Math Thinking. Math Talking.

 We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.

Maria Mitchell

https://www.themarginalian.org/2013/08/01/maria-mitchell-diaries/

I am currently taking my Primary/Junior Math Specialist AQ this spring. There has been a subsidy available for years to take Math AQs and I was on the path to finish this specialist 5 years ago when I moved into the library role but of course then my focus shifted and I finished the two AQs I need for my teacher-librarian specialist. Last year I did Teaching First Nations. Metis and Inuit Children through ETFO with a colleague and it was a great learning experience. I am glad to be back studying math and pedagogy together though, it's definitely one my my favourite things about being back in the classroom. 

For a recent prompt we were asked to read this article and respond with our ideas by analyzing the teacher's work in the classroom and using the framework: 

What? 

So What? 

Now What?

My response to the prompt was the following:

One teaching decision that the teacher made that stood out for me was choosing Aniyah’s to present, calling on students to interact and question the presentation and knowing/deciding when to interact with the student’s discussion and line of questioning regarding the fractional representation on a number line. On page 15 of the text it states, “Teaching does not cause learning.” and that really was an “aha” moment in the reading for me as I connected it back to my previous reading of Trevor Mackenzie’s book Inquiry Mindset. This book really helped me to structure how I viewed teaching/learning and a lot of the ideas are echoed through this reading and the pedagogical decisions made by the teacher throughout the short but impactful discussion of fractions

This sketchnote that is from Trevor Mackenzie’s website outlines some of the ideas from the book and I can see that the teacher’s knowledge of effective pedagogical practices is connected to numbers 2, 4, 7, 8 and 9. I also think that her specialized knowledge of math content played a big role in this routine as she would have needed to pose a question related to both fractions and number lines that goes well beyond memorizing facts and quickly assessing which students would be able to use their representations to ask probing questions of Aniyah in order to go beyond the “agreement/disagreement” of her presentation of her math thinking.

As I have been out of the traditional classroom for the last 5 years I have interacted with students as much in their math learning so while this article didn’t change anything about what I think about teaching, it did highlight for me the importance of viewing the teaching and learning of math from an inquiry stance. I noticed in the example that has the teacher had the students listening and questioning the mathematical representation shared by Aniyah she ensured that they were using probing questions to not only support Aniyah in sharing her thinking but to provide an opportunity for other students to hear and see math concepts being discussed in a broad sense beyond the idea of “right/wrong” which would effectively shut down the learning of any students who didn’t have the same response. I think the choice in students to present demonstrates the teacher’s knowledge of her students and I would be interested to know the timing of this interaction during the school year as choosing students to share and present this type of prompt would be different at the start of the school year to now (Spring) and even then there might be students who are never ready for this kind of focused attention from the class.

This important is important because the discussion provides time and space for students to check in with their own thinking about how they represented the problem, they see each other as co-learners within the math classroom and that the teacher is not centred as the “lead “ of the learning. I especially liked how she structured the discussion as not a time for “agreeing or disagreeing” but consider, reiterate and think about the math ideas being explored. 

I am very interested to see how I might look back at my reading and learning from Inquiry Mindset and from this new information in order to  influence my classroom practice with our weekly routine involving math talks and problem solving. We often explore numberless word problems or visual representations of problems in order to think creatively about the math ideas we are exploring. This is an example of a Which One Doesn’t Belong? (WODB) that we did recently.

We usually chat together in their small table groups and then students share out what they discussed. I wonder how the thinking would change if I followed the same routine of thinking and writing independently and then 1-2 students sharing and answering questions as outlined in the reading? Would it work for this kind of math talk prompt or would a different problem be needed?

Ball, D. L. (1970, January 1). Uncovering the Special Mathematical Work of Teaching. SpringerLink. Retrieved April 22, 2023, from https://link.springer.com/chapter/10.1007/978-3-319-62597-3_2 

MacKenzie, T., & Bathurst-Hunt, R. (2019). Inquiry mindset: Nurturing the dreams, wonders, and curiosities of our youngest learners. Elevate Books Edu.

*****

Whenever I learn something new I want to try it right away in my own practice. I decided to find a few math talk prompts that I was already planning to use and to integrate the discussion protocol outlined by the teacher in the article. The students were asked to write down their thinking and ideas using any format and combination of number, pictures or words they wanted. They then shared with their elbow partner at their desk. First the first prompt I had a few students come up and share how they saw and counted the dice and we stuck to the same "questions only" protocol for the discussion.

As I circulated through the room I noticed that most of the students immediately started to count the dots on the dice and only a few counted the dice themselves. I decided to have those students present their thinking and asnwer questions as it might prompt students to see the picture in a new way. I was happy to see how many students were using our learning about multiplication and grouping to organize their thinking on the page. 

For this prompt the students only saw the first group of dice and then they recorded their thoughts. Then we saw the second group, recorded ideas and finally the third. 

For this prompt we first looked at the image of the bags and discussed with our partners what we know/wonder about the problem. Students then worked independently to solve and we discussed as a class. Again, I was happy to see how many students were working with multiplication and equal groups having moved their thinking past a 1:1 counting.

Both of these prompts were explored on the same day in our math class.

The next day we explored this #unitchat

from Math for Love.

And they WOWED me!!

I posted this picture with the questions "How many?" and "How do you see them?". I had planned to ask them to consider fractions after we had discussed our first ideas but one of my students came right out with the fractions.  You can see from my list om the right that I tried to track the different strands within math that we were exploring as students shared their thoughts. I modeled the question asking this time as each student presented how they saw the #unitchat and how they counted or labelled their ideas.

I am excited to explore this thinking routine more often in math (and possibly other subjects) as we explore more #unitchats and other number talks. 

I'm also curious about how I can bring more inquiry mindset into our math class. 

How might we incorporate student's natural questions and ideas about math? 

How might this help my students develop a deeper understanding of math and connections between ideas/concepts?

To All The Things I Should Have Done...

 But I Didn't Do. 

Has there ever been a time when being an educator hasn't been a constant struggle of feeling like you aren't doing enough? 

This is a question that has been on my mind for quite a while. I promise you that I am okay. I know that people who are kind and caring will wonder if I am burned out or overwhelmed and I promise that I am not either of those things. But I still question whether or not I am ever doing enough. 

Enough at work. Enough in my volunteer endeavors. Enough advocacy. Enough reading. Enough professional development. Enough at home with my kids. Enough rest. Enough exercise. 

Enough. Enough. Enough. 

The hustle and grind culture of our society is a lot. Seriously. Every time I see someone posting about a webinar they are in, or a book they are reading or time they are spending with their kids and family I wonder if I should be doing those things. Have I picked the right activities to spend my time on? Have I prioritized the right things? Will I wish I picked something different? Am I teaching my daughters about rest and rejuvenation or am I modelling a constant hustle to the next thing? 

With all of this in mind, I have been working to be very intentional about the activities I am choosing to engage in throughout my day, both at home and at work. If I am feeling the pressure to do something based on outside forces I have really worked to pause and consider if I want to do it for me or do I want to do it because it feels like "I should".  What factors influence me in how I use my time and what I pursue?

This has meant for the last few months I haven't done a lot of things. If I felt like I needed silence or quieter time after a busy and noisy day at school then I haven't joined in with EduKnitNight and connected with my friends. Instead, I've snuggled on the couch with my kids and a movie or a book. Or binged a mindless show on Netflix. If we made weekend plans to ski then I haven't brought any schoolwork home. If my kids have an evening activity and takeout is easier than I haven't cooked. 

At school, I haven't pushed through "covering" curriculum. We read together. We write together. We explore math and science and art and social studies. But we also play. A lot. My Grade 3s have become experts in Free Choice activities. They explore all the materials in our class every day, multiple times a day. During our 20-minute Soft Start, at the end of most learning periods, at the end of day. This gives me time to work with individual students on their specific learning needs, to observe their social interactions and support social development, to assess new skills one on one through discussion and observation. I can prompt their learning and listen to their ideas instead of relying on written assessments. 

Have we done a "spelling pattern/list" each week? Nope. Do my students write in their journals each week? Nope. Do we read a new picture book every day? Nope. 

The learning we do is very rich though. We talk about spelling patterns, we talk about making connections to our reading, and we are starting to explore writing paragraphs. The growth in my students from September to now is astounding. They have worked! I see my students gaining confidence as readers, writers, and problem solvers. I see them understand the need to care for our classroom space as a communal space. I see them connecting to learning from earlier in the year. I see them seeking out new passions and friendships. 

I have heard Liz Kleinrock speak on a number of occasions and the idea of "rest as resistance" really resonated with me. So as I think back on all the things I "should have done" over the last few weeks and months that I didn't do - I am not sad, upset, or concerned. I centered myself and my family when at home. I centered my students and their needs when at school. The learning is still happening- my professional learning, my students' learning at school, my daughters' learning of the value of their time at home, and my own understanding of rest. 

It's just happening at a slower, more human pace. My pace. My students' pace. 

And we like it. 

Routine. Familiar. Customary. Methodical.

 

https://organisemyhouse.com/inspirational-daily-routine-quotes/

Routines. I am sure this will not come as a surprise to anyone who knows me that I thrive on routines. I like the planning of them. I like the predictability of them. I like to familiarity of them. And I have noticed that many students also really seem to crave routines. 

I was asked recently about how I plan for math in my classroom as a colleague is going to for an interview with a new board. This educator has been working as an occasional teacher and hasn't had to plan a math program for their own classroom. It was great timing as I had been thinking about my math routine as I am working to layer in new pieces and to solidify our literacy routine (which is proving to be a harder task). 

I like to have a weekly routine for math which includes the daily Minds On. Years ago I worked with a group of educators at my school and then in a wider community within out family of schools looking at spiralling the math curriculum and it really helped to cement my belief in how I think math should be taught to ensure "sticky learning".

This TedTalk was the spark for our work and it's a must see!

As I plan for my math program, I am always working on spiralling through the curriculum and constantly re-touching a variety of topics. I am currently using the SCDSB's Scope and Sequence to plan the major components while looking at ways to spiral back.

• For our Minds On on Mondays we do a “Which One Doesn’t Belong” that helps support their ability to communicate their thinking using math vocabulary.

• Tuesday and Thursday we do an activity called “Roll and Write” which involves a differentiated menu that works on their math fluency with adding and multiplication. They work through at their own pace.

• Wednesdays are Number Talks

• Fridays are Esti-Mysteries from Steve Wybourney’s blog.

Each morning the students do a Poll of the Day (which will eventually lead into our data management learning) and a few times a week we do a morning math meeting which a gives me time to do small mini lessons on different topics.

Right now we are focusing on adding and subtracting tens patterns and doubles. I will change out the topics as we spiral through the curriculum. Starting this week we will be adding in multiplication, identifying repeating and growing patterns, and skip counting.

After two or so months of following these routines I think we are ready to start layering in Math Journals so students can start to communicate their math knowledge in various ways. We started with this modeled example and discussed how it showed our thinking by using math vocabulary, numbers, operations, pictures and how we organized our response.

I then discussed our Math Journal success criteria and we read through our first problem, which was about place value, 2-digit and 3-digit numbers. I haven't yet assessed their journals to see how they did (it's on Monday's To-Do list!) and then we will decide our next steps.

If you've made it this far in my blog, I bet you are thinking that I must have a really good handle on my Literacy Routine... and you would be wrong. This year, like many others, I feel like I am constantly assessing, reacting and working to plan to meet students where they are on their reading and writing journey. Unlike other years, I am also on my own learning journey connected to the Science of Reading, phonics, orthographic mapping, fluency, and more. I am also finding that my students needs range from working on developing their knowledge of letter sounds, decoding CVC words and those with digraphs and blends, to reading full chapter books in the course of an evening. Many of my students are working on proper letter formation and need support with sentence stems and/or scribing to write simple sentences. I also have students who are ready to explore paragraphs. It's the largest range of developmental steps I have seen in  a Grade 3 classroom. 

I had a conversation about this with my admin as we approached writing progress reports. I wondered how to deal with the "progressing well" vs "progressing with difficulty" options. (And why there isn't a "progressing" option available?) In year's past I would have assessed many of my students as "progressing with difficulty" based on what I was seeing in my my class in terms of decoding and writing. However, this year it's a full third to half my class. So in the ongoing discussion of "learning gaps" due to the pandemic, maybe they aren't "behind" maybe this is just what Grade 3 is right now (and for the next little bit)? 

And they are "progressing". We are at the point now where most of  my students have mastered all their letters sounds, can decode CVC words and are working to understand CVCe words. Our spelling is aligned with our reading work and I can see students working to segment letter sounds as they write. We are progressing, dare I say we are progressing well?

So back to my literacy routine. It's been haphazard at best. The components are there. We are reading. We are writing. We are spelling. We look at grammar. We've talked about the elements of a story. We read out loud. We are working on answering comprehension questions together. 

But is it a routine?

Nope. 

I am hoping to start a routine that follows a two-week cycle so that we can work through all the different types of literacy tasks and components. I want to start working with smaller groups of students and think that by adopting a two week cycle for our routine I'll be able to organize the materials and activities for this. It must also be said that the students have not quite demonstrated that they are fully ready for this (it's been an ongoing goal) so it will be a joint effort as we adopt this new routine and work on our ability to complete task independently.

I do think that a routine for our literacy work is necessary and needed. I have noticed that students are excited and ready for learning in math when they know which Minds On we are going to explore each day. They express which activities they enjoy the most and look forward to participating. The next 10 or so days will provide more information as to what activities work on which days and in which order. We will also be layering in our Writer's Workshop as students are demonstrating that they are ready to explore some free choice in writing and writing forms. Maybe this iteration of our routine will hit the mark. Maybe it won't. 

Thankfully, we have time to keep working on it. 

After all, the curriculum expectations are end of year goals, are they not?

Stay tuned.