Making Thinking Visible While Measuring Angles

Warning: Unless you are familiar with both "Making Thinking Visible" and an inquiry-based teaching approach, you may not find this particular blog useful.  If you are, please read, comment and add your suggestions!  I don't profess to be an expert by any measure or degree.  (I'm making a funny...)

I will soon be starting an inquiry into angles in mathematics, which fits well with How the World Works and our primary six/grade five study of structures.

After taking the "Making Thinking Visible" online course offered through Harvard as a staff last year (google it to find all the thinking routines/take the course to dramatically improve your teaching and your CV!), it has become clear to us all how well the thinking routines fit in with our inquiry model in a PYP school.  Last year, I used them extensively within my transdisciplinary themes, but this year I'm getting more comfortable using them in stand-alone mathematics planners.

The conceptual understanding I want students to arrive at is: Angles can be measured and constructed for a variety of purposes.

In order to do this, students are going to start by doing a THINK/PUZZLE/EXPLORE routine.  This can be used as a mini assessment.

Students will make obviously connections that go beyond geometry.  Angles are a very important concept in geometry though they are not often thought about in our daily lives. However, angles impact our lives in more ways than we think. Students will begin to understand that we all use angles without even realizing.

We will do a THINK/PAIR/SHARE with the following questions:

1.              How do people in various professions use angles to complete their work?

2.              How do all people use angles in their everyday lives?

3.       How do you use angles?

After time spent walking around the school in pairs and identifying angles, then coming together to list them, students will get an “Angle Facts Worksheet” in which they will have to draw the examples they found. 

Students will also undertake a “building a house” activity that promotes understanding of angles; students will do the CREATIVE HUNT thinking routine with the word TRIANGLE, identifying its parts and purposes (How does it work?); the main purpose (What is it for?); and the audience (Who is it for?).  Students will make a ‘target diagram to explore this idea.

After ample inquiry time, students will watch two khanacademy.org videos on identifying and measuring angles.  After they complete their viewing, they will do the CONNECT/EXTEND/CHALLENGE routine.

Students will then engage in some Mathletics exploration and problem solving to do with angles and finally do a HEADLINE routine to summarize their overall understanding of the importance of angles.  This will serve as a good summative overview.

 Reflections on planning a mini-inquiry using the thinking routines:

By using the “backwards by design” planning model in addition to incorporating the visible thinking routines in my mini-inquiry into angles, I feel really empowered about how I can teach students to think and explore through mathematics without using direct instruction at the outset.  Though it wasn’t my intention, I find it interesting that I used three UNDERSTANDING ROUTINES (Connect/Extend/Challenge, Think/Pair/Share, and Headlines) while planning an inquiry into angles.  It makes sense in that this is a rather straightforward concept, but can be taught/learned with a depth that I haven’t explored before as a learner or as a facilitator.

The fact that I plan to use a CREATIVITY ROUTINE (Creative Hunt) will also be an interesting trial: I'm hoping it will allow us to see that you can go beyond basic facts in geometry and see things from different angles.  (Pardon the pun!)  I like the idea of extending student thinking beyond the factual and exploring the creativity and play behind things, even when dealing with empirical, proven information.

I'm so thankful that I am learning how to be playful in mathematics, and teaching my students to be the same.  The best part?  They're learning more deeply through their exploration and play, and they're having fun.  You can't argue with that combination, can you?