Mathematics
My approach to teaching mathematics is based around John Munro's 'Multiple Levels of Text Processing (MLOTP) Model' for text comprehension (Munro, 2014). When a person reads a text, they are constructing meaning in a range of ways (Kintsch as cited by Snowling & Hulme, 2005). Munro’s MLoTP model breaks these aspects into seven levels of integrated meaning: word, sentence, conceptual, topic, dispositional, metacognitive and personal (Munro, 2014). He believes that at each level of the text, a reader uses a particular set of actions to extract meaning. When the reader understands the text at each of these levels, they are forming an accurate interpretation (Munro, 2014, p.11). This approach is not limited to reading texts. It can be used as a framework for teaching any subject, including mathematics.
Pr. Munro used the example below in my EDLA630 Unit, to demonstrate how the framework can be used to teach other subject areas.
Word Level
The word level of the MLOTP Model explains that students need to know the vocabulary of the topic they are learning for any subject. It states that students firstly need to be able to say the words they are learning. For example for the word family factorise, factorising and factorisation. They also need to be able to write about their learning, using the letter pattern (f-a-c-t-o-r-i-s-i-n-g) and symbolic form of the words (representing the factors of an expression using brackets). The word level also states that students need to understand the type of word they are learning, which will help them to know what the maths question is asking them to do. For example the word factorise is a verb. If a student was asked to factorise something, they would understand that they need to preform some sort of action (representing the expression by its factors).
Sentence Level
The sentence level in relation to the subject of maths, would refer to the equations and expressions of the maths topic. For example (2x + 3)(x - 1) is the factorised expression of 2x² - 2x + 3x - 3. Students need to be familiar with these number sentences by knowing what they mean, how to say them and how to write them.
Discourse Level
The discourse level in relation to the subject of maths, would refer to the questions and problems of the topic. For example a question could be:
I have 3 bags with x amount of lollies, plus 12 lollies. Or I have 3x + 12.
Factor 3x + 12
Students would then be able to use their vocabulary knowledge of factorise to write down the factors of 12.
1x12
2x6
3x4
They would then make the connection that there are 3 bags of x lollies, and there can also be 3 bags of 4 lollies
or the 'common factor'
=3.x + 3.4
They will then know that when both expressions share the same factor, they can be represented using brackets.
=3(x+4)
Topic Level
Students should explicitly know the topic of what they are learning according to the MLOTP model. For example students should know that factorising is a process of algebra, therefore algebra is the topic. Students would need to understand that algebra refers to maths which deals with symbols such as x, y.
Dispositional Level
The MLOTP model describes the dispositional level, the purpose and intention of the text. In the case of teaching factorising, it would refer to why factorising is important. They would discover from their experiences with factorising problems, that it can be used to simplify rules to make them easier to work with.
Metacognitive Level
The MLOTP model also explains that students need to be able to tell themselves the strategies required for their learning. For example to factorise an expression the strategies would be:
-Reading the problem, equation or expression out loud
-Identify the verb and define what it means/is asking you to do
-Write the factors for each part of the expression
-Find the common factor
-Draw what the expression looks like now
-Write the expression in its new algebraic form by using the common factor outside the brackets, with the remaining sum inside the brackets.
Pr. Munro used the example below in my EDLA630 Unit, to demonstrate how the framework can be used to teach other subject areas.
Word Level
The word level of the MLOTP Model explains that students need to know the vocabulary of the topic they are learning for any subject. It states that students firstly need to be able to say the words they are learning. For example for the word family factorise, factorising and factorisation. They also need to be able to write about their learning, using the letter pattern (f-a-c-t-o-r-i-s-i-n-g) and symbolic form of the words (representing the factors of an expression using brackets). The word level also states that students need to understand the type of word they are learning, which will help them to know what the maths question is asking them to do. For example the word factorise is a verb. If a student was asked to factorise something, they would understand that they need to preform some sort of action (representing the expression by its factors).
Sentence Level
The sentence level in relation to the subject of maths, would refer to the equations and expressions of the maths topic. For example (2x + 3)(x - 1) is the factorised expression of 2x² - 2x + 3x - 3. Students need to be familiar with these number sentences by knowing what they mean, how to say them and how to write them.
Discourse Level
The discourse level in relation to the subject of maths, would refer to the questions and problems of the topic. For example a question could be:
I have 3 bags with x amount of lollies, plus 12 lollies. Or I have 3x + 12.
Factor 3x + 12
Students would then be able to use their vocabulary knowledge of factorise to write down the factors of 12.
1x12
2x6
3x4
They would then make the connection that there are 3 bags of x lollies, and there can also be 3 bags of 4 lollies
or the 'common factor'
=3.x + 3.4
They will then know that when both expressions share the same factor, they can be represented using brackets.
=3(x+4)
Topic Level
Students should explicitly know the topic of what they are learning according to the MLOTP model. For example students should know that factorising is a process of algebra, therefore algebra is the topic. Students would need to understand that algebra refers to maths which deals with symbols such as x, y.
Dispositional Level
The MLOTP model describes the dispositional level, the purpose and intention of the text. In the case of teaching factorising, it would refer to why factorising is important. They would discover from their experiences with factorising problems, that it can be used to simplify rules to make them easier to work with.
Metacognitive Level
The MLOTP model also explains that students need to be able to tell themselves the strategies required for their learning. For example to factorise an expression the strategies would be:
-Reading the problem, equation or expression out loud
-Identify the verb and define what it means/is asking you to do
-Write the factors for each part of the expression
-Find the common factor
-Draw what the expression looks like now
-Write the expression in its new algebraic form by using the common factor outside the brackets, with the remaining sum inside the brackets.
References
Snowling, M., & Hulme, C. (2005). The science of reading a handbook (Blackwell
Handbooks of Developmental Psychology). Malden, MA: Blackwell Pub.
Munro, J. (2014). Effective literacy teaching: The High Reliability Literacy Teaching
Procedures Approach. Melbourne: EdAssist.
Handbooks of Developmental Psychology). Malden, MA: Blackwell Pub.
Munro, J. (2014). Effective literacy teaching: The High Reliability Literacy Teaching
Procedures Approach. Melbourne: EdAssist.
P-2 Junior
A graphic organiser I created to assist students in making connections between multiplication and division.
I rarely use worksheets such as this in the classroom but believe they have their place in assessing student learning. This particular worksheet was used for assessment as it showed students to show their understanding in written and picture form. Students enjoyed the fun of being a "Shape Detective".
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A think board I created to assist students with a division task. Students had to select a number (Appropriate numbers were provided by the teacher on the whiteboard), and create representations of their number by showing: a word sentence, an array, a group drawing and repeated addition equation.
I believe hands on learning in Mathematics is important, and is especially important for the younger year levels. I think that math's books have their place for prediction, reflection or drawing for working out. The picture above shows me and 1/2 students solving a problem to do with arranging a rubix cube. I thought it would be a fun idea to have a race to see who could put their cube together correctly the fastest.
An extension activity that allows students to show their knowledge of a maths topic, by having them create their own problems to solve. The sample above is a student's attempt at creating their own division problem. It shows that although she is able to write the problem, and draw the solution (people with 2 lollies each), she still needs to develop her of multiplication in algorithmic form.
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3-4 Middle
This was an introductory activity for grade three students to learn about prisms. After a prism game to begin the lesson, and a class discussion to define a learning intention as to what a shape has to have to be a 3D prism, students could select a 3D shape to make. After this student's checked if it was a prism using the 2 criteria mentioned in the learning intention.
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Sample Lesson Plans
P-2 Junior
CRT Prep Maths Lesson.docx |
I completed this Unit on my final teaching round.
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I planned this lesson based around an activity I found on the NRich website. The students really enjoyed the activity due to its "hands on" nature.
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3-4 Middle
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5-6 Senior
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This assignment was about the effectiveness of Maths Interviews and Open Ended Tasks. It was conducted using a grade 5 student from one of my teaching rounds.
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