Students need to be able to identify key information in a problem statement so that they can decide on appropriate approaches for solving the problem.
Close reading in mathematics can help students to recognise:
- the language and structural elements of mathematics texts
- how the these two elements work together to construct knowledge (Fang and Schleppegrell, 2010).
close reading (Fisher, Frey & Hattie, 2016) of the language of a problem will enable students to identify key phrases and mathematical terminology. Students should then be able to identify:
- what is known (i.e. from a given problem statement)
- what needs to be found (i.e. the type of answer expected)
- what mathematics might be useful (i.e. where this is suggested in the problem statement).
The close reading strategy below could be used for any worded problem where students need to engage with context to formulate a mathematical solution.
Understanding the strategy
The strategy involves three steps:
- Present students with a worded problem.
- Ask students to read each sentence.
Identify the key words, terms or phrases in the problem statement.
Identify a phrase which highlights the type of answer required.
- Have a class discussion about the key information to ensure all students have correctly understood the problem. Some prompts for discussion are:
What does the (term or phrase) mean? (i.e. clarifying terminology)
What do we mean by (term or phrase)?
What is the problem asking for?
What type of solution is needed?
What do you know?
What do you want to find out?
Example of using close reading
The example below shows how this strategy could be used in a Year 10 class where students are asked to solve a problem related (VCMNA341).
A parabola has x-intercepts at 2 and -3 and a y-intercept at 3.
Find the quadratic function and sketch a graph, showing all key features.
The teacher presents the problem, and scaffolds students' understanding of the problem using the below prompts that are specific to the problem:
- What does the term parabola mean?
- What shape is a parabola?
- What does y-intercept mean?
- What type of function will this be? How do you know? How will you 'find' it?
- What are the 'key features' of a quadratic function which you should include when sketching the graph of a parabola?
Classroom discussion and reasoning a solution
The teacher ensures the key terminology is discussed.
- A 'parabola' is the graph for a quadratic function, so the function could be written in any of these forms:
- 'x-intercepts' means that the parabola cuts the x-axis at (2,0) and (-3,0).
- 'y-intercept' means that the parabola cuts the y-axis at (0,3).
- 'Key features' for a parabola refers to x-intercepts (where they exist), y-intercept and turning point.
Students annotate the problem statement during the discussion and then solve the problem independently.