Imagine: multi-modal learning


I love the word, the idea, the song (melody, lyrics, riffs).

We received a (much-wanted) piano – a gift from a stranger (quick digression: husband asked at a local garage sale if they had a piano. The answer was no but that their brother had one to give away but it was in Bega – a good 6-hour drive away! Husband goes off on a road trip with 2 mates and now it’s home…a piano with stories…gotta love that).   Not a day goes by without it being played by my daughters and recently, me. Yes, I’ve decided to re-learn.

If you’ve been following my blog before, you’d recall that I have tried to do this before and, in fact, used the experience as an inspiration to introduce Algebra. That was a few years ago and the interest waned. But now, we’ve got a REAL piano. with a story.  So re-learn, I must.

I chose to learn “Imagine”. I got the free music sheet from here. I had a go and then hit YouTube (as you do) and found this tutorial. This guy made it looked easy and talked about chords. So there I was, tinkering away and said aloud, “I wish I could play chords on the piano” et voila! my fairy godmother appeared! Actually, it was my 15 year old daughter.  She learned the skill from her Music elective and she showed me how. And guess what, there are patterns (again). So now, my ‘version’ is a hybrid of the sheet music, the video tutorial and the face-to-face tuition I got from my daughter. THIS is multi-modal learning!

There’s much here that can be adapted to classroom learning and I will list a few. Please feel free to contribute any more you can glean out of this.

  1. Motivation drives learning. Have purpose.
  2. Learning through (work)sheets is possible. It is a point-of-reference.
  3. Learning through videos is possible.
  4. Direct instruction can be a real boost.
  5. Immediate and specific feedback is invaluable.
  6. Articulating (identifying) difficulties can become learning opportunities.
  7. Learn from anyone; kids can teach.
  8. Identifying patterns can be a catalyst for learning.  Abstraction is necessary for transference (and I’m really excited about this transference bit – building my repertoire and dreaming of improvisations – haha)
  9. Practice. There is a difference between knowing and mastery: I now know how to play Imagine but mastery is still a dream.
  10. Learning is relationship-building.

Imagine a classroom where these are at play.

Can’t chuck a u-ey

This is cross-posted in Inquire Within.

Photo credit: wallyir from

I’m really loving inquiry learning. As Edna Sackson has pointed out, I’m on my own inquiry journey. Perhaps because I’m new to it, I find it really is full of surprises – maybe it’ll always be full of surprises by its very nature. This is a positive spin on a journey that is fraught with uncertainties because inquiry is that – keep asking questions though there are no guarantees the line of inquiry will lead to expected destination.

The uncertainties sometimes shout at me like the sign above – “Wrong way, go back“.  My experience with inquiry learning, however, is that once on it, I literally “can’t chuck a u-ey”; the only way is to keep going onward; there is no going back.

This is powerful stuff for me. I am realising that as I learn, I keep moving forward – there is no reverting back. Inquiry as a process is just that – it may branch off to who-knows-where and may seem to lead back to the beginning but the journey itself transforms the traveller.

There is no “wrong way, go back“. There’s still, stop, go, look, listen, turn left, turn right but there is no chuck a u-ey.

Inquiry as a process transforms the learner. In this case, the learner is me, the teacher.

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!

Creativity in Problem-Solving

Problem-solving is arguably at the core of mathematical teaching and learning. That is, various concepts and skills are taught/learned in the hope of solving more and more complex problems. Logic is very much valued.

I have always sensed that mathematics (re: Logic) and creativity are contradictory.

I just read an interesting article on observations on Real Science : sometimes (often even) logic stumps scientists and creativity paves the way to solve problems. The article talks about diversity-induced far view talk reliant on metaphors and analogies. I learned today that the idea of far view, or distancing oneself via abstraction, is a strategy for creative thinking (read more on Scientific American). The way I see it, it’s a logical way of thinking outside the square or taking on a different perspective.

My point is, logic does not necessarily clash with creativity. Used in tandem, the likelihood of finding solutions is increased.

The challenge now is translating this into practical applications in the classroom! I already use metaphors and analogies in teaching (re: Analogies and Algebra post). I must encourage students to think of their own. Also, I need to harness more the potential brought by the innate diversity of  every class – this means, at least, more opportunities to work in group to solve problems…futuristic perhaps?

Analogies and Algebra


In the course I attended recently, we spent a fair bit of time on discussing Analogies as a teaching-learning strategy.  There is probably not one person who has never used this strategy before, particularly if you ascribe to the thinking that we learn by connections.  Hence, the initial omission.

However, I’ve learned today how good this strategy really is. Hence, the special mention.

Analogies and Algebra

Undoubtedly, the abstract nature of Algebra – it’s very power – is the reason people are generally averse to it. Having overcome the obstacle of why we use x (variables or pronumerals) to begin with, I thought the next problem was balancing equations. My observations proved otherwise. Balancing equations was not an issue (drilled as they were that whatever you do to one side, you do to the other to keep them balanced).  Rather, the problem really was why we needed to isolate x in the first place, to find its value. Pretty obvious, I thought.

The analogy I used today involved the use of a bowl with chocolates and crackers. The question was how many chocolates were in the bowl.  I showed them the bowl. They could see hints of chocolate hidden by a mound of crackers. A quick discussion ensued. Soon enough they realised that the best way was to remove the crackers so the chocolates can be seen. Light-bulb moment. It was wonderful.

For the record, I’ve actually extended this activity to involve revision of the distributive property of multiplication (I had 2 bowls with equal number of chocolates and crackers), substitution of pronumerals (to work out total quantities) and simplification of equations. As soon as I rewarded one insightful comment with chocolate, I got a whole class motivated to contribute to the class discussion, rather Pavlovian. Not enough chocolates for everyone, but I obviously chose the right brand of crackers – everyone had some!