I recently listened to The Math Pod recording with Cathy Fosnot and Stephen Hurley from VoiceEd Radio.
This podcast really helped me to think about the different lenses that we use to teach math. This is where my thinking went.
This caused me to connect with ‘lenses’ I have heard, particularly out in the media, include thinking about math as needing to be ‘back to the basics’. I personally assume that this lens implies that math is a ‘pure’ subject. A subject with right and wrong answers, set algorithms that need to be memorized and strategies that are inflexible and rigid.
I also think about the ‘lens’ that I have traditionally used, that includes a) figuring out what needs to be covered in the curriculum; b) finding out where the students are at; c) developing a rich task that allows to enter from their own developmental level; d) providing opportunities for students to build rich math talk and increase the discourse; e) share strategies and learn from one another, assess, consolidate and so on.
But where do you go from there?
This podcast was very enlightening because it was a strong reminder that we need to sequence multiple rich tasks to allow for the progressive development of math strategies and conceptual understanding, along important pathways of learning.
It also gave me great pause to think about the significance of ‘context’, and the importance of designing the sequence of rich tasks within meaningful contexts. This blew my mind, because I realised that I was focused on context as a day-to-day construct, not as embedded within sequences of tasks. Providing a meaningful contexts in this sense, helps students to not get lost in the abstraction- a very common occurrence for students still operating at more concrete levels. Context also enables multiple pathways of growth toward becoming efficiency.
I have realised that it is not about finding the perfect problem, or designing that great problem to be solved. It is about crafting a sequence of problems where students are able to access key strategies, but also able to invent their own strategies – within important contexts that reach across and between problems.
Rather than thinking about this through the lens of moving students along a linear path from the concrete to the abstract, with contexts that change daily, we can use sequencing to enabling multiple paths that foster deep understanding about patterns, relationships and properties about numbers.
Therefore, I would have to say that using a ‘lens’ of looking at math as a pure subject, would also be to assume that students do not need context, and only learn along linear paths from concrete to abstract. But we know that students do not learn along a linear path, using the same strategies, and we know that context, if harnessed effectively, can produce very meaningful math learning.
I also think that the deepening understandings that emerge from this sequencing and contexts will lead to greater memorization of basic facts as well, for those of us who do see the importance of freeing up that working memory to do more complex tasks. This understanding is what helps to build more efficient mathematicians.
When it comes to math, there are no easy ways out. The reasoning, skills, procedures, concepts, strategies are all challenging! Does this mean that it is too hard to learn? Never. In fact, I think that it is perhaps the most important things to learn as it helps with thinking in all other areas of life. If we can really get at the heart of helping students to become more efficient in math, then we will have students that can understand relationships, patterns, and ways to figure out what we don’t know in many contexts within our lives.
As for my next step, I am going to really delve in to looking at how to find sequences of rich tasks, and supporting contexts that incorporate Indigenous perspectives.
I will also strive to understand student development and how to help them to become more efficient and develop deeper strategies. This is important to use as a lens for future math work, and moving beyond the lens of ‘this is what I need to cover in the unit, this is where my students are at, and this is the problem they need today’.
What is your next step?