Tag: assessment

Can programming help students appreciate Maths more?

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I love it when things start to converge in my mind. This post will attempt to encapsulate this convergence; attempt being the operative word. As Jack Dorsey said, simplifying the complex is not easy. Try I must to help me document my thinking.

I blogged about Maths not = calculating in reference to Wolfram’s computerbasedmath.org initiative and mentioned it in comments on relevant posts of other bloggers and to anyone who cared to listen. I recently attended webinar with @ColinTGraham on Teaching Maths Effectively which led me to Project Euler. I signed up to this project and had a go using Microsoft SmallBasic, a free and easy to learn/teach programming language. I read @garystager’s post on  Charlie Rose‘s interview with Jack Dorsey, Chairman and one of the three co-founders of Twitter; I watched the interview as well. I think perhaps that only developers can really appreciate Stager’s (and Dorsey’s) view on elegant code (I happen to as I was in Software Development for years before going into teaching).

One of the challenges of maths teachers is making maths relevant. Also, Wolfram mentioned that students often do not see, much less appreciate, the beauty of maths – especially when drowned in the number-crunching (read calculation) jungle.

Anyway, I’m coming to a conclusion that there is definitely room and reason for integrating programming in school and not necessarily as a separate subject/course. In my previous high school, I did suggest this as an extension activity for a very smart girl and in fact, introduced her to SmallBasic. My suggestion to use some Maths lesson time was rejected for various reasons including there’s no one really able to support this idea and struggled to justify the suggestion. Fast forward to now and the previous paragraph is justification enough.

I’ve only done a couple of problems on Project Euler. It offers much opportunity as an assessment tool – you need to decode the problem in order to code. The process can run the full gamut of the digital Bloom’s taxonomy – from remember through to create. For example, what does multiple mean? I used to say it’s the times table of a number. But, how do you code that? Well, a number is a multiple of a given number if the remainder is zero when you divide – there are programming functions for this (language-dependent). Now, there’s a definition not often mentioned. And “below 1000” provides an opportunity to apply inequalities.

Project Euler definitely provides an avenue for computational thinking that Stager and Dorsey espouse and openly enjoy. Upon solving problems, you get access to the solution and the forum so you can compare your own code. The pursuit of elegant code is very obvious in the forum. What this means, too, is that participants are naturally differentiating the task – motivated by finding the most efficient solution – often due to deep knowledge of maths (including finding patterns) and not so much programming ability. How awesome is that??? Actually, reading some of the comments help one appreciate the depth and beauty of maths that Wolfram – and passionate maths teachers – allude to.

Programming is problem-solving. It promotes analytical and logical thinking but not at the expense of creativity as both Stager and Dorsey argue. In fact, I daresay a good programmer has to have a healthy dose of creativity. Programming provides instant feedback (read: gratification or frustration).

Though much can be learned from programming, it really is not for everyoneI…not because it’s hard necessarily but because it doesn’t appeal to all such as carpentry does not appeal to me, for example; I’m sure carpentry provides fantastic opportunities to apply mathematical concepts and more besides. I understand apprehension to even try to include it as a teaching strategy, but there is help out there. Just as there is a community of developers out there, so there is too of teachers.

Where to now?

As an IT integrator, I plan to approach the Maths and the Technology Departments (the elective programming course was dropped due to dwindling numbers). I’ll walk them through my rationale mentioned above. Then, who knows?

Do you know any other initiatives similar to or linked to the ones above?

Revision Relay

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This is a quick post to share an idea and related resource.

Year 8 is about to have a maths exam next week with multiple topics: Algebra and Equations, Fractions/Decimals/Percentages, Angles, Circles/Areas and Ratios. To make revision a bit more fun, I’m doing it as team work and relay style.  The main objective is for students to identify topics they need to personally revise, i.e. assessment for learning.

There are 2 relay games and these are available as aWord document – ready to use or even alter to suit your needs – ie different topics and/or year group. To use, cut the relay questions – this one is ready for 3 groups; duplicate for more groups. Cut into columns.

  1. Divide students into 5 per team – assign names or ‘tribes’ if you like to suit a Survivor challenge theme
  2. Assign each student a number from 1 to 5  (or they pick themselves)
  3. Give Relay 1 questions to each group and a piece of blank paper for solutions. No discussions allowed at this point.
  4. Student 1 answers Q1 and pass answer and questions to Student 2.  Student 2 needs Q1 answer to solve Q2, Q2 answer to solve Q3, etc.  It’s up to you if you want students to work individually or cumulatively help each other such that by the time they get to Q5, the whole team works on it. This is my preferred option for differentiation purposes, i.e. those I think need the  most help will be Student 5.
  5. First team to get the correct answer wins.  If a team’s answer is wrong, trace back for errors.
  6. De-brief to help students identify where they might have struggled a bit and therefore need more revision.
  7. Run Relay 2 in the same way, i.e. build on from Student 1 with Q1 to the end.

That’s it. This idea can also be used at the start or end of school as well or even just as a team-building exercise, e.g. before a group sets off on a project.

Can you think of any more adaptations?

Concentric Circles of Learning

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I like collaborative work and social constructivism, i.e. learning from and with others. Today, I got to use this method in collaboration with another year 8 maths teacher.  This post is both a lesson idea as well as a reflection on this type of learning.

As an introduction to the new topic of Circles, this lesson was designed to assess (for learning) what the students already knew about Parts of a Circle. Instead of the usual questioning and Diagnostic Test methods, we decided to do this:

Lesson Idea

1. Pair up students within each class. We used class buddies.

2. Each pair list as many parts as they can remember in 3 minutes. Materials: PostIt notes or small piece of paper

3. Each pair is paired up with another pair, i.e. group of 4. We had 9 groups with one having more than 4 members.

4. On butcher paper, each group constructs (draws) circle/s and labels the parts accordingly.

We were only going to give them 10 minutes to do this but the students were engaged in discussion and construction (some got very artistic) so we extended this to 15 minutes. Materials: butcher paper, compasses.

5. Each group presents to the whole group (2 classes) their posters and is asked to describe one part in detail, e.g. Diameter as a line passing from a point on the circumference to another point on the circumference passing through the centre (or something along those lines).

This was actually a good conceptual review as well as literacy exercise.

6. For homework (and reinforcing what was learned), give a worksheet on labelling parts of the circle.

Concentric Circles of Learning

Concentric circles are circles within circles, all sharing the same centre point. I think this is a beautiful metaphor for learning. At the centre is the individual learner. When this learner learns from and with others, his/her learning circle radiates outwards and gets bigger and bigger, as does personal learning and knowledge. As in the lesson above, each learner brings his/her own knowledge to share firstly with one other, then with another two, then to a bigger group and so on.

While there were technically two teachers in the classroom, more teaching and learning happened between students. Today, we (my colleague and I) did not teach. Today, we facilitated learning at individual and group levels. Collaboration happened at many levels today (and before today where planning was concerned). Today was a good day.

Where this metaphor falls short is that in fact, there are many concentric circles and these circles overlap as they do in Venn Diagrams. But, that’s perhaps another post!