't actually care which side of the table anyone is sitting at, (Since two seatings are the same if the ordering starting with Abigail and going clockwise is different) you can pretty much model your seating arrangements by thinking of the ordering only. Given that there are 7! choices for the ordering (since we can fix Abigail to be the first), which you got. Then you can seat Bethany next to her on the left or the right that's one $2(6!)$.
Now we need to deal with the situations of sitting across form each other. The issue here is that if you seat the people $A,\_,\_,B,\_,\_,\_,\_$ then this is a valid seating arrangement since you can place $A$ on the left corner of the table in which case $B$ is not sitting across from them. Same situation is when you get $A, \_ , \_ , \_ , B , \_ , \_ , \_ $ in which case you can seat $A$ on the right corner of the table and $B$ is not across. Thus if you only care about the order of the guests clockwise from $A$ then the only cases that need to be excluded are the ones when $A$ and $B$ are next to each other. The ones where they are across from each other can still be valid seating arrangements by rotating them.
Note: this does depend how one interprets sitting across.
I chose to interpret it as the situation where a line connecting to the two people is perpendicular to an axis of symettry of the table.


text:
Review: Maya to Aztec
Maya to Aztec: Ancient Mesoamerica Revealed by Edwin Barnhart
Here is another excellent lecture series by Edwin Barnhart. Just earlier this year I listened to, and greatly enjoyed, his series on the civilizations of North America. Now he is on his home turf, for Barnhart is a specialist in Maya archaeology. Surprisingly, however, I thought that the lecture series got off to something of a rough start. He jumps right into the Olmecs without enough framing or background. But soon enough I got my bearings, and the rest was a delightful trip through Meso-American archaeology.
Although I was somewhat more familiar with the basics of the Mayans and the Aztecs than with the ancient peoples of North Americans, I was still astounded at the depths of my own ignorance. It is frankly incredible that you can go through the American educational system and learn infinitely more about the Babylonians, Egyptians, and the Greeks than about the Mayans and the Aztecs. Granted, much of what we know about these civilizations was discovered fairly recently. The Mayan script was only deciphered in the 1970s; and as Barnhart points out, there is so much left to be discovered, including whole cities. Barnhart himself discovered a city (Maax Na).
The pyramids, pictoral script, and ancient date of these civilizations naturally bring up associations of Egypt. Yet the comparison is somewhat misleading, since the peoples of Meso-America consisted of a patchwork of cultures, sharing obvious similarities but equally important differences, whose fortunes waxed and waned through the centuries. Egypt, by contrast, was a singularly homogenous culture. Mesopotamia is likely a better comparison in this regard. But, of course, the Meso-American cultures have many distinct features.
One of the most important is the elaborate calendar system. Barnhart, an expert on paleo-archaeology, goes into great detail in explaining the Mayan numeral and calendrical systems. What is striking is not only the great complexity of the system, but also the cultural importance of the calendar. It was used by the entire region; and its keepers—who were religious men—communicated with one another even while their own states were at war. The calendar was filled with significance and omens, and was always consulted before important tasks. Barnhart speculates that the cyclical nature of the calendar also explains why cities were periodically abandoned.
Another peculiar feature is the Meso-American ball game, which was played across the region. This ball game was not just a sport, but a kind of living metaphor for Meso-American cosmology. I am not familiar of any other examples from the ancient world of a sport being so culturally central. And, of course, there is the human sacrifice—especially among the Aztecs. It is difficult to hear about these practices nowadays; though I do wonder which area had more religion-inspired killings during this time: Meso-America or Europe?
Barnhart ends the lecture series by narrating the first European contact and the eventual destruction of the Aztec Empire by Hernán Cortés and his men. (There is a new series on Amazon about Cortés, which was made to commemorate the 500th anniversary of the fall of Tenochtitlán, which happened in 1521.) It is an exciting and a depressing story, as the work of centuries is burned or buried. But Barnhart ends on a positive note, observing the many ways that these cultures have survived, and expressing hope that the modern descendants of the Maya, the Aztecs, and the many other cultures will take control of their heritage. For my part, now I really want to go to Mexico.
By Roy Lotzin Books, Education, History, Reviews, Uncategorized November 26, 2019 November 25, 2019 598 Words1 Comment
Review: Two Books by Henry Adams
The Education of Henry Adams : An Autobiography by Henry Adams
Once more! this is a story of education, not of adventure! It is meant to help young men—or such as have intelligence enough to seek help—but it is not meant to amuse them.
Everyone agrees that this book is difficult and odd. An autobiography of an American man of letters, the son of a diplomat, grandson of a president, historian, journalist, secretary, all told in the third person, written for his private circle of friends. At once claiming to be the story of one man's life, a critique of the educational methods of the nineteenth century, a parable of the fin de siècle, and a new theory of history, the book is, in reality, none of the above, and is instead the sigh of an old man looking back on his life.
I must admit that I found this book exasperating in the extreme. One quickly gets the impression that, when Adams uses the word "education," it is meaningless or worse than meaningless. He goes to London with his father, and becomes intimately acquainted with the workings of British politics, all during the difficult years of the American Civil War, and complains that he received no useful "education." He teaches at Harvard for seven years, a professor of Medieval History, and concludes: "On the whole, he was content neither with what he had taught nor with the way he had taught it. The seven years in teaching seemed to him lost." He becomes a journalist in the capital, and then works on a seven-volume history of America during Jefferson's presidency; and still, after all this, he insists he has received no useful "education." And after every phase of his life, when Adams rings the same gloomy bell, the reader asks: "What on earth would satisfy you, Mr. Adams?"
Another exasperating element is the degree to which Adams assumes a familiarity with the intricacies of 19th century politics. Reading the chapters when he was in England felt like reading a grocer's shopkeeping books. It was disjointed, jerky, and, worst of all, didn't explain a thing. At first, I assumed this difficulty resulted from Adams's originally writing the book for his circle of friends; but the obscurity goes even further: it is as if Adams wrote the book only for himself. The book swings wildly in tone from dry note-taking to half-formed and half-coherent abstractions, all written in a prose style lucidly opaque.
Adams also gives the impression of being a bit muddle-headed. He spends some time talking about Lyell's geology and Darwin's evolution, and it soon becomes apparent he understands neither. He goes on long tangents about "force," while it is obvious that what Adams means by that word is as meaningless as what he means by "education." He ends the book on a very confused and seemingly pointless attempt to give a mathematical explanation of history, but never reaches above vague commonplaces, endlessly repeated. I seldom came across an insight of his that was insightful.
In short, the impression was that Adams had taken all of the stuff of his life—his doings, his friendships, his thoughts, his career, his background—and left it out to bake in the hot sun, until all the savor and succulence was scorched out of it, leaving only a tough jerky that wearies the jaw in the attempt to chew the husk.
Still, after all this, I must admit that this book has a strange power. There were times I could not put it down, even when I felt I wasn't understanding a thing. Adams always seemed to be only two steps away from a great insight, an astounding thought; but he never quite reaches it, which is why the book can seem so tragic. He was always searching and never finding; and the reader is left in doubt what he was searching for, and whether anyone will ever find it. In his elegant, knotty prose, he turns out aphorism after aphorism—all apparently insightful, but in reality empty—popping like soap bubbles leaving nothing but air. And what saves the book is that Adams knew this, and yet could do nothing better.
Mont-Saint-Michel and Chartres by Henry Adams
Saint Thomas did not allow the Deity the right to contradict Himself, which is one of man's chief pleasures.
I read this book in preparation for my visit to Chartres, which was just last week. I had not been very fond of Adam's most famous book, his Education, but I had high hopes that his writing would improve when his focus shifted to something other than his own life. Yet I have found the two books discouragingly similar.
As a stylist Adams appears, at least superficially, quite strong. His sentences are clear and mostly elegant, occasionally epigrammatic. But stylistic problems appear on a higher level of organization. Both Adam's autobiography and this book were not originally written for publication, but for his close circle of family and friends; and as a result, Adams seems to explain everything except what most needs to be explained. His ideas float against a background that he does not provide, making his train of thought appear out of context. In this he reminds me of George Santayana, who similarly omits to signal where he is going and why he is going there, though Adams lacks the philosopher's occasionally forays into sublimity to compensate. The result is rather irritating, superficially clear but actually opaque, like overhearing an eloquent old man talk to himself.
But my gravest complaint about Adams, both here and in his autobiography, is his tendency to organize his books around central ideas that I find vague and vapid. In the Education, this takes the form of his armchair theorizing about "force," the Dynamo, and the laws of physics as applied to history, and even more prominently in his main theme of "education," his conception of which remains unclear to the very end. In this book it mainly takes the form of his insistence that "The Virgen" was personally involved in the construction of Chartres Cathedral. To be fair, he tends to treat these ideas (and himself) with a considerable amount of irony; but the irony does not amount to full satire, leaving it unclear whether he is merely kidding or if he intends these ideas to be somehow insightful.
Again, just as in his autobiography, here the dominant mood is notalgia. Though extremely successful, Adams apparently felt out of harmony with his world and yearned for a time when society was simpler and more unified. This leads him quite naturally to the Middle Ages, to the poetry, to the great cathedrals, and to the theology of St. Thomas Aquinas, which unite art and science into a seamless whole. Consequently this book, far from being historical analysis, is more of a personal appreciation of the French Medieval period, spinning off into fantasy or speculation wherever it suits him. This self-indulgent tone is grating to somebody trying to learn about Chartres.
Now that I have gotten all this criticism out of the way, I must admit that the book, like his autobiography, has its merits and charms. He is obviously fond of this period, and so writes in a tone of enthusiastic admiration that proves quite infectious. This keen appreciation for the "spirit" of the Medieval period is the book's most useful attribute, helping to put the reader in the mindset to appreciate the epoch's art, poetry, and thought. I found Adams's chapters on architecture, specifically on Chartres, to be stuffy and difficult to follow—for here, as in his chapters on British politics in the Education—he assumes a level of familiarity (specifically about the French royal family) that the reader is unlikely to possess. But when context is provided by an external source, Adams can be quite pleasant. When I visited Chartres, and saw its magnificent stained glass for myself, his chapters ceased to be so vexing.
The chapters I most enjoyed were the final three, about philosophy—specifically, Abelard, St. Francis of Assisi, and St. Thomas Aquinas—since here my background was not so lacking. Yet even here it must be said that Adams's comments are more in the spirit of an amateurish aficionado rather than a serious student. He interprets Aquinas as an "artist" rather than a thinker, repeatedly disqualifying himself from passing sentence on Aquinas's arguments (though he says some perceptive things in spite of this).
By contrast I thought the chapters on poetry were the worst, since they mainly consisted of excerpts of poetry, in Latin or Medieval French, with repeated assurances of their high quality and their untranslatable beauty. (His mostly bland translations serve to prove his point.) But in general Adams's approach to poetry is the same as his approach to architecture and theology, mostly confined to passionate declarations of affection, without much attempt at analysis or insight.
(Cover photo by Benh LIEU SONG; licensed under CC BY 2.5; taken from Wikimedia Commons.)
By Roy Lotzin Biography, Books, Education, History, Reviews, Spain & Europe May 31, 2018 1,533 WordsLeave a comment
Review: Emile
Emile by Jean-Jacques Rousseau
If all the philosophers in the world should prove that I am wrong, and you feel that I am right, that is all I ask.
My reaction to Rousseau is very similar to my reaction to Thoreau, whose back-to-nature ethic owed much to Rousseau's philosophy. Though constantly impressed with the breadth of their vision and the force of their rhetoric, I find the personalities of these two men—at least as manifested in their books—to be grating and unpleasant. When I am not underlining brilliant passages, I read Rousseau through gritted teeth and with frequent interruptions to roll my eyes.
I see much in common between these two Romantic devotees of nature. While Thoreau's dour and stern demeanor is not comparable to Rousseau's sentimental imagination, the two of them are self-involved, prickly, and vain. Both praise wild isolation at the expense of society because neither seemed to fit into the latter. Though the two of them were brilliant in the extreme, neither of them seemed to have reached the level of intellectual maturity that allows feelings to be submitted to reasons and other perspectives to be considered. Both of them fire off opinions with wild abandon, saying what feels good, without taking the trouble to thoroughly argue their points, to consider competing ideas, or even to make their own thoughts consistent.
To pick just one example of this last tendency in Rousseau, at one point he says: "Amid the uncertainty of human life, let us shun that false prudence which seeks to sacrifice the present to the future; what is, is too often sacrificed to what will never be. Let us make man happy at every age lest in spite of our care he should die without knowing the meaning of happiness." And yet, almost immediately after this pronouncement, he insists that his titular pupil, after having fallen in love and proposed marriage, postpone the delight of union for two years—leaving his beloved to go travel—in order to learn to master his feelings. The book is rife with such inconsistency. And not only that but, as in Thoreau's case, Rousseau's manner of life was notoriously inconsistent with the principles he espoused, adding hypocrisy into the bargain. That a man who sent his own children to an orphanage should write a manifesto of education is rich indeed.
But Rousseau must be read and praised, this book above all, since he—as well as his American disciple—contributed a great deal to our common stock of ideas and the expansion of our cultural faculties. Under the guise of a treatise on education, Rousseau has written a universal reflection on human life, comparable to Plato's Republic or The Brothers Karamazov for its omnidirectional scope. The novelistic device of describing himself as a tutor educating a child allows Rousseau to illustrate his philosophy of society, ethics, government, love, history, travel, religion, literature, and much else along the way, besides to his groundbreaking views on education.
Rousseau begins with his famous dictum that nature makes everything good, and it is human society corrupts our natural goodness into evil. His stated purpose is to illustrate how natural goodness can be preserved in a growing boy destined for life in society—that is, without Thoreau's recourse of reverting to a state of nature. With this principle in mind, Rousseau blasts mothers for hiring wet nurses to breastfeed their children rather than doing it themselves. And though Rousseau's reasons are fallacious, this advice probably did the world much good, since, in addition to the emotional bonding, breastfeeding allows important antibodies to be transferred from the mother to the infant.
After infancy gives way to childhood, Rousseau's real educational work begins. Here he made another important contribution to child-rearing, by insisting that children's minds are not suited to adult ideas and methods. A child is a different creature altogether and education must be suited to a child's capacities and predilections. Lectures, sermons, and catechisms must be avoided; and using punishment and reward only corrupt the child. Instead the tutor must find ways to motivate the child to learn without ever seeming to do so. Rousseau the tutor is constantly devising tricks and schemes to get his imaginary pupil, Emile, to learn valuable lessons in a "natural" way—that is, relying on the child's intrinsic motivation and using no explicit instruction. Everything in Rousseau's model must simulate life and the child must work on his own conclusions following his own curiosity. The tutor is much more a guide—and, behind the scenes, an impresario—than a real teacher.
Following this procedure, lessons on magnetism and morality are woven into a magician's act. Geography is taught by getting lost in the forest. Geometry is taught by attempting to draw and map. Botany and agriculture are taught through gardening. And so on, covering sciences, arts, and moral lessons. This way, Emile grows up into a competent, strong, and thoroughly honest boy with no social pretensions and no vanity whatsoever. At least, Rousseau assures us that this would be the result. By the time Rousseau takes Emile into Paris, as a young man, the student is disgusted at the foppery of the men, the arrogance of the philosophes, and the affected manners of the women.
More contentiously, Rousseau would not teach his pupil anything about God or religion until the age of eighteen, considering such subjects too abstruse and profound for a child to understand. He would not even teach Emile to read until shortly before that. And this is not all that occasioned scandal. Rousseau famously interrupts the story of Emile's education to include the Profession of Faith of a Savoyard Vicar, the most well-known, influential, and controversial section of the book. Though couched in the language of philosophy, the Profession is essentially an argument against both organized religion and atheism in favor of deism, based on feeling alone. Voltaire, a deist himself, considered this the book's only worthwhile section, only lamenting that it has been written by "such a rascal." It was largely this trenchant criticism of organized religion that led to the book getting banned and burned in Paris and Geneva. And yet, ironically enough, the idea that inner conviction is a surer basis for faith than logic was to become a pillar of religious thought in the coming centuries.
The last section of the book consists in finding a mate for Emile. This is by far the most unpleasant part of the book. Rousseau's view on women and their upbringing is reactionary and sexist to the utmost, not to mention unpleasantly marred by Rousseau's own sentimental (and sexual) fantasies regarding women. Rousseau's ideal companion for his pupil is named Sophie, and her education differs markedly from Emile's. Sophie is to be a kind of passive doll, a creature not fit for reason or art, whose job is to caress Emile and to make his life easier. Rousseau describes their courtship with the drama of a novelist and the passion of an onanist. Both the principles and the writing are revolting.
Finally, after enduring a forced separation for his beloved—a very unnatural thing for Rousseau to recommend!—Emile settles down happily in blissful union with Sophie, and prepared to educate his own children along Rousseau's lines.
This summary does not exactly do justice to Emile, since it omits all of the manifold digressions that Rousseau yields to in the book's wandering course. Some of these are among the best sections of the work; others are pointless rambling. Even when he is not off in the bushes, Rousseau can be very repetitive, giving us five sentences where one would do, spending three paragraphs harping on a minor point. The final result is a book much longer than it has to be. This is Rousseau's most conspicuous stylistic flaw, which he excuses in typical Rousseau fashion: "If this book is to be well written, I must enjoy writing it." Unfortunately the author's pleasure is often gotten at the expense of the reader's. Yet the book's best moments are masterful, rising to heights of power and lyricism that cannot be forgotten. Immanuel Kant famously had to read the book twice, the first time just for the style, the second for the content.
The flaws in Rousseau's ideas are many and grave. Most obviously, Rousseau's educational program is impractical in the extreme, relying on a perfectly wise tutor to devote twenty years of his life to a perfectly malleable pupil. This may be excused, however, by treating the arrangement as an explanatory device and not a real proposal to be emulated. More seriously, Rousseau's conviction that nature is intrinsically good is, I think, incorrect and even incoherent. Natural disasters, such as the Lisbon Earthquake in Rousseau's own lifetime, demonstrate that nature can be cruel and merciless; and in any case, how can you know what nature is, or where nature ends and human culture begins? Besides, doesn't Rousseau advocate many "unnatural" things? The level of control exercised by his tutor over his pupil's reality is far greater than any real parent or teacher.
Yet even when strictly viewed as an educational treatise, there is much to be praised in the book. Rousseau's emphasis on experiential rather than theoretical learning was quite valuable. And his conviction that education must take into account the child's development and maturity was a revolution. I also share his suspicion towards using external rewards and punishments to motivate children, since the bad is avoided and the good is sought for artificial, rather than instrinctic, reasons.
Of course the book's merits extend much further than education. Taken together, Rousseau's philosophy touched on every aspect of society, from philosophy to fashion, from labor to love. For all his naïveté, Rousseau seemed to have correctly sensed that his society was artificial and could not last. Thirty years before the revolution, he says: "The crisis is approaching, and we are on the edge of a revolution." And he then goes on in a footnote: "In my opinion, it is impossible that the great kingdoms of Europe should last much longer. Each of them has had its period of splendor, after which it must inevitably decline." Like Thoreau, Rousseau was a prophet and a true original, embittered by being misunderstood, isolated, and ostracized, whose all-too-obvious faults concealed the revolutionary reach of his vision.
By Roy Lotzin Books, Education, Philosophy, Reviews May 7, 2018 May 6, 2018 1,770 Words1 Comment
Review: Cracking the GRE
Cracking the GRE by The Princeton Review
Compared with Europe, America has a strange fixation with standardized tests. Administrators and bureaucrats seems to view these tests as tools of accountability, allowing for standard measurement across the system with no possibility of error. But the result is often quixotic: the attempt to come up with a test that creates a normal curve in scores, a test immune to differences in social and cultural background, and a test that measures something predictive of future success, irrespective of the field or career.
As far as these tests go, the Graduate Record Examinations (GRE) is well done. The math sections only include the most basic techniques, focusing instead on tricky word problems or painstakingly lengthy operations, which theoretically would put all students—regardless of math background—on an equal footing. The essays focus on equally fundamental skills: creating and defending a thesis, and critiquing somebody else's thesis. The verbal section is a straightforward vocabulary and reading comprehension drill. In sum, as far as possible, I think that the GRE is focused on fundamental skills needed for study.
The catch, of course, is the "as far as possible." For no matter how much the test-makers try, a physics major and a history major will not be on an even footing in the math and verbal sections. What is more, by making vocabulary such an integral part of the exam, people from more privileged backgrounds—whose well-educated parents work white-collar jobs—have an obvious advantage. This is not to mention the upper hand that the well-off always have in competitions of this sort: the time available for studying (without worrying about multiple jobs or rent), and the resources (private tutors and so on) to prepare adequately.
In any case, can even a well-designed test give valuable information at the graduate school level? For lower-level education, where students are taught the basics of academic skills, a general test seems more plausible. But as students apply to Masters and Doctorate programs—the final steps of vocational and academic specialization—the usefulness of a generalized skill exam is far more questionable. The ability to write an essay in 30 minutes taking a stance on a randomly generated quote (one of the essay tasks) is perhaps hardly related to the ability to, say, write a detailed exploration of the post-Soviet period in Poland.
Granted, I can see why admissions offices like tests such as this one. First, it is a quick and easy to cut down the hefty stack of applications. What's more, the GRE scores do provide a standard measurement across varying backgrounds (but what is it a measurement of?). And even if the admissions office sees the GRE as purely pro forma—something that is not uncommon—the obstacle of a $205, 4-hour test may help whittle out those less interested in applying.
However convenient it may be for these admissions officers, I personally cannot help being frustrated with exams like this. At present, Educational Testing Services (ETS), its creator, is the Standard Oil of the testing business. To apply to any institution of higher education in the United States, you must pay a toll—in time, stress, and money—to this organization. If I thought that this ritual improved educational quality in any way, I would tolerate it; but I have trouble believing that.
ETS is not the only entity that benefits from this arrangement, since the competition for scores gives rise to innumerable test-prep companies and products, such as this book. I have used the Princeton Review on numerous occasions, and have consistently appreciated their prep-books. This book provides quite a bit of value for the price: including dozens of specific techniques, and 6 full-length practice tests.
Because the Princeton Review can't use real ETS questions, they must come up with their own. And this is no easy thing, since their questions must replicate exactly the look, difficulty, and type of questions on the real thing. For what it's worth, in my own experience I have found that the real ETS verbal questions are easier than the Princeton versions, while the ETS math section is more difficult than Princeton's—though admittedly this difference is fairly small.
A world where we didn't have to spend months preparing for standard exams would be ideal. But in the world we live in, Princeton Review books are a valuable aid.
By Roy Lotzin Books, Education, Practical, Reviews November 27, 2017 November 26, 2017 741 Words1 Comment
Review: Excellent Sheep
Excellent Sheep: The Miseducation of the American Elite and the Way to a Meaningful Life by William Deresiewicz
I still remember my first exposure to Deresiewicz. I had recently dropped out of graduate school—full of disgust and indignation—and as a form of self-therapy I was busy reading everything I could find about the flaws of higher education. Naturally, I jumped on Deresiewicz's essay in The American Scholar: The Disadvantages of an Elite Education. It seemed to put into words so many things I'd been thinking.
A few days later, I was in the car with my mom and my brother (we were dropping my brother off at his elite university), bitterly complaining, and at great length, about the evils of the system. My mom turned on the radio.
This book is an odd jumble. While barely more than 200 pages, it attempts to be a manifesto, an exposé, a path to tranquility, a work of cultural criticism, and a philosophy of education. Needless to say the book fails to be every one of these things, but this doesn't mean it fails to be any of them.
Deresiewicz's first section, wherein he talks about the flaws in the system, is the most successful, since it is what he knows about. In a nutshell, the problem with American higher education is that there is an enormous amount of pressure and prestige for precious little substance.
Young people have more hoops than ever to jump through: if they want to go to Harvard, they must be super students. They can't afford to stop for one moment. They need to get excellent grades, take all the toughest subjects, be leaders in extra-curriculars—at least six!—maybe found a few clubs themselves, outcompete their peers in the SAT, and in general tick off all the rights boxes.
The problem, of course, is that the things that look good to the college admission office often have dubious educational value, and are most often the product of privilege as much as talent. The vignette that most stuck with me was about the "college enrichment programs" that took young people on carefully choreographed trips, so they would have some good stories for their college essays. (This is not to mention the writing assistance, sometimes bordering on ghost-writing, that the wealthy can afford.)
The ironic part is that all of this stress and effort does not lead to social mobility, since the wealthy already start with such a big advantage. Each cohort of students at elite universities is disproportionally upper or upper-middle class. This is no coincidence, since universities need a sizable number of "full-freighters"—students whose parents can afford to pay the enormous tuition costs—in order to stay afloat.
Even more ironic is that it doesn't even lead to an excellent education. As the university becomes increasingly reliant on wealthy students, the students increasingly get treated like customers. The university cannot afford to fail them; it cannot even afford to make them uncomfortable, which is arguably a prerequisite to genuine learning. Grade-inflation is rampant. Universities focus on hiring a few research professors, because these professors bring more prestige. Though experts, these professors are often not especially good teachers; and besides, there aren't very many of them. The bulk of the teaching gets done by contingent faculty, chronically underpaid, always underappreciated, who come and go, without the time or resources to teach to their potential.
Instead of education, these universities focus on ranking. The problem is that the ranking is not based on quality of instruction, but on things like admission rates: the more selective, the better. It benefits elite colleges to advertise to students who have a very low chance of getting in, since if they apply and get rejected, the school looks better.
The result is a system obsessed with prestige at the expense of learning. From the moment students arrive to their final graduation speech, students are praised for being the best, the brightest, the most wonderful. And yet they are enmeshed in an educational system that encourages them to put themselves into boxes for admissions, that rarely challenges their fundamental beliefs, and that leaves them with a sense of entitlement, a sense that they deserve all of the nice things their elite education will give them.
So what should an education do? This brings us to part two and three of Deresiewicz's book, which I thought were much weaker. He has a lot to say about the value of a liberal education, about self-discovery, taking risks, questioning beliefs, developing a philosophy, finding your real passion, and lots of other nice clichés. To be fair, these are clichés for a reason: in some form or another, they are the goal of a true education. Nevertheless, I didn't find Deresiewicz's prescriptions particularly insightful or inspiring.
Finally, Deresiewicz aims his sights at society as a whole. What has this educational model done to our country, and how can we fix it? All the recent presidents, as products of "the system," come in for a good bashing—especially Barack Obama, who Deresiewicz finds to be arrogant, condescending, technocratic, while totally blind to genuine ideological differences. The book ends with a widespread, sweeping, universal condemnation of the entire upper and upper-middle class. Their time has passed, he thinks, and they must be removed from the stage of history, just as the old, aristocratic WASP class had before them.
What are we to make of all this? It's clear that the book bites off far more than it can chew. Ambition is certainly not a problem; but when ambition so far outpaces execution, it certainly is.
One weakness is that this book is so personal. By his own admission, Deresiewicz—the offspring of upper-middle class, Jewish parents, a former professor at Yale—is bitter about his experience in elite education, and it shows. For many years, it seems, he was dissatisfied and unfulfilled, consumed by feelings of envy and empty accomplishment, which accounts for both the self-help and the invective.
But emotion is a perilous guide. While at his best he is sardonic and witty, at his worst he is alternately whiney and preachy. His torrents of feeling often blow his vessel into strange waters—like the psychology of achievement addiction, or the dysfunction of government—where he thrashes about ineffectually.
This thrashing led to some tiresome writing. He has a tendency to write in epigram after epigram—none very clever—pounding and hammering his opinions into your head, while supplying few particulars and little evidence. He makes sweeping generalizations, all written in antitheses: "Everybody is doing this, and nobody is doing that," "All of us care about this, and none of us pays attention to that," and so on. He rarely qualifies his points, he does not address counterarguments, he does not betray even the least doubt of his righteousness and the system's evilness. (The book's condescending title is indicative of its fervor.) If I were his writing teacher, I would tell him it needs more work.
This book could really have been a long essay, focusing exclusively on the flaws of elite universities. The rest feels like self-indulgence and padding, an excuse to air his views and sell a book.
But for all his shortcomings, I think that Deresiewicz is making a vital point. All of his complaints boil down to one insight: meritocracy is insidious.
Now, how can this be? Isn't meritocracy good? Isn't is the only fair and just system? Well, there are several obvious problems. For one, what is 'merit'? Any meritocracy must begin with some notion of worth; and this notion will always be shaped by cultural and economic pressures. You simply cannot measure the inherent 'worth' of a person, so you end up measuring people against some arbitrary standard—like analytical intelligence or academic pedigree—imposed by the outside.
But even if we could agree on a universal measure of 'merit' (which is impossible), there would be no guarantee that we could measure it perfectly. Some people will be lucky, others unlucky. And even if we could agree on a standard and measure it perfectly—two impossible conditions—we are still left with the question of reward. If somebody is in the top fifth percentile, how much wealth do they 'deserve'? This will also be arbitrary, and whatever decision will likely not satisfy everyone.
So you see, first a meritocracy imposes an arbitrary standard, and then denies the existence of luck, and then distributes rewards along this standard arbitrarily. A meritocratic system is not necessarily fair—since people's worth cannot be measured—nor is it necessarily effective—since chance will always play a role—nor is it necessarily just—since meritocratic systems can still be highly unequal. The most insidious part is that it makes people believe they deserve their rewards: the rich deserve their wealth, the poor their poverty.
This is essentially what Deresiewicz is complaining about. The American elite educational system tends to reward certain qualities that are not necessarily desirable (and which are usually associated with wealthy families), and then treat this unequal distribution as justified. But when you think about it, is it really fair that educational resources and prestige be concentrated in very few, very expensive institutions, instead of distributed more evenly throughout the system?
I agree with this fundamental critique. However, I am far from sure that I know how to fix it. For his part, Deresiewicz puts his faith in the old tradition of the liberal arts education.
While I am naturally very sympathetic to this idea, I always ask myself: Are the liberal arts compatible with big institutions? Can a tradition predicated on free thought, on questioning authority, and on open enquiry—a tradition that is not oriented towards job skills or economic gain—be made compatible with an organization of power and wealth? Can we really expect students to pay enormous tuitions to induct them into the life of the mind? Or can we expect tax-payers to support universities that do the same?
To me is seems that, in the United States, by asking our universities to be both liberal arts colleges and pre-vocational training, we are asking the impossible. The first tradition teaches us how to live, while the second teaches us how to work. The problem, it seems to me, is that in the United States we have come to identify so fully with our jobs that we can't see the questions as separate. Deresiewicz definitely falls into this error, which he exemplifies by his endorsement of the "follow your passion" advice for a better life.
As I finish, I am left with more questions than when I started. And, as cliché as that sounds, that is still the sign of a good book.
By Roy Lotzin Books, Education, Reviews March 9, 2017 1,819 Words1 Comment
Review: Tools for Teaching
Tools for Teaching: Discipline, Instruction, Motivation. Primary Prevention of Classroom Discipline Problems by Fredric H. Jones
Have you ever looked at the work kids turn in these days and wondered, "What will happen to this country in the next 50 years?" When you watch Larry sharpen his pencil, you know that the future is in good hands. It's inspirational.
Last year I switched from teaching adults to teaching teenagers. Though I'm still teaching English, the job could hardly be more different. With adults, I could focus entirely on content; my students were mature, intelligent, and motivated, so I could think exclusively about what to teach them, and how. With kids, I am dealing with a classroom full of energetic, distracted, unruly, loud, and sometimes obnoxious humans whose main motivation is not to fail the upcoming exam. They're not there because they want to be, and they would always inevitably rather be doing something else.
This probably makes me sound jaded and disenchanted (and I hasten to add that I actually have a lot more fun teaching kids, and my students are great, I swear!); but the fact is inescapable: when you're teaching in a school setting, you need to worry about classroom management. Either you will control the kids, or they will control you.
It is the hope of every beginning teacher, myself included, to manage through instruction. We all begin with the same dream: to create lessons so dynamic, so enriching, so brilliant, and to teach with such charisma and compassion, that misbehavior isn't a problem. But this doesn't work, for two obvious reasons. For one, we don't have unlimited control of the curriculum; to the contrary, our room to maneuver is often quite limited. And even with complete autonomy, having interesting lessons would be no guarantee of participation or attention, since it only takes one bored student to disrupt, and only one disruption to derail a lesson.
Even if you're Socrates, disruptions will happen. When they do, in the absence of any plan, you will end up falling back on your instincts. The problem is that your instincts are probably bad. I know this well, both from experience and observation. Our impulsive reaction is usually to nag, to argue, to preach, to bargain, to threaten, to cajole—in other words, to flap our mouths in futility until we finally get angry, snap, yell, and then repeat the process.
But no amount of nagging creates a motivated classroom; and no amount of speeches—about the value of education, the importance of respect, or the relevance of the lesson to one's future—will produce interested and engaged students. In short, our instinctual response is inefficient, ineffective, and stressful for both teacher and students. (Again, I know this both from experience and observation.)
Some strategies are therefore needed to keep the kids settled and on task. And since teachers are chronically overworked as it is—the endless grading and planning, not to mention the physical strain of standing in front of classes all day—these strategies must be neither too complex nor too expensive. To the contrary, they must be relatively straightforward to implement, and they must save time in the long run.
This is where Fred Jones comes in. Fred Jones is the Isaac Newton of classroom management. This book is nothing less than a fully worked out strategy for controlling a room full of young people. This system, according to him, is the result of many hundreds of hours of observing effective and ineffective teachers, trying to analyze what the "natural" teachers did right and the "unnatural" teachers wrong, and to put it all together into a system. And it really is systematic: every part fits into every part, interlocking like the gears of a bicycle.
This makes the book somewhat difficult to summarize, since it is not a bag of tricks to add to your repertoire. Indeed, its main limitation—especially for me, since I'm just assistant who goes from class to class—is that his strategies cannot be implemented piecemeal. They work together, or they don't work. As a pedagogical nomad who merely helps out, I am not really in a position to put this book into practice, so I cannot personally vouch for it.
Despite this, Jones manages to be utterly convincing. The book is so full of anecdotes, insights, and explanations that were immediately familiar that it seemed as if he was spying on my own classrooms. Unlike so many books on education, which offer ringing phrases and high-minded idealism, this book deals with the nitty-gritty reality of being a teacher: the challenges, frustrations, and the stress.
The main challenge of classroom management—the problem that dwarfs all others—is to eliminate talking to neighbors. Kids like to talk, and they will talk: when they're supposed to be listening, when they should be working, whenever they think they can get away with it. This is only natural. And with the conventional classroom approach—standing in the front and lecturing, snarling whenever the kids in the back are too loud—talking to neighbors is inevitable, since the teacher is physically distant, and the kids have nothing else to do.
Jones begins by suggesting board work: an activity that each student must start at the beginning of class, something handed out or written on the board, to eliminate the usual chaos that attends the beginning of the lesson. He then goes into detail about how the classroom should be arranged: with large avenues to the teacher can quickly move around. Movement is key, because the most important factor that determines goofing off is physical proximity to the teacher. (This seems certainly less true in Spain, where people are more comfortable with limited personal space, but I imagine it's quite true in the United States.)
This leads to the lesson. Jones advocates a pedagogical approach that only requires the teacher to talk for five minutes or less at a time. Break down the lesson into chunks, using visual aids for easy understanding, and then immediately follow every concept with an activity. When the kids are working, the teacher is to move around the classroom, helping, checking, and managing behavior, while being sure not to spend too much time with the students he calls "helpless handraisers"—the students who inevitably raise their hands and say they don't understand. (To be clear, he isn't saying to ignore these students, but to resist the impulse to re-teach the whole lesson with your back turned to the rest of the class.)
This leads to one of the main limitation of Jones's method: it works better for math and science than for the humanities. I don't see how literature or history can be broken down into these five-minute chunks without destroying the content altogether. Jones suggests frequent writing exercises, which I certainly approve of, but it is also hard for me to imagine teaching a lesson about the Spanish Reconquest, for example, without a lengthy lecture. Maybe this is just due to lack of imagination on my part.
When it comes to disruptions, Jones's advice is refreshingly physical. The first challenge is remaining calm. When you're standing in front of a crowd, and some kids are chuckling in the back, or worse, talking back to you, your adrenaline immediately begins to flow. Your heart races, and you feel a tense anxiety grip your chest, intermediate between panic and rage. Before doing anything, you must calm down. Jones suggests learning how to relax yourself by breathing deeply. You need to be in control of your emotions to respond effectively.
Then, Jones follows this with a long section on body language. The way we hold our bodies signals a lot about our intentions and our resolve. Confidence and timidity are things we all intuitively perceive just from looking at the way someone holds herself. How do you turn around and face the offending students with conviction? How do you signal that you are taking the disruption seriously? And how do you avoid seeming noncommittal or unserious?
One of the most brilliant sections in this book, I thought, was on dealing with backtalk. Backtalk can be anything, but as Jones points out, it usually takes a very limited number of forms. Denial is probably the most common; in Spanish, this translates to "Pero, ¡no he hecho nada!" Then there is blaming; the student points her finger at her neighbor, and says "But, she asked me a question!" And then there is misdirection, when the offending student says, "But, I don't understand!" as if they were in a busy intellectual debate. I see all these on a daily basis. The classic mistake to make in these situations is to engage the student—to argue, to nag, or to scold, or to take their claim that they "don't understand" at face value. Be calm, stay quiet, and if they keep talking move towards them. Talking back yourself only puts you on the same level.
The penultimate section of the book deals with what Jones calls Preferred Activity Time, or PAT. This is an academic activity that the students want to do, and will work for. It is not a reward to hold over their heads, or something to punish the students with by taking it away, but something the teacher gives to the class, with the opportunity for them to earn more through good behavior. This acts as an additional incentive system to stay on task and well behaved.
The book ends with a note on what Jones calls "the backup system," which consists of the official punishments, like suspension and detention, that the school system inflicts on misbehaving kids. As Jones repeatedly says, this backup system has been in place for generations, and yet it has always been ineffective. The same small number of repeat offenders account for the vast majority of these reprimands; obviously it is not an successful deterrent. Sometimes the backup system is unavoidable, however, and he has some wise words on how to use it when needed.
Now, if you've been following along so far, you'll have noticed that this book is behaviorist. Its ideas are based on control, on incentive systems, on input and output. As a model of human behavior, I think behaviorism is far too simplistic to be accurate, and so I'm somewhat uncomfortable thinking of classroom management in this way. Furthermore, there are moments, I admit, when the job of teaching in a public school feels more like working in a prison than the glorious pursuit of knowledge. Your job is to keep the kids in a room, keep them quiet and seated, and to keep them busy—at least, that's how it feels at times. And Jones's whole system can perhaps legitimately be accused of perpetuating this incarceration model of education.
But teachers have the choice of working within an imperfect system or not working. The question of the ideal educational model is entirely different from the question this book addresses: how to effectively teach in the current educational paradigm. Jones's approach is clear-eyed, thorough, intelligent, insightful, and eminently practical, and for that reason I think he has done a great thing. Teaching, after all, is too difficult a job, and too important a job, to do with only idealism and instinct as tools.
By Roy Lotzin Books, Education, Practical, Reviews March 6, 2017 March 7, 2017 1,919 Words1 Comment

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For all that is going on in the debates of Christmas this week nothing has brought us more email than a story we haven't even covered: Megyn Kelly stating that Jesus and Santa Claus were white men. She did this (shown in the video segment below) in response to an essay on Slate.com from a person describing her issues growing up black with a predominantly white Santa.
Santa is a controversial character without going into the whole race thing. We feel that like Christmas itself the history of Santa Claus is not known or appreciated and the whole practice is mostly mishandled by many who celebrate Christmas.
But to mix race into the discussion as a topic of the war on Christmas — well, that's a whole new level of loony tunes.
First of all, the essay on Slate.com was an opinion piece and, frankly, a good one. If that was this person's experience with Santa as a black kid we'd be wise to listen to her experience. Her suggestion of making Santa a penguin does nothing for her argument, but that's another topic for another day.
This simple truth of the matter is that we don't really know what race Jesus or Santa were.
Even more basic, who cares?
The fact that this would be publicized as an issue is laughable. The opinion piece was gaining no traction and there has never been a movement afoot to change whatever Santa or Jesus is to anyone. Both are portrayed as predominantly white. So what? That doesn't make it right and it doesn't make it wrong. The very idea is irrelevant to Christmas.
While discussing this isn't an active part of the whole "war on Christmas" making this a controversial issue will only detract what should really be promoted about Christmas in the first place.
For the record, the one who appears to be winning this debate…is Jon Stewart of Comedy Central (he seems to be scoring the most points in this season of "war"). Not O'Reilly, not Palin, not the FFRF or American Atheists, Inc.
That alone should highlight how absurd the media conversations about Christmas have become.