Second Grade Math Wall

I visited a wonderful second grade classroom last week!

Number bond, words and a place value chart for the number 152.

In the classroom, students were working on adding two-digit numbers. Some examples follow:

Adding 34 + 5:

Adding 24 + 32 on a place value chart
(from p. 29 of the Primary Mathematics Standard Edition 2A Textbook):

Decomposing addends to tens and ones to add 24 + 32:

A little harder to see…this student didn’t need to decompose the 24 and 32 into tens and ones, she just grouped the ones and the tens:

Next up, subtraction problems. Maybe with less circling/grouping of tens and ones.


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Implementation challenges: It’s not necessarily the curriculum

Sometimes the strategies used in the Singapore Math materials look different. Number bonds, bar models, place value charts, arrays and area models can be unfamiliar to parents. Most schools adopting Primary Mathematics host Parent Nights to walk parents through the new materials, the program and to share why the school decided to switch from their old curriculum.

I’ve done dozens of these parent nights and common concerns run through the questions. After a presentation and Q & A parent session this week, a parent approached me about her son’s home enjoyment that afternoon.

“How am I expected to help my fourth grader?” she asked, “This Singapore Math is so different.”

She opened her son’s 4A workbook and showed me the problems she couldn’t help her son with:

Unfortunately for this parent, there’s nothing “Singaporean” about order of operations.

She couldn’t help her son because she didn’t remember elementary school math. In fact, she had never heard the term “Order of Operations”. I tried, “Please Excuse My Dear Aunt Sally,” something many adults were taught back in the day… Nope, that drew a blank as well.

After I explained what the order of operations is, I offered the parent two pieces of advice.

1. Include a note with her son’s home enjoyment, something along the lines of “We struggled with these problems.” The teacher needs to know this. Home enjoyment is practice for your student and provides feedback for their teacher. The teacher needs to know if the lesson taught that day at school could be completed individually by the student that night at home. If not, there was a breakdown somewhere.

This parent note tells the teacher a couple of things:

  • The student was able to complete the first two parts of the assignment that included problems with two operations, but couldn’t work the final exercise where the problems had three operations.
  • Something was lost between the teacher’s lesson and this student. Was he in the bathroom? Did the teacher’s lesson and guided practice not include three operations? Are there attention issues? Did the student just not “get it” and not ask questions? Many things could have created this disconnect. Was it a single student, or are there more that struggled?
  • This parent may not be able to help her son with 4th-grade math.

2. Pick up a copy of a book on elementary mathematics. One of my favorites is Arithmetic For Parents: A Book for Grownups about Children’s Mathematics.  In the foreword, the author includes insights from his time in an elementary classroom:

Elementary mathematics isn’t simple at all. It has depth and beauty.

The book is written for parents that want to be an active participant in their child’s studies, as well as the “reader who wishes to return to his childhood mathematics, from a different angle.”

Good math teaching is just good math teaching. While there are some differences in the strategies used in the Singapore books, teaching math so students understand the concepts as well as master the algorithm or rule is the goal.

Do you help your child with their home enjoyment? What happens when you are fuzzy on the concepts your child is learning?

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Sometimes it’s the littlest things that make a big difference

A friend of mine teaches kindergarten. She’s an amazing and engaging teacher. I was, literally, just hanging out in her classroom one day while she was teaching her math lesson. When I asked what concept she would be teaching, she replied “lesson 1.8 from the KA book” – yep she’s that organized.

After the lesson, she asked me for two yeahs and two hmmms from her lesson. When I observe teachers, I try to focus more on the students’ understanding during a lesson and how that relates to what the teacher was doing. Put on the spot then, I mentioned that sometimes she spoke too quietly. I think the students missed some of the discussion. Right away, I knew that was a lame thing to say. When I do teacher observations, I typically take time reflect before sharing my thoughts. So the next day I went back with better insight.

Her lesson had been strong. There was a focus on the key concept of sorting objects into groups, manipulatives were used (stuffed animals and school supplies), there were opportunities for extension. Overall, it was a well-planned lesson. And yet, the students weren’t as engaged as I would have expected. I typically use the 5 Whys technique to get me quickly to the root of a problem. As I reflected on the lesson, my internal dialogue was:

  1. I noticed that the teacher sometimes speaks too quietly for the kids to hear her. Why?
  2. Well, actually, she’s speaking loudly, then softly. She’s trying to be very engaging to a class of new kindergarteners. Why is she working so hard?
  3. She can see the kids are wiggly and having trouble focusing. Why are they having this trouble?
  4. They are sitting at their tables, spread out across the room,  four to a table, facing each other. They are focusing on each other, instead of the teacher. Why are they at tables?
  5. They’re at tables because they are going to work in their workbooks after the discussion part of the lesson. Aha!

So I say to the teacher:

What if the discussion (or teacher-directed) part of the lesson, with the stuffed animals and the school supplies, took place on the rug? Isn’t that where you do most of your other critical, ‘Hey kids, I need your attention work’ with the students? Then, when you are done discussing the concept, in this case, sorting objects into groups, the students can go back to their tables for the guided practice part of the lesson, and work in their workbooks.

“Doh!”, says my friend,” why didn’t I think of that? I always introduce lessons and give directions on the rug. You have changed the way I am going to teach math, forever” and then we had a High Five! moment. Because she is a friend, after all and sometimes we tend towards hyperbole…. Not all observation discussions are as full of love and happiness.

Take note, though. This teacher ASKED for feedback from a random lesson I had wandered in on and was open to ideas to improve a pretty good lesson.

And when put on the spot, I gave an analysis I might otherwise have not. Reflecting on the lesson led us to dig deeper into the what was really happening in the classroom. In the end, it yielded an “aha!” moment that will change the way the students experience this teacher’s  math lessons.


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Understanding trumps tricks

My friend Allison (MIT graduate in Mathematics) recently explained why she struggled with inequalities as a child.

To help students remember which way the inequality sign pointed, the teacher drew an alligator mouth. You know the lesson. Here’s an example from

And the song lyrics:

And one from

And this simple shortcut or trick was the cause of all of Allison’s troubles with inequalities.

She explained: “everyone knows, the bigger fish eats the small fish”:

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