Connect Extend Challenge

MATHS – Decimals (Connect/Extend/Challenge – Think/Pair/Share)

My year 7 Maths class has been studying decimal numbers over the last few weeks. I tried the Connect/Extend/Challenge routine at the end of this unit. I typed up a chart with connect/extend/challenge across the top and think/pair/share down the left hand side. Students initially thought silently and wrote their ideas in the Think/Connect box. They then discussed ideas with their partner and jotted down any extra ideas in the Pair/Connect box. We then repeated the process with the Think/Extend box and then the Pair/Extend box.

The process really encouraged substantial discussion during the class share time, which was a stark contrast to the usual discussion involving only one or two students. This class tends to be quite passive and very reluctantly engages in discussion.

Connections:

Students generally made connections to examples of decimals rather than deep connections of concepts (which I was expecting, being forewarned by the case study in the Visible Thinking paper that it can take weeks of modelling this tool to the class before substantial and deep connections are made). For example, students connected decimals to:
• Sports results
• Measurement
• Fractions
• 1.25 litre coke bottle
• digital time

An interesting connection was made by one student who made a memory link by connecting decimals to the alphabet. The letter D is closer to A therefore, when dividing decimals, the decimal point jumps to the left and the letter M is closer to Z, therefore when multiplying, the decimal point jumps to the right.

Extend (How has your thinking been extended or pushed into new areas)

As expected, students mostly suggested skills which they had learnt, such as: dividing decimals, multiplying decimals with lots of zeroes, jumps (moving decimal point to the left or right). Whilst affirming their suggestions, I kept prompting for students to think more deeply about how their thinking had been extended by developing an understanding of big ideas and deeper concepts. I explained that when they develop an understanding of the big ideas, it is often accompanied by an ‘aha’ moment. It can feel like a light has suddenly switched on in our brain as we suddenly develop a deeper understanding. I suggested some examples from my own learning of mathematics.

This prompted one student to contribute that his understanding of decimal points was extended when he realised the number gets larger when jumping the decimal point to the right.

It was an exciting moment when thinking was made visible by one student who said she now understands the connection between decimals and place value. She now realises that decimal places are based on ten (tenths, hundredths, thousandths and so on).

Challenge (what is still a challenge or remains a puzzle for you?)
We ran out of time to complete this section but will follow up with this during the week.

The use of this thinking routine was an introductory session to the use of the tool. I can see exciting prospects ahead as students extend their thinking in a visible way.

Lois
August 9, 2008 8:11 PM


Steve Tobias said...
What a wonderful reflection Lois. The Connect/Extend/Challenge routine is a simple way to find out what the students' know. What's more it is an effective means of sharing ideas, thoughts, conceptions and misconceptions in the classroom. I liked the way you managed the connection phase - many students fail to make the connections between real life maths and text book maths. The moving of the decimal point is a great example of this. That student not only understands what is happening when you move the point to the right/left - they can see the connection multiplication, division and powers of ten. Essentially this is the basis of the Base Ten system - very powerful learning. The challenge for the teacher is to take this 'aha' moment and see how wide you can spread this with other students.

August 11, 2008 2:30 PM