Differentiating in Math

A few years ago, when I started teaching fourth grade, our school's "policy" was that students who scored __% (it varied) on the beginning-of-year math assessments (which also varied), and were deemed "strong in math" by previous teachers, were moved up to the next grade level for math.  The third, fourth, and fifth grade teams had to align our schedules so that math happened at the same time in all classes, so that students could go to which ever math class they were assigned to without missing other subject-areas.  In a lot of ways, this worked for our school -- the kiddos who were moved to the grade-level above felt good about themselves, their families felt good about the "challenging" math instruction their kiddos would receive, and at least some teachers felt good about having all of the students in their math class working on the same grade-level standards. This method of "differentiation" was also pretty easy; we made the decision at the beginning of the year about who was in which math class, and it basically stayed the same all year.

However, it wasn't a perfect system. Other trends started to emerge. Within math classes, the range of abilities was still quite wide, but it was now students working well below their own grade-level mixed with younger students working one or two grade-levels above. The kiddos who were "left back" in their own grade-level math classes started to say that they were "bad at math."  The younger students who were pushed forward consistently out performed the on-grade-level students, often dominating class discussions, but also sticking to themselves during partner or group work.  Families of children who were not pushed forward but felt that they should have been complained that their kids were bored and/or not challenged, which sometimes came to a head when a student would be moved mid-year; although this also led to more questions about what qualified a student to move up and how and when.

Last year, when our school fully departmentalized fourth and fifth grade (and got a new principal), we decided to move away from this system.  We justified the shift for a variety of reasons, including that we had a new curriculum, which was more rigorous than our previous curriculum, and that there was new a district-wide focus on mathematical discourse, which we felt required students to engage with peers at a variety of levels.  We also felt that this change would help us address the culture around math that had developed in our school -- with kids thinking they were "bad" at math if they were working on grade-level.

To ease the shift, we also put in place a few opportunities for students to continue working in more homogeneous math groups within and outside of the math classroom. I held "lunch bunches" with the students who were essentially repeating fourth-grade math to set individual goals and reflect about their math growth. Another teacher pushed into my room two or three times per week to pull a small group of these "high kids" to work on challenge problems. Once a month we held "math seminars" where we split the kids across fourth and fifth grade to work on more critical-thinking problems at different levels.

I learned a lot from these experiences! It turned out (not actually surprisingly) that some students who were good at mathematical computation, and even interpreting basic word problems, really, really struggled with open-ended questions. Other students who had weaker computation skills, were very strong in reasoning. And many students struggled with communicating precisely about their mathematical thinking.  As a result, I introduced more problems that required reasoning, practiced math vocabulary to improve discussions, and looked for more ways to have students demonstrate their understanding about concepts.

Even as I'm typing this, it's hard for me to believe this was all just last year!  Thinking back about all of the questions and challenges we faced last year, I'm realizing how quickly some of the issues resolved themselves, while others we've still barely addressed.  I've come a long way in my own way of thinking about and planning for math instruction and differentiation. This year, I have a completely different group of kiddos, with different strengths and areas of need which has led me in different directions.  As I remember all the things I tried and learned last year, I'm realizing that some practices have already become second nature and many more are still very much a work in progress.

More on this soon 😉

Me by the Numbers

Of course, at the beginning of each year we always start with those obligatory "getting to know you" activities. Now that we are departmentalized, I wanted to do those general "meeting and greeting" activities with my homeroom, but I also wanted to do some more math-specific activities with each of my three math classes.  We did not rotate classes for the first two days of school so that we could have a little more time to bond with our new homerooms, and then on day three we did a "practice rotation" with slightly shorter periods and extra time for reviewing expectations. Our math activity on this day was something I called "Me by the Numbers."

This activity was particularly important for this year because, for the first time in a few years, I had never taught any of my students before.  Because I've moved grades a few times, I've had quite a few classes where I've actually already taught at least half of my kiddos. Even when I hadn't taught a particular kiddos, I had known all of the students in the grade reasonably well and could often remember anecdotes or details about them from their previous teachers. This year, though, I had never taught this cohort -- I'd moved to fourth grade by the time they were in first.

The connections I build with my students and their families is one of the things I value most, and it's a huge contributor to my classroom management approach.  So this year I was really nervous about how I would connect and bond with so many (58!) new kids and families. Granted, I'm still at the same school, so there were a few kiddos in this crew who I had known as babies when I taught their older brothers or sisters, but for the most part, we were all new to each other.

As it turned out, I had no reason to worry because these kiddos are such loves! They wanted to know everything about me as much as I wanted to know everything about them. I shared my own "Me by the Numbers" and added in some stories about my pets, where I went to school, and how long I'd been teaching. They were so into it!

Then, while the kiddos were working, I got to walk around, ask questions, make connections, and learn more about each them -- how many siblings do you have? what are your hobbies? how long have you lived in the neighborhood?  Instead of sending these home after we completed them, I held onto them so I could refer back to them during the first few week as I tried to put names and faces with personal details. I've found it really helps to know who likes sports, who loves to travel, who has pets, and who is an only child.  I don't necessarily use these facts all the time, but when I want to write a meaningful word problem or share a great book, I know who I can turn to!

 

Learning for Pleasure

For years, the debate about reading homework -- “daily reading logs” versus “weekly reading responses” versus “reading for pleasure" -- has raged among educators and parents. Each side has its own strong arguments and the truth is there is no right or wrong, so I won't even attempt to join the fight. However, I've recently been thinking about how our discussions about homework in other subjects differ from the reading conversation.

It is not uncommon for schools to assign 20-30 minutes of nightly reading, in addition to the standard "10 minutes of homework per grade." Even schools that don't assign "any" homework often still require some type of reading outside of the classroom. What message does this send to kids and families?

Math homework is easily as debatable as reading homework -- from “assign only review” to “provide immediate practice of the day's objective” -- yet I've never heard "math for pleasure” thrown into the mix.  In my experience, most writing homework is given a specific assignment, like writing a book report, biography, or research paper. And I've definitely never seen "nightly science, in addition to..." on any homework sheet. Why is this? What does it say about the purpose of homework?

Essentially we've created a narrative that reading doesn't count as homework, because reading is more important than the other subjects. Students should read for the sake of reading, to improve as readers, and to be more successful in their lives. Teachers, myself included, pass around infographics (like this one) about how far behind a student can fall if they "miss" those 20 minutes per night, but there are no infographics about the importance of getting 20 minutes of math per night. While I'm certainly not arguing that reading isn't important, it also isn't the only thing that's important.  

It's possible that the emphasis on reading started because as a society, we have traditionally accepted that some people are "just not math people" and "some people can't write."  Of course, as growth mindset work has taught us, there’s no such thing as a "math person" and anyone can learn to write. So I’ve been thinking... how we could apply the same line of thinking to math homework, writing homework, even social studies and science homework, that we're comfortable applying to reading.  

Math for pleasure -- whether logic puzzles, critical thinking tasks, or math games -- would be just as valuable for our students as reading for pleasure.  Writing, too, could be assigned with the same open-ended direction that we provide for reading.  Students could write fiction stories, poetry, editorials in response to topics they care about, or simply journal about what's going in their lives. What if we asked parents to check that their children had successfully "learned for 30 minutes" each night before they sign their agendas?

Obviously any homework debate will eventually come down to accountability, but here I think we can also continue the same logic we've used about reading homework for years. Teachers know some kids won't do the homework at all, some will say they did even if they didn't, and some will get too much parental support, but most of us assign homework anyway.  We know that if we let the pendulum swing too far to the “never assign homework” side then we risk sending the message that the academic work is not that important. Likewise, if we swing all the way to the other side, we risk sending a message that school work is only to please a teacher or earn a grade - which isn't right either.

What we really want is students who see that the things they learn in school don't exist only inside the four walls of their classroom, who recognize that learning, even learning for learning's sake, can be enjoyable, and who pursue their interests with passion and determination.  Listening to most homework debates, you would assume that homework will always stand in opposition to these goals, but could it be that rethinking homework could actually get us closer?  I think it's possible.