Week+6+-+Building+concepts+of+area,+perimeter,+and+volume

=**Week 6 Thoughts and Reflections** = = = What an interesting lesson and a great source for reflection. For a start, where did all the time go? The lesson appeared to just fly by and even making the adjustment to the time for the last rotation through the activity stations, our class time was over. And I have so much more planned!

So, let's start at the beginning and see where the time went...

We took some time to talk to one another about the **practicum placements** and while this had little to do with the lesson and my plans for it, this was a significant thing for you all and whether or not I allocated time for discussion or not, a) this was probably far more interesting for you than class and b) you would have found the time to discuss this. As teachers it is important to recognize that significant things happen to our students and that we need to find time and space in the class to allow for this. In the same way we would accommodate each other, so too is this a great opportunity to model respectful behaviour to our students. Acknowledging these special times does not have to mean that students have free reign - and tacit approval - to derail each class with off-topic comments and behaviour and finding the right balance may be tricky, but it may be just one more thing that helps make your classroom a safe and inviting place for students to be.

It's not clear to me that the problem **of the divided 8 x 8 square** becoming a 5 x 13 rectangle was solved by all today. Again, while the answer may not be the sole focus of posing such problems, routes to its solution from whoever would like to contribute their ideas may be of interest to the group as a whole. I invite any and all to post up their thoughts in the Other Topics page. I heard Andrew, Ryan and Jason P. with some interesting suggestions for solutions... perhaps you'd like to start the ball rolling? In hindsight, I spent too much time on this but as it seemed to provoke some interesting ideas and keep many guessing, I let this take more time than originally planned. (Umm...)

The **Square within Square problem** appeared to be a very engaging activity for all of you and although I had not originally planned for this, as you had so many interesting ways of tackling the problem I decided to ask you all to share your solutions. This was a great segue to move into the discussion with the TIPS4RM exemplar that offered a glimpse into 4 grades worth of solution strategies. Many thanks for that! More time taken than planned! In addition, take a look at the file on the website (week 6) that shows the curriculum development of perimeter, area and volume across the 4 grades. It may help to ground our discussions of this problem in the curriculum.

All of the **Activities with Curriculum Connections** were well thought out, engaging and thought provoking. Many thanks for this weeks' //energetic eight//. I trust that you found the in-class discussion and feedback from your colleagues to be of value as you write it up. Good job to you all!

Finally, the **consolidation group and whole-class discussions** at the end of class (which I had planned for!) offered some great insights into the activities and not only what did or did not work in our (contrived?) setting but what we may face in our own classrooms. As Sheila and Steven's comments suggested, our students will have many different ways of approaching problems. Preferencing one - (written, for instance) - over others (pictorial, model, graphic, verbal... etc.) may mean that we just lost some students, and before the activity even started! The first step to address this problem is being aware of it, so I hope you felt the additional elaboration was worthwhile.


 * Reading discussions:** Yes, I know that we didn't have the time for this but I encourage you to think about the questions on the discussion handout (see website, week 6) in relation to what you've seen and read from the Boaler & Humphreys book and your experiences in class. If nothing else, take the time to talk to a colleague about this as the topics around establishing equality in student participation is a challenge for **all** teachers; new and seasoned!


 * Other thoughts** **Portfolio:** There were several questions about the portfolio so just to reiterate. The portfolio is (at least) the sum of your previously submitted work. It will not be assessed separately but as you have the opportunity to resubmit any of your work for reassessment (providing we speak about it first), it stands as a competed product of your engagement with the class - your own exploration of mathematics-for-teaching and ways of teaching mathematics. I hope that you also find it a useful collation of work for teaching job interviews.


 * Readings:** Read, at the very least, the Black and Wiliam article and come prepared to discuss and question assessment. It's a big deal in teaching and something that keeps on coming up as a challenge for new teachers, so please come prepared with thoughts and questions!

Until next week, .... Adrian