Stretching students’ thinking without reinventing the wheel – ask a question!

As a teacher, it is so easy to think we have to keep reinventing new activities to ensure students are challenged, engaged and most importantly, learning. Whilst it is certainly important to maintain a degree of ‘freshness’ in one’s teaching, it really doesn’t mean we have to go and reinvent completely new activities. Sometimes asking a simple question at the end of an activity is all that is needed.

I learnt this recently when I was teaching some of my Year 2 students about patterns using the same activity I used a couple of years ago. My students were both tasked with continuing the pattern (based on  Nelson Maths activity) of L’s, see below.

Screen Shot 2014-04-01 at 5.02.18 PM

Students had to work out what the 10th L would look like and how many counters would be needed. They worked on this until they reached the 40th L. Most students were able to work out that this was the counting by 2s pattern starting from an odd number. I thought to myself, ‘great, they get it now onto the next activity.’ I was just about to hand out a follow up activity when I realised that this certainly was one pattern, however, there were other patterns as well. In order to make this activity more challenging, I said could anyone work out the 100th L in a different way (without using the counting by 2s pattern)? This really got my students thinking. For some of them, they needed the hint of referring to the number above the L as well as the number of tiles required to make the L. I got two groups to come up with a different rule.

Using this L pattern activity in this way made me realise I need to make sure my students’ are genuinely challenged before rushing to the next activity. Adding just one simple question to their activity made it more challenging. I learnt that it is so important for me to continue asking questions like ‘Can you think of another pattern? Can you show me in another way? Why do you think that?’ to ensure my students are suitably challenged.

How else do you challenge/stretch your students’ thinking in maths or other subject areas?

Making Mistakes (on purpose) in the Classroom

I recently participated in a twitter chat where it was discussed how important it is to model not knowing the answer to everything and making mistakes. It made me reflect on the fact that I need to do this more in my teaching.

Recently in maths as a tuning in activity, I wrote the statement of 2 groups of 4 but I drew 4 groups of 2 like this:

 

4 groups of 2

We spoke about what was wrong with my picture. I said things like, but this is 2 groups of 4 as there are 2 dots and 4 groups. It was great to see them fired up and hearing their reasoning such as:

  • Your picture is not right because you have 4 groups instead of 2 groups.
  • Your picture is not right because each group has 2, whereas you should have 4.

My students really enjoyed ‘correcting’ my misconception and it was great to hear their reasoning. They said things like “But you’re a teacher and you’re making mistakes!” I responded by saying, “Even teachers can make mistakes. Thanks for teaching me and correcting my mistake.” This activity got me thinking that I should do this more often in maths, where I pose a problem which I know to be wrong, but I pretend that it’s right and get the students to articulate why it is incorrect.

What type of mistakes do you make on purpose in the classroom? How have your students responded?

Extending Year 1/2 Students in Place Value with Decimals

I have some Year 2 students who are working well past the Year 2 Australian Curriculum Achievement Standards for Place Value. These are students who are confident with working with numbers into the millions. As a result, I decided to extend them by teaching them about decimals. It helped that they possessed a solid understanding of fractions, so I could connect this to decimals.

Firstly, I used a pro forma from Nelson Maths to connect fractions to decimals:

Decimal tenthsWe spoke about what each square represented. I asked ‘What is one of these squares called?’ Students answered ‘One tenth’. We then spoke about how the line in fractions (eg 1/10) means divided and when we put a fraction into the calculator we get another number. Students put 1/10 into the calculator and got 0.1. They did this for 2/10, 3/10 and so on and each time they shaded this on the pro forma writing 1/10 and 0.1 beside each shading. They began to understand that decimals were another name for fractions. However, one student whose understanding was not as solid as the others, recorded in his book 0.3 is 1/3 and 0.4 is 1/4 besides his shading.

In the following session, these students modelled decimals using place value mats that had tens, ones and tenths. We used straws to represent the tens and ones. We used a rolled up piece of play dough (the same length as a straw) cut into tenths to represent the tenths. My students chose a decimal to make and they wrote both the decimal and fraction name underneath their model. They took photos on iPads to show me their work, which looked like this:

Modelling decimals

I found these Nelson Maths based activities to be really helpful when introducing decimals and my students all felt comfortable modelling and describing the decimals they made by the end of the numeracy sessions. It was also valuable to connect the known (fractions) to the unknown (decimals) when teaching decimals.

How have you taught decimals in the classroom? What issues have you faced when teaching decimals?