Wednesday, 15 October 2014

A Literacy Comprehension Approach To Maths Problem Solving

From my own experience and that of many other teachers I have worked with, I have found students struggle with word-based mathematical problem solving and mathematical literacy. 
Sound familiar?

Many teachers have found their students struggle with word-based mathematical problem solving as Reilly, et al., (2009) showed in their study. However they also showed that using a Reciprocal Teaching approach to address mathematical literacy provided an increased evidence based understanding of word-based problem solving by the students. 


Reciprocal Maths (based on the Reciprocal Reading system) first described by Palincsar and Brown (1984) is an instructional strategy designed to improve comprehension of mathematical problem solving through the use of reading strategies, with the further aim of increasing student independence. 


This highly effective approached uses the stages of: connecting, predicting, clarifying, visualising, questioning, solving, summarising, and reflecting. Strongly linked to literacy, students support each other in co-operative groups but work individually and record their though processes, working out, and reflections.


Using role cards similar to those used in Reciprocal Reading, students work through problems together and record their work individually but share their results and strategies, allowing the group members to support and learn from each other. This process like Reciprocal Reading should be teacher led, and over time as students become proficient with the process they will be able to work in groups independent of the teacher. Students using this method do work through problems at a slower pace but you will find they have a deeper understanding of the problem and strategies they used and be able to discuss their working out process with more clarity.

Below is an example of how students would use Reciprocal Maths to solve a word-based problem.


Write the problem out here:
Jake baked 115 muffins, which was 17 more muffins than Jill. How
many muffins did Jill bake?
CONNECT
      What past maths problems does this remind you of?
This reminds me of a problem that was in last week’s test.
      How did you solve a similar problem last time?
I found all the numbers and minus them.
      What strategies did you use to work out a similar problem?
I used subtraction.
PREDICT
      What do you think this problem is asking you to do?
I think the problem is asking me to subtract Jill’s muffins from Jake’s muffins.
      What operations do you think will be needed?
Subtraction
      What different ways do you think could solve this problem?
Reversing the operation might also work or I draw a number line.
CLARIFY
      What is the problem asking us to do?
It is asking us to find out how many muffins Jill baked.
      Are there any words or ideas you are not sure of?
No.
      What information is AND isn’t needed to solve this problem?
IS:  Jake 115,  Jill 17 more, how many            ISN’T: all the other words
      What operations are AND aren’t needed?
ARE: subtraction     AREN’T: addition
VISUALISE
      What pictures can you make in your head about this problem?
I imagine Jake with 115 muffins in lines of 5 in front of him. Next to him I imagine Jill with the same. Then I imagine a wicked teacher destroying 17 of Jill’s muffins with a laser gun one at a time.

      Draw a picture, diagram, table or any other visual way to show this problem and its solution.
QUESTION
      What questions do you have about this problem?
None
      Are there any tricky parts to this problem?
The word ‘more’ makes it sound like you should add the numbers.
      What do we need to do first? Then what?
First we must take 115. Then we must split 17 into 15 + 2 because 15 is easier to take away from 115 than 17. Lastly we should minus the 2.
SOLVE
      Solve the problem and show all your workings out and thinking.
115 – 17 =
115 – (15 + 2) =
     115 – 15 = 100

     100 – 2 = 98
      Re-read the problem and judge how reasonable your solution is.
I think my solution is reasonable because if Jill has 98 muffins, it means that Jake has more muffins.
SUMMARISE
      What strategies did you use to solve this problem?
I use subtraction and place value partitioning.
      Give reasons to justify why you think your solution is correct?
If I add 17 to 98 I get 115 which means Jake has 17 more muffins than Jill.
REFLECT
      What worked well?
Underlining words that seemed important in the problem helped me choose the right operation. The visualising helped me figure out I needed to split the 17 into 15 and 2.
      How would you change your solving strategy next time?
I would use the same strategy but I would try another one as well to see if it also works.
      What could the group improve on next time?
We could encourage each other by saying what each person did well.
      How well did you contribute to the group work out of 10?
8 because I could have helped Mary when I finished early.