The Demand of Word Problems Two challenges: reading and processing + Students can decode and read the problem, BUT cant interpret what its asking them to do You can teach strategies and systems!
Reading or Processing? Students need to be taught how to read like mathematicians Math problems are not the same as stories or articles; they are read to identify the question being posed Students who can read fluently may still have trouble identifying the problem they need to solve Connections to Previous Lit Sessions: SLIT1: Why Are Secondary Texts Difficult? SLIT2: Teaching Vocabulary SLIT3: Reading Purposefully & Strategically
The Breakdown To solve a word problem, students must be able to: 1.Understand what question is being asked 2.Locate relevant information within the problem (and overlook irrelevant information). 3.Translate the words into equations. 4.Determine which functions are required to solve the problem
Word Problem Strategies Require students to use a standard strategy that they can apply to every word problem they encounter. Teach its components explicitly, and use and model the strategy consistently.
Features of Effective Strategies 1)Memory devices that help students remember the strategy 2)Steps that use familiar words and begin with an action verb to facilitate student involvement 3)Steps that are sequenced appropriately 4)Metacognitive strategies that use prompts for monitoring performance
Gallery Walk Identify components of each strategy (what do the acronyms stand for, what are students expected to do). Identify a strength and/or weakness for each strategy. Would you want to use it with your students? 3 minutes at each station
STAR Strategy Empirically validated mnemonic that helps students recall sequential steps. SEARCH the word problem: Read the problem carefully, ask yourself questions (what do I know? what do I need to find?), write down facts TRANSLATE the word problem: Translate words into an equation in picture form. ANSWER the problem. REVIEW the solution: Re-read the problem, ask yourself, Does the answer make sense? Why, check your computations
RIDGES Strategy Appropriate for upper elementary through secondary grade levels Helps students formulate a plan to solve the problem Read the problem I know statement: List information given in the problem. All information should be listed – relevant or not. Draw a picture, table, etc. This should help students pick out relevant information Goal Statement: Student expresses, in own words, the question the problem is asking. Equation Development: Write equation for problem (i.e. length + width + length + width = perimeter of football field). Solve the equation: Plug given information into equation. Solve.
SQ-RQ-CQ Strategy Guides students to find important elements & determine how they should be solve in a logical order Builds in self-questioning to help students find & correct their own mistakes Survey the math problem: read the problem to get an idea of its general nature, talk with students to discuss what parts are most important Question: Determine what problem is asking you to do. Re-read problem: Focus on specific details of problem. What parts of problem relate to each other? Consider what form your answer should be in (units) Question yourself about operations involved: Determine specific operations required, and list the order. Calculate: Perform each operation in order listed. Question: Review steps, determine if answer is reasonable.
How Do I Choose? There is no magic formula – Pick the one YOU are most invested in for YOUR students. Pick a strategy, laminate and post it – have students practice it religiously! No best strategy for English Language Learners or Special Ed students Pick a strategy to arm them with so they can tackle those word problems
Making the Strategy Work I laminated mini posters of our grade level problem- solving model so students could keep them at their desks until they had the steps memorized. - A real math teacher Gradual Release of Responsibility EVERY time, WITHOUT fail, for EVERY problem! It will take time for the strategy to take holddont scrap it! TIME AND CONSISTENCY
Some Considerations… Recognize student characteristics (cognitive and behavioral) and preferences Promote individualization of strategy use Program for generalization Provides opportunities for students to generalize the strategy to other problems
Start by building skills, not answering questions. Remove the distraction of the numbers so students can focus on building the skills that leads them to the answer Students methods of reaching the solution are much more important than what the answer actually is
Allocate time to practice each step separately. Set up targeted practice time for each step of your strategy Identifying the question Spotting key information Identifying correct operation to work out answer
Be clear about what the question is asking. Is the following an addition or subtraction problem? In the annual Michigan vs. Ohio State football game, there were 74 points altogether. Michigan scored 40. How many points did Ohio State score? 74 – 40 = ??? This is how the question can be solved, but mathematically speaking not totally accurate 40 + ?? = 74More accurate mathematical representation Not every calculation involves a number missing from the end. By making sure you know exactly what is being asked, you can teach the skills of solving equations where the middle or start is needed.
Get your kids on high alert! Provide a collection of word problems where this irrelevant information to ignore, or a conversion to make. Make mistakes on purpose while modeling how to answer a question and reward the first person to spot any errors you make. All of these strategies should get your class poring over their word problems with renewed energy. I have 23 new messages in my email inbox. While unsuccessfully attempting to balance a cup of coffee in one hand, a chocolate-chip cookie in the other, and try to see whether my best friend has replied, I accidentally click and get rid of 8 messages. How many do I have left. Jose is 140 cm tall and so he is too small to be able to ride on the Belly Flop rollercoaster. The height limit is 190 cm. How many meters does he need to grow?
The Bottom Line Choose one strategy and stick with it (even if students show initial resistance). Empowering students with consistent strategies and explicitly-taught math vocabulary will help us close the literacy gap (from the math classroom).