Story-telling

I just read this story-telling post by @billgx which inspired me to write this post; it’s’ been a while, I know!

Bill’s post has just highlighted the power of stories – something I’ve been tossing around in the old brain for a while.  I thought it best to capture just a few of these thoughts for future use in teaching and learning.

We are always telling stories. Stories don’t have to be oral or written narratives. Just yesterday in my digital photography workshop, I alluded to photos as telling (or capturing) stories. It is sometimes difficult to glean the story depending on the medium used but the story is definitely there.

We enjoy listening to stories. Stories can be affirming with a by-product of connecting the audience to the story-teller – or the content itself.  I still remember when I told a class about Descartes before launching into the Cartesian plane. As a teacher, listening to our students’ stories afford us a glimpse to who they are and knowing students is important for good teaching and learning to happen.  Ditto for students.Here is a story-writing exercise I once did with a class just to get the creative juices flowing:

  1. Give each student a piece of paper.
  2. Everyone starts off with the same line, e.g. “Today as I got to the school gates….
  3. Then, everyone passes the paper to the left (or right) and then write a sentence to continue on.
  4. Continue the round robin, with prompts for introducing the ‘problem’ or ‘resolution’ or ending. 

Make sure you make time to read a few out or perhaps publish the stories. Depending on the age group, it might be necessary to establish some ground rules as you would for anything ‘anonymous’.

This might even be useful in a maths class, e.g. get students to do round-robin solution – each one just does one step. This may drive home the point of the importance of reasoning and ability to follow someone else’s line of thought.

Revision Relay

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?

Reasoning in Maths

My year 8 class started a unit on Reasoning in Geometry today. Still going along the theme of teaching big-picture style as I did with Equations, I introduced this topic with a lesson inspired by @ddmeyer’s “How we talk about shapes” and @edteck’s (Peter Pappas) “Basic Communications exercise”.

The premise is this….

Reasoning requires knowledge of  facts and language (read, write, talk – words and symbols).

Anyway, rather than just state my premise, I went through the activities outlined in the linked blog posts above. The activities certainly made it clear to the students why we name shapes (in the way we do) and how literacy in words and symbols facilitate communication.

This places a big emphasis on literacy in Mathematics but that’s because I think Maths is a language in itself, a man-made tool to help people make sense of – and manipulate – our world. To further emphasise literacy, I also defined Geometry, listed terms we will use as well as discussed properties of shapes and why it makes sense to call a triangle a triangle, etc.

The very nature of the activities engaged the students and a quarter into the lesson, some even said “I’m really enjoying this lesson” or later yet, “I feel I’m really learning” (they do usually learn something but awareness/articulation of learning takes it up a notch). Throughout the lesson, they  also saw how their learning – over time – is valuable to build on; such is the spiral nature of maths education.

To make sure the lesson flowed as planned, I created a powerpoint.  It’s good to go for anyone who wish to use it but you really must read first the posts by Dan Meyer and Peter Pappas to see where I’m coming from.

Am I wrong to emphasise  literacy in maths?

Teaching Equations big-picture style

I started Equations with my year 8 maths. I love equations – probably why I love Algebra – and have decided to buck the textbook trend.

Lesson

Instead of teaching technique by technique, I decided to go with the big picture. And really, students in year 8 already know this big picture. I started the lesson by asking them “What do you already know about equations?” and listed these 4 main “principles” :

  1. There’s an = sign (expressions don’t; it’s a number sentence)
  2. Left hand side is the same as the Right hand side (LHS = RHS) in value, i.e. size and direction
  3. Solve for the unknown (x) by isolating it or making it the subject (sentences have subjects) AND
  4. Use inverse or opposite operations

After this discussion of less than 10 minutes, the students doing worksheets that spanned at least 3 sections of their textbook. I pointed out that the answers were on the back of the worksheet. Why? They replied that the focus was on the working out. (Conditioning works) 🙂

Using these principles, you don’t really need to distinguish whether or not it’s one-step or two-step or “what do you do to x to get x +3?”. I had a student who said she couldn’t answer the latter (from the textbook) when she’s already solving problems like x / 3 = 8, or even 2x + 15 = 6. That’s because the reason we use inverse operations is because we want to isolate x ; that’s the context.

I also had a student ask how they know if they’re on the right track. The textbook says – and rightly so – check by substitution. Instead, I said well check whether the principles still hold, i.e. is LHS = RHS? If not, then you’re definitely off-track. So really, check correctness through checking by principles and by substitution.

I purposely did not teach move it to the other side and change its direction (e.g. +5 in the LHS becomes -5 in the RHS). Sure, that’s what eventually happens after applying inverse operations but I insist in not doing this shortcut….not until I’m convinced that the students know why.

Rationale

Those who’ve been following me in this learning (and teaching) blog would recognise my constant battle with keeping maths relevant and meaningful (even fun) for those who are not naturally good at it. Maths has a lot of techniques and short-hand ways of doing things which, though can be followed step-by-step, often detracts from the beauty of maths itself and its many applications.

In doing this approach I’m hoping to have more time for practice (or drill) and (equation) fun (so many interactive games out there). I hate the term drill and use ‘practice’ because maths is a language too and fluency requires practice, not just understanding. For example, I know and understand the rudiments of Spanish and French grammar but nowhere near as fluent as I am in English (I am ESL) because I don’t practice those two as much as English.

I am hoping this will work, i.e. I don’t know if it will but I sure hope so.

Concentric Circles of Learning

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!