math

On our way…

This week we accomplished a lot in our math class.  I mean, not much of it had to do with curriculum and I am sure none of it will end up on progress reports (I’ve received two reminders that those aren’t going away!) but it was a great week anyway.

The highlight of my week came on Monday. I have three students who were with me last year has grade 2s and they are repeating with me again this year as grade 3s. On Monday I had occasion to describe a picture as “one one-fourth” of something. One of them said, “Hey. Wait.” then he muttered “one one-fourth” a few times and said, “I had no idea that’s what one-fourth means. It means one out of four of something. One-fourth…get it? One out of four. I never knew that before.” I taught a lot of fractions last year. I thought I did a pretty good job. But for some reason this understanding clicked for him in that moment. I was immediately reminded of something Christine Tondevold says:  Number sense can’t be taught, it’s caught!  In other words, as she explains in this blog post, kids need experiences with numbers in order to understand them. I know that this “discovery” comes after a lot of teaching, but he didn’t really get it until that exact experience. 

The other thing I am feeling good about is the formative assessment I accomplished. I don’t think I wrote a single thing down, but I know a lot about my mathematicians already. I had everyone working in their math notebook and noticed how they print numbers and organize their thinking. I had everyone counting objects – some they could touch while counting and some that were on the board so they were encouraged to use other strategies.  We did a three-act math task every day I was able to start to establish our routine for Number Talks. Finally, we spent three days working on a math card game (a game like memory, but a match is two numbers that add up to 10.)

This is what I know we need to work on:

*Grouping objects to count them (sort of a surprise)

*Mathematical thinking (not a surprise)

*Organizing and communicating our math thinking (not a surprise)

*Working independently

That last one is going to be my biggest challenge. For a few years in a row, I have had a lot of kids in one grade and only a few in the other. This year I have nearly equal amounts. It’s a lot easier to have four kids working on an independent math task while I teach the other grade than it is asking 10 kids to be independent while I work with the other 10. I am determined not to make worksheets the independent activity every day, but I know that I will need to do that now and then. I do have 6 iPads and 2 laptops I can make into a workstation. It’s starting to sound like I am going to be doing Guided Math! I suppose that was bound to happen eventually. 

On the agenda for this week:

*Learn another card game that can be used as an independent activity

*Start some math work disguised as science work (measuring puddles as they evaporate throughout the day)

*Strengthen our Number Talk routines

*Photocopy math interviews so I can start them the week after

math, Measurement, Number Talks, Social Emotional Learning

Week 1: Done

This week we did many of the same activities I used last September for the first week of school. Namely we measured things that are a meter apart. Once again I was hoping that all I had to do to keep everyone a meter apart is show them how big a meter is. Don’t you love my optimism? Once again, we finished the week still needing practice.

As I sit here today working on my plans for the coming week I’m reflecting on how quickly everyone did fall back into some of the Number Talk routines that are common in my school. I typically have a class mostly inherited from one teacher, but this year it is a mixed group. I’m at a dual-track French/English school and I have more transfer students from French Immersion than I’ve ever had at once. I wasn’t sure how many of them may have used a “thumbs up” for Number Talks, or how many may have discontinued this during online school in the spring.

Last week we did a lot of counting for our Number Talks. I know I originally got this activity from Graham Fletchy, but I cannot find it! Basically I had a plastic cup (noisy) and I dropped small stones into it while making sure they could not see the objects falling. The class had to count as I dropped and then tell how many were in the cup based on what they heard. It’s a great activity that helped us talk about listening closely while also establishing our Number Talk routine. I’m definitely doing the “popping balloons” activity (from Graham Fletchy) this week, and few others I’ll report on next week. I didn’t expect to need to spend time on counting (grade 2 and 3!) but we need it anyway. Many students went right to rote counting and reciting and I want to make sure everyone remembers (and is able) to match a number to a “plunk” in the cup, or to an object they touch or see. I suspect we just need to get back into the groove of school, but one can never tell in September!

This week I will also be plopping everyone online for a few minutes. I want to make sure everyone can sign in and knows where to find our class page. I hope we don’t ever end up back online again, but I need to make sure everyone is ready…just in case!

For our regular lessons, we’ll do some more measuring. Looking at our class numbers I’m predicting some reorganization AND I want to stick with a gentle start to the year. Everyone in grade 2 seems to like measuring.

math

Back in the groove: Part 2

Well, that was a long gap! I stopped blogging last year because I had to cut some things off my “to do” list. I was taking two courses, I was teaching full time and parenting full time, and I was surviving a pandemic. Math blogging got the ax because I was working on a math writing project and I found I was tired of writing about math and didn’t want to reflect on it quite as closely as blogging forces me to do.

So here I am five sleeps away from another first day of school. I’m really glad I at least blogged about September 2020 because that’s helping me get started on planning September 2021. I already have the measuring activities in my day plans for next week. I don’t know if I will go from there to coding and dancing or to some of the patterning things I like to do with manipulatives. I am definitely doing some estimation jars. I need to meet my people before I can make set plans though.

Last year 15 of 19 students were in grade 3. That’s roughly 25%. This year 8 of 19 are in grade 2. That’s roughly 40%. It’s a game changer! I’ve had splits like this before and it’s very hard right now to predict how I am going to manage this. Stay tuned.

I’m not taking any courses this year. I am, however, working on a thesis. I’m predicting that blogging my math reflections will fit nicely with that. Math is not the focus of the thesis, but I am working a project about creativity in the classroom and math will definitely be part of it. In fact, I am now going to end this post so I am read about creativity as a mathematical process.

math, Number Sense & Numeration, Number Strings

Back in the groove

On Wednesday of this past week I realized I had gotten back into the groove of teaching math. I had been in it but fell out at some point. I knew I was not enjoying math and that I was feeling every day like I had missed the mark – the lesson was too easy, or it was too hard, or there were some interruptions that derailed us too easily. At some point I realized that there were so many different math strategies being used in the class that it was hard to have a conversation about our math. I decided that this week we would talk about all the strategies but we’d focus on making sure everyone could use a number line. We finished the Fosnot “Measuring for the Art Show” unit in about 3 days (should take more than that, and has typically taken me 10 days.) I decided to spend some time doing number strings and reinforcing the use of the number line to do it.

Here you can see we are using a lot of different strategies. Someone even suggested the traditional algorithm and several students knew how to use it. I’m crediting “at home learning” for that because this hasn’t happened in many years for me!

After two days of this, I asked everyone to complete three problems that I put on the board. They each have a whiteboard they were using to do this. “Do these three problems, and then you I want to take a photo of you and your work. Then you can clean up for lunch.” I thought that was good! But several of them were annoyed at ONLY being given 3 problems. I had to add more to the board. So, to recap, they wanted to do more math instead of get lunch.

I finally said, “Look, if you want to do this all day you could make up problems for each both er.” Then they spent the rest of the day making up problems for each other. A few of my friends weren’t sure what to do. I cancelled reading groups for two days to do math groups instead. By the end of that they knew how to add double digit numbers with the Base-10 Blocks and with the number line. We’ll get to the mental math eventually, but I needed to give them a few strategies to hang on to until then.

This week we’ll move on to another Fosnot unit called “Ages and Timelines” which has us focused more on subtraction, or rather “finding the difference” between two numbers. I feel like it will be a good fit for us.

I’m not sure if completing all of my math interviews would have helped. I still have a few to go (lots to go!) but what I already know about the class is that we are coming to the math from a variety of places. One of my small groups clearly knew what they were doing even though they had struggled with the first lesson and had given themselves a 😦 when I asked everyone to self assess. I asked them to explain.

Them: Well, I didn’t know this is what you meant.

Me: You don’t know I wanted you to add the numbers?

Them: No.

So, to recap, after two days of me saying “Add these numbers up.” They didn’t know what I meant. Like I said, we’re coming at this from a lit of different places. But I think we’ll mostly be in the same place, together, by the end of next week.

Geometry, math, Mathematical Processes, Patterning & Algebra, Social Emotional Learning, Spatial Sense

Month 1: Done

It feels like school just started. And yet, September is nearly over. In fact, it ends this week. We are headed into our fourth week of school. At this point I would usually know if my class was going to be reorganized due to school enrolment, but it’s all still being organized. I’ve decided not to worry about it and carry on.

This year I am using a curriculum planning guide I created last year and updated over the summer to reflect the new curriculum. Of course, the Ministry has also released some suggested long-range plans of their own. (Found here.) I was really intentional about where I put things on my own calendar, and I liked the sequencing I was using last year. In addition, I like how it was spiralled and we came back to every concept at least once over the course of the year. When school closed in March, I had already covered everything at least once – even probability! I am inclined to stick with my own plan. However, I am also going to consult with the Ministry suggested timeline just to see how that team has set it all up.

Last week my class spent some time on patterns. We made patterns with manipulatives, and we made patterns with numbers on the 120 chart. It was fun! I was initially worried about using manipulatives, but have decided the hassle is worth it. I spent time every afternoon washing manipulatives in hot water and soap so we could use them again the next day. I bought some colanders at the dollar store to help with the draining and drying. It’s working out okay.

I feel like there were one hundred different things going on, but the fast pace and changes from one thing to another seemed to be what we needed so I went with it. We have been doing some dancing for our Daily Physical Activity (DPA) and several of the dances we used were patterned repeating dances. In coding this is called a loop, so that is what I have been calling them. This is our favourite:

By the end of the week we had met all the goals on our success criteria:

*making repeating, growing and shrinking patterns with math tools, numbers and our bodies.

*explaining our patterns to others. (a math process skill)

*being creative in math. (another math process skill)

*persevering through the hard parts. (This is one of the social emotional learning goals in the new math curriculum.)

So what’s next? According to the Ministry long range plan, the one organized by guiding questions) I should be doing some data management about the class. We should be gathering info about our height, our siblings, etc. and graphing it. They also have movement words this month. I’m still not feeling 100% certain about reorganization, so I think I’ll put that off for a week.

On my plan, I have some work with 2D and 3D shapes. We need to be describing them by their attributes at this point (we’ll work on them more in depth later.) I am going to stick with this, and add the movement expectations (E 1.4 relative location, and E1.5 directions for movement). These fit with the work we have been doing already. I also have the robots on loan from the resource centre, so I am going to want to use those. I have a fun lesson plan from the math project I’m involved in and I need to try it out. This is why I borrowed the robots actually. So this week we’re going to work on movement and we are going to work on following patterns on the 120 chart with the help of our robots. And I am now going to spend some time today figuring out how to make a giant 120 chart since my hundred carpet is now banished to the attic until the pandemic is over. I’m tempted to start number line work simply because a long number line is going be easier to create on the floor than a hundred chart.

math, Problem Solving, Spatial Sense

Stay apart

I started my school year with three students. We had a staggered entry and my two grades straddled the split between who started Wednesday and who started Thursday.

I was thinking a lot about physical distancing. Kids don’t really know how long a metre is – they really truly don’t! A metre, a mile, a moose – these units of measure are things they are still trying to figure out. In addition, they are busy figuring out where they exist in space. They aren’t all really sure where they end and someone else begins.

I decided to start off by asking them how big a meter is. I wanted them to have a frame of reference and a benchmark for how far apart they should be from one another.

We watched a video about the importance of staying 1 metre apart from each other. I said to the three, “Do you know what a meter is?” They did not. Makes sense since they are in grade 2. I asked, “Can you find some things that are as long as this meter stick? Some things that are 1 meter long?”

We then spent an hour measuring stuff in the room and in the hall and then we had to go outside for another thirty minutes of measuring because my three friends were obsessed with holding the metre stick up to things and asking, “Does this count?” Sort of like when we were driving across Ontario in August and my own children were obsessed with asking, “How much longer?”

Some really cool things happened during this time. We found out that you can stand at certain spots beside our tables and be a metre apart, but if you stand at other parts you are not a metre apart. We discovered that three floor tiles are equal to 1 metre. This was true for the white tiles in our classroom, the white tiles in the hallway, and the blue and yellow tiles in the hallway. We discovered that 2 1/2 bricks on the hall wall are 1 meter long. And the ladder on the play structure is less than a meter. So is the storm drain.

I spent a lot of time asking them if they were a meter apart and they had to use these benchmarks to figure it out.

The rest of the class joined us the next day and I couldn’t take 20 kids out to measure stuff in the hall so we used the photos from the day before. They had to basically memorize the two benchmarks we focused on and they were sort of good at it. They were very good during the lesson! They were less good at doing this in the wild. They even had trouble with the “Superhero arms” measure of distance. They are kids after all.

So I’m plotting my next step now. In the new curriculum both grades need to do some work with centimetres and meters. (E2.2) For now I am going to be content with helping them develop a feel for how long a metre is. We have moved into doing some work with figuring out how to use manipulatives, especially now when sharing has become complicated.

Executive Skills, math, Patterning & Algebra, Problem Solving

Calendar

I’d normally have the first week all organized by now.  I’ve been going through my notes (mental and written down) as I try to plan out what my first week of school will be like.  There are quite a few of my old tricks that won’t work this year because of “you know, social distancing” as my son likes to say.  And, truth be told, I could still get a big assignment change so I am not putting too much effort into getting excited about exact plans. But there are certain things that can happen no matter what my assignment turns out to be and no matter who will be in my class.

Last year, I added a new calendar routine to my class and I really liked how it all unfolded.  I had the whole year on the board at once, and I loved how the students used it to count “how many days until” things would happen.  I’m not usually one for celebrating birthdays in class, so I wasn’t expecting them to do their favourite thing:  add their special day to the calendar.  We added the holidays together as the approached and talked about how some holidays are always on the same day (Feb 14 = Valentine’s Day) but others float around according to the cycles of the moon (Passover). This is a grade 2 social studies expectation and I liked how that became part of an ongoing conversation in our room.

This year I have decided to do it a bit differently.  Instead of printing a complete calendar, I found some blank calendar pages here.   I am going to fill out September (maybe only the first 2 weeks?) and then get kids to help fill out the rest.  I made a poster to post beside the calendar:

Screen Shot 2020-08-30 at 7.10.34 PM
You can have a copy

I want the students to fill in the dates on their own because there are so many patterns to the counting on calendars.  If they are filling out the dates themselves I think it will help them see the patterns. During the first week, maybe in the second week, we are going to work on this together.  I still haven’t sorted out all the details though because, “you know, social distancing!” is going to effect this for sure. Maybe the students can have their own mini version to work on at their desks.  (I keep reminding myself that some kids are going to really love working alone at their desks!)

I’m going to keep this at the front of the room because we referred to it so often!  I want it up close.  I know things will be different now because we can’t have any carpet time, but we didn’t really use it for that anyway. It was just an ongoing topic of conversation all year. Kids like to know when things will happen. This helped with that. I’ve been reading a bit of executive function skills and some of these are the ability to organize, to be able to plan things, and of course manage time. I know that I personally need a calendar or day book for this, and I really do much better if I have written it down.  My phone calendar is great for reminders, but I still need to physically use a pen and paper to write it down before a scheduled activity is in my brain. I need to know when something is due and then I need to write out a plan for how to do that slowly over the course of a week or more.  I need specific small deadlines (because one of my executive functioning strengths is that I am goal oriented) to keep my on track. The wall calendar seemed to provide support in all of these areas for the kids in my class last year, and I suspect it will help this year as well. 

So…20 minutes of each day of the first week…sorted!

math

Math Project

So i’m working on this math project which I don’t really want to write about just yet…but I will at some point!

At a meeting last week and another today there was some information shared about how the new Ontario math curriculum came to be. It was fascinating to me to learn about the research that went into figuring out what to put in, what to move here and there, what to eliminate.  I know a lot of people have lamented the fact that “teachers have not been consulted!”  But I’m learning just how many teachers were consulted and how many educators were deeply involved in this process.  I think some people are under the impression that the actual Minister of Education has whipped up a few documents in his basement one night and, um, well…he didn’t.  Here is a video about the process.

The research that was done before the curriculum was written involved looking at curriculum documents from around the world, analyzing their content, their organization and research about the implementation of that curriculum.  The research around how children learn math and what and when they should learn it was also considered.

I know a lot of teachers are feeling a lot of trepidation about this new curriculum.  I think the timing of it’s release and implementation is the main complaint.  I agree – it’s a weird time for us all to figure out how to do something new that could wait.  We’ll be consumed by figuring out how to do new things, like keeping our students physically distant and/or teaching online, that can’t wait. It will be tricky and stressful to also figure out a new curriculum, which does have some significant changes from the old one. It’s overwhelming to think about it all!  But I get excited about math things so I’m not feeling that, which is probably why I comfortably signed up to be part of a huge math project on top of my Master’s courses and full time teaching and full time parenting.

math, Number Sense & Numeration, Problem Solving

Baking

Are you still baking bread? At the beginning of the world-wide shutdown, everyone was baking bread and cookies and their own pizza. We are still doing this – we were doing this before. We’ve slowed down a bit because it’s been too hot to turn the oven on. But yesterday I made some bread and today my daughter is baking cookies.

She wants to do this all by herself. I have a recipe that’s meant to be easy for children to follow, and she has a lot of kitchen experience for a 9-year-old. She’s only needed help so far with the “1 slash 2 cup” of butter. We’ve talked about 1/2 dozens of times but it still eludes her. I showed her how to use the markings on the butter to figure out 1/2 of a cup. She then needed help with 1/2 cup of honey. Partway through pouring she realized she had the “1 slash 4” cup and thought it was going to be too much because she only needs “1 slash 2”. We’ve talked about this a bunch too, but in the moment she was confused again.  I coach her through it.  “1/4 is 1/2 of a 1/2.  So if you have 1/4, you have 1/2 of what you need.  So what do we need to do?”  She figures it out, I pour her another 1/4 cup of honey, and she’s back to working on her own.

I’ve been thinking a lot about baking and the learning that goes along with it. Little of it actually shows up in our curriculum. There’s problem solving, some collaboration (her brother doesn’t like chocolate so this is always part of our conversation when making cookies), communication, following instructions and, of course, measurement and fractions. At home this type of learning is very important to me. I want my children to head off to university with the ability to cook more than Kraft dinner, grilled cheese and scrambled eggs. The curriculum connections are a bonus. At school I cook or bake with my class maybe twice in a school year (less if there are students with allergies or special dietary needs in the class.)  I learned to cook at my grandma’s house, at my parent’s house, in Home Economics classes, and in neighbourhood 4H clubs.

If I was in charge of the curriculum, I’m not sure what I would eliminate in order to make space for cooking in the elementary grades.  I’m not sure there is anything we should exchange for cooking time. Secondary students still have the option of doing catering courses so they can learn to cook. Mostly I feel like learning to cook is part of how we pass our family and cultural traditions and values down to our own children.  I know some parents don’t teach their children to cook, but maybe that needs to be up to them.  Maybe this is one thing the schools have let go of for good reason. If I cook with my class it’s because we have a connection to something we’ve read about, or it’s a snow day and we need to fill the time with a worthwhile but fun activity.  I don’t feel compelled to teach them life skills like cooking or sewing.

 

 

math, Math Workshop, Mathematical Processes, Problem Solving

NOMA Summer “Book” Club #1

Today we at the Northern Ontario Math Association (NOMA) had our first summer book club meeting.  Instead of reading a book together, we are finding resources on the Internet we can read for free – things we can get without having to wait for delivery!

Today we discussed a webinar found on TheLearningExchange called “Teaching Math Through a Social Justice Lens”.  I highly recommend this learning series. It is basically a problem-based math teaching approach. Students are using real-world numbers to think about real-world problems with a social justice focus.  In this exact case, the students were mostly focused on an inquiry that had them wondering about their shoes – where in the world do they come from, who makes them, how much are those people paid to make them, etc.

Preparing for this has had me thinking about some social justice issues I could cover in my primary class.  We study water in science, so it would be interesting to do something with water bottles – collect data on the number of bottles used in our school, how much we save by using refillable bottles, what is the environmental impact on not only using them but having them delivered to your local store, what is the financial impact on buying disposable water bottles…etc.   I definitely need to think more about possible topics, but I also want to make sure I am paying attention to what my students are interested in.

The great thing about a book club is that other people think of things that I don’t. In our conversation there were a few important things that were brought up.  Some of the issues might be upsetting to families who feel the teacher is trying to push their own political agenda.  Some issues might be upsetting to students (we talked about all the amazing data related to Covid-19, for example, which our students might not be ready to analyze in the next year…or more!) And we have to make sure we are still teaching math and not just doing these projects that use the math. We want them to have a certain sense of exploration and problem solving, but we also need to make sure they know how to do all the necessary calculations for their particular developmental needs and grade level.

One of the big hurdles for me in my own thinking and teaching has been how to come up with projects that have my students doing math, literacy, science, social studies across the day instead of each happening in their own separate, compartmentalized time block. I have this figured out with literacy, but math…I’m still working on it. As I watched this webinar I feel like I have a new understanding of how to create inquiry problems that students could work on all day and still hit all the topics.  Now, I do think I wouldn’t jump right into this in September (though maybe with the right problem I could…) and I definitely think I will need to still have a time set aside on most days when we are focused on learning to do calculations.  But I’m thinking of some social justice and global citizenship issues that could really take over the class (in a good way!) for a solid week.

I’m also still trying to wrap my head around having students part-time in school and part-time at home but still working and I think this integrated approach would be a good way to have them working at home on things besides worksheets.

I’m still thinking through all of this!  But the book club was a good way for me to consolidate some of my thinking…and it gave me more to think about!

 

Relevant article:

Caswell, B., Stewart Rose, L., & Doura, D. (2011). Teaching Mathematics With a Social Justice Focus. Inquiry into Practice: Reaching Every Student Through Inclusive Curriculum, 81–88. https://wordpress.oise.utoronto.ca/robertson/files/2017/03/Teaching-Mathematics-with-a-Social-Justice-Focus.pdf