Jours 6 et 7 : 3D Trig and manipulatives

I have been teaching MCR3U for 14 years now.  In the past, I taught in much the same way I learned.  I showed the students everything I knew while they took notes and then I assigned homework.  This approach worked with the small percentage of students that probably would have already understood whether I taught it or not.  The others struggled.

Recently, as a numeracy coach/leader in my school board, we have been studying spatial reasoning and ways that we can help students develop this type of reasoning.  While reading this support document : Paying Attention to Spatial Reasoning, there was something that stuck with me :

Spatial thinking is malleable and can be improved through education and experience.

Alors, si je peux Mettre l’accent sur le raisonnement spatial, je devrais pouvoir aider les élèves à mieux comprendre les concepts enseignés.  Je pourrais développer ce raisonnement chez eux en respectant la recherche qui dit que : « les habiletés de la pensée spatiale peuvent être améliorées avec la pratique. »

With this in mind, I changed the way I approached this « lesson » on three-dimensional trigonometry problems.  One of the changes I have made in our school is that I have put storage carts in every classroom with a variety of manipulatives.  This way we and the students have constant access and we don’t have to provide one type of manipulative because we chose it.  The students can choose, which is a mathematical process as well.

J’ai passé à travers le chariot et j’ai montré le différent matérial aux élèves :

• géoplans
• géolegs
• déci-blocs
• cure-pipes
• solides transparents
• réglettes cuisenaires

Le but étant de soutenir la modélisation d’un problème en trois dimensions avec l’utilisation du matériel de manipulation.  Les élèves n’ont pas de la difficulté à résoudre les triangles, si le schéma est présenté..mais la difficulté est avec le schéma lui-même. Donc, s’ils peuvent le visualiser et le dessiner, ils devraient pouvoir répondre à l’attente.

Avec des exemples en main, j’ai animé la leçon en permettant à chaque élève d’utiliser le matériel, de visualiser les changements/mouvements décris dans le problème et de faire le schéma.  Ils devaient ensuite faire vérifier leur schéma avant de procéder aux calculs.

I noticed that almost every student drew the problem in a different way, but « in the same way » if that makes any sense.  They all had the angles in the right places, the measurements opposite the proper angle but had their way of seeing it.  I approved almost every drawing.  Had I « taught it », I would have drawn it my way and would have lost 60-75% of my audience.  They owned their own problem now and the trig came easily after that.

Here are some examples of how my students used the manipulatives :

Did this approach cure the problem immediately?  Absolutely not, but as the research states we need to keep practicing.  So, we will be working on this for a couple days and I will make sure to keep encouraging the use of the manipulatives, as well as visualisation to help them get their drawings right.