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 – ( 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. |
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