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The Numerate Educator involves the demonstration of personal numeracy using flexible application of mathematical concepts, and it demonstrates the importance of effective teaching. Also, it consists of the analysis of the Australian Curriculum that is relevant to the mathematical concepts being taught. The ideas that are taught in class will be linked to various Proficiency Strands. For this paper, three videos will be analysed; Video A which involves the sharing of chocolate bars, video B which entails the transformation of simple numbers to palindromic numbers, and video C which teaches mental computation strategies while focusing on nine times tables. The first part of the essay involves the identification of concepts being taught and linking them to the Australian Curriculum and Proficiency Strands. The second part consists of the identification of three best practices in the videos.
Video C focuses on Kelly Rhinehart’s lesson at Humpty Doo Primary. She specialises in teaching year 5 and 6. For this lesson, she teaches the year five students the concept of numbers focusing on nine times tables. The students are taken through several mental computation strategies where they learn mental computation skills and develop automaticity. The students are supported in the description and justification of their approaches to various mathematical problems. Also, the teacher provides the students with a chance to choose tasks that they feel confident to carry out. The teacher utilises a specific routine throughout the lesson. She started with tuning in which involved nine times tables with a big dice where the students were expected to provide the answer to different multiplications of nine using their fingers to compute in three seconds. The solutions required in one or two seconds needed the students to calculate and provide the answer mentally.
Next, the students engaged in explicit teaching where the students were given questions in pairs where they had to calculate the answer and explain the process. The teacher did some of the questions on the board and welcomed the students’ contribution in computing the answer. Afterwards, the students engage in development activities independently without the assistance of the teacher. They get the solutions by themselves, and the teacher moves around to see which students have understood the concept and which ones have not. Finally, they engage in a reflection session where they discuss the importance of the skills that they have been taught in class. The concept is in line with the Australian Curriculum which requires the multiples to be explored (ACMNA098). Also, the students were taught how to apply mental strategies as stated in the Australian Curriculum. Some of the Proficiency Strands applied include problem-solving and reasoning. Problem-solving is witnessed as the students are given problems to solve in pairs and the teacher assists them in addressing some on the board. Reasoning is seen when the students are taught to use their fingers to find solutions to multiples of 9.
Video B is a recording of the lesson carried out by Mary Psaila at Pleasant Street Primary School. She teaches year six students about number and algebra focusing on palindromic numbers. The teacher engages in planning, delivering, and reflecting on the lesson. When planning, she ensures that her strategies cater for students with a range of abilities. She prefers open-ended questions, resources, and activities since they ensure that she caters for the needs of all the students. Before choosing resources and designing activities, she thinks about how specific students will engage with them in their learning process. In the class, the students are allowed to carry out the activities at their own pace as they create palindromic numbers from simple numbers. The structure of the lesson allows whole class instruction, group discussion, and personal learning which enables the students to develop the skills they have learnt.
The Australian Curriculum requires teachers to help students in the identification and description of varying properties of some numbers (ACMNA122). The teacher ensured that she explained the properties of palindromic numbers to the students and illustrated how to transform simple numbers to palindromic numbers as stated in the Australian Curriculum. The Proficiency Strand applied in this lesson is understanding where the teacher explained and described the properties of palindromic numbers and ways of differentiating them from other sets of numbers. The teacher tried to ensure that all the students get the concept and allow students to do the activities at their own pace since they have different abilities. Each student is given a task that he or she can handle comfortably. Also, the use of open-ended approach enabled the teacher to cater for all the students from those who are poor in mathematics to those who are good at it (Spodek, 2014). Towards the end of the class, the whole class reflected on what was taught to ensure that each of them clearly understood the concept.
In video A and video C, the teachers utilised hands-on activities. For video A, the teacher makes copies of the chocolate bars which she uses to explain the concept of fractions and sharing to the children. With the pictures, it is easier for the students to understand the idea and become active in class (English, 2012). Also, the children could refer to the chocolate bars when trying to answer the teacher’s questions. For instance, in the beginning, she showed them a whole chocolate bar and asked them how much she would get from it, it was easy for the students to tell the answer since they could see that the chocolate bar was whole thus the teacher would get 100 per cent of it or 1/1 of the chocolate bar. To demonstrate the concept of sharing, the teacher made copies of the chocolate bars which could easily be cut. Afterwards, she put the children in groups and worked with one group at a time. She made the children cut the chocolate bars several times as she explained the fraction that each would get. She engaged the children at this point to ensure that they understood the concept.
For video C, the teacher used a big dice for the tuning in session. The dice were used to help the students with the nine times table. She taught them how to find the solutions using their fingers. For instance, if it is five multiplied by 9, the students would put down the fifth finger and count the remaining fingers on both sides starting with the left hand, the answer would be 45. The students were able to provide these answers within three seconds. However, when they were required to give the answers in a second or two, they were forced to use mental computation to provide the solutions. I consider this to be the best practice since it enables the children to visualise the answers and hence find the solutions even faster. When explaining a new concept, it is advised to provide the students with hands-on activities that would enable them to create a clear mental image of what the idea is about (Reys, 2016). They can easily relate the concept to real life situations and understand it even more. Also, hands-on activities made the students livelier and involved in the learning process compared to them listening to a teacher the entire time. When students are engaged in the classroom activities, the high chances are that they will understand the concept being taught.
In video B and video C, the teachers implemented peer discussion. In video C, the students were put into groups of two. The teacher assigned them each a complex mathematical problem which they were expected to find the solution. Although the answer was important, the teacher wanted the students to explain the whole process of how they arrive at the chosen answer. In this way, the students helped each other to think as they tried to find the correct answers. The teacher went around the class to ensure that the students were doing the right thing. It is crucial for the students to understand the whole process of finding an answer since it makes the work more comfortable for them when they want to compute the correct solution. The students discussed among themselves the correct answer and in the process, they taught and reminded each other of what they had already learnt. Afterwards, the teacher requested some of the groups to state their task and explain the whole process they used to find the answer. In this way, the concept the students understand the entire concept and they help other students to understand at the same time (Skemp, 2012). It is a best practice as it maximises the students understanding of a new concept.
In video B, the teacher requests the students to discuss among themselves why they chose specific simple numbers and transformed them to palindromic numbers. She wants them to carry out this activity before they explain their reasons to her and the rest of the class. In this way, students learn how to justify their answers and how to prove that they have the correct solution. It is during a timeout, so the teacher does not interfere with the students’ discussions. The students are left to explain to their neighbours why they settled on the simple numbers that they choose. It is a best practice since it engages all the students in the learning process. Also, it enables the students to learn how to justify that their choice of numbers is correct. If a student can explain to another their answer, then it will be easier for them to explain it to the teacher and the rest of the class. It gives them confidence in their answers (Siemon, 2011). Also, it makes the class active since the students do not only have to listen to the teacher explaining, they also have to do the explaining themselves. Peer discussion is important in improving the students’ understanding and their confidence in explaining their answers.
In video A and video B, the teachers carry out the formative assessment by taking part in the student’s activities. In video A, the teacher sat with the students in various groups and asked them questions concerning the activities that they were carrying out. She asks the children what would remain if the pieces of the chocolate bars were shared among the children and the teacher. The students can express their answers in fraction form. It is a best practice since the teacher can correct the students at an early stage when they make a mistake. Also, the teacher can tell the strengths and weaknesses of the students. She helps them to find the answers when they are stuck using the chocolate bars which enables them to visualise the problem (Clements, 2014). She directs the children on how to cut the chocolate bars and to share them out among their group members. With such assistance, the teacher ensures that the students remain on the right track in the lesson. Also, the children’s understanding is boosted since the teacher is there to elaborate any concept that could have missed during the whole class instruction.
In video B, the teacher explains the concept to the students and tells them how to transform simple numbers to palindromic numbers. Afterwards, she gives each student a task to carry out. She goes around the class evaluating the work done by each student. She asks them questions and demonstrates to them how to find the palindromic numbers. She mentions that the students have different abilities and she ensures that she gives each student activities that match with their abilities. With her presence, the teacher can guide the students on how to find the palindromic numbers and how to differentiate them from other numbers. It is a best practice since the teacher can track the performance of the students in the class (Reys, 2016). She can identify the students who need support and dedicates time in helping them to develop their learning.
Various practices have been utilised to ensure that the students understand the concepts being taught. It is essential for the teachers to understand the ability levels of the students as it helps them to know which tasks to give them. In this way, the teachers manage to develop the learning of all the students at their own pace. It is vital for teachers to illustrate the concepts using resources that enable the children to visualise and internalise the concepts. Also, having in-class activities ensures that all the students are actively involved in the learning process. With this analysis, the best practices of effective teaching are determined, and the concept elaborations from the Australian Curriculum documents are linked to the in-class activities.
Australian Curriculum Assessment and Reporting Authority [ACARA]. (n. d.). The Australian Curriculum: Mathematics (Version 8.3), All curriculum elements.
Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach. Routledge.
English, L. D., & Halford, G. S. (2012). Mathematics education: Models and processes. Routledge.
Reys, E., Lindquist, M, Lambdin, D.V., Smith, N.L., Rogers, A., Cooke, A., Bennett, S. (2016). Helping Children Learn Mathematics (2nd
Australian Ed.). Milton, Queensland: Wiley.
Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2011). Teaching mathematics: Foundations to middle years.
Skemp, R. R. (2012). The psychology of learning mathematics: Expanded American edition. Routledge.
Spodek, B., & Saracho, O. N. (2014). Handbook of research on the education of young children. Routledge.
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