# Unit Coordination

### Christian – Part 1

*The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.**—Common Core State Standards for Mathematics, p. 8*

**CSS.MP1 Make sense of problems and persevere in solving them.**

Christian was a first grader we worked with during the Spring of 2017. We were interested in investigating his mathematical thinking so we presented him with addition tasks, but did not have him solve the problems with paper and pencil. The task we gave him consisted of two numbers printed on a card, his first numbers were 20 and 13, and he was asked how much altogether. For this problem, he quickly responded 33. The second step of the task was to turn the cards over; on the backs of the cards were the corresponding number of worms printed for him to count. He counted the worms and his count confirmed his answer of 33.

We then gave him the numbers 19 and 13. He stared at the cards for 15 seconds and then said, “Oh, 23,” leaned back he appeared satisfied with his results. He was asked to count and upon counting he ended up at 32, looked confused, and said, “No, I got it wrong.” When asked how he got his first answer, he said that he thought of the three but forgot the one (pointing to the 1 in the tens digit of 13). “Oh, it should have been 33.” His confusion began when his count was not the same answer that he first determined. He tried to use his mathematical thinking to resolve this discrepancy but without success.

Our belief was that he had used a prescribed mathematical method that consisted of using place value to combine digits. As many teachers know, young children can be successful with this method. The difficulties occur when students are asked to cross a decade using this system and need to regroup. To confirm our belief, we gave Christian the numbers 14 and 13. He quickly answered 27 and then turned the cards over to verify his results. His current mathematics allowed him to be successful in some situations but not in others.

Christian has what I described as a prescribed method of mathematics. I use the term prescribed because it is not a method he developed, rather one that has been given to him. He has an understanding of an addition procedure he needs to carry out, but it is limited to a specific class of addition situations. The results were not meaningful for him as seen in his satisfaction with his initial response to the problem of adding 19 and 13.

So how can we help Christian to make sense of these problems? Understanding how is exactly what our work here at AIMS is about. Join me in my next blog as we guide Christian towards understanding and meaningful mathematics.

### Introducing Stef the Moose

Some of the most precious and meaningful memories I have from teaching kindergarten came from a classroom stuffed bear I called Mr. Teddy. He was part of six kindergarten classes. He would go home with a new student every Monday and return to class on Friday with a new story to tell that had been… Continue Reading

### “If I Could Turn Back Time” – Part 2

In my last post I wrote about one of my first experiences teaching math to second graders. At the time (way back in 1996!), the math adoption we were using was MathLand, which was very conceptually based. I had several teacher friends that were also educators comment that they loved MathLand and felt it really… Continue Reading

### Prioritizing Reflection for Me and My Students

One of the best experiences as a teacher for me is when you see a child have an “ah-ha” moment. The look on their face, their body language, their emotion. These moments bring me so much joy. I have seen so many of these moments working with 1st graders over the last few years. I… Continue Reading

### What’s That in My Reflection?

Most of us, when hear the word reflection, think about what we see when we look in a mirror, but it can also mean to think back on an event. For example, if I asked you to reflect on the food choices you made today, you would have to think back on the meals that… Continue Reading

### Building Understanding in Mathematics

This week I’m writing from Mexico. Every year, my church travels down to build houses for families in need. We work with local churches to supply building materials and manpower to build simple homes. The work could not occur without the help of local pastors, who help by identifying the families and local contacts we… Continue Reading

### Brittany

In the Common Core State Standards for Math, counting-on is considered “a strategy for finding the number of objects in a group without having to count every member of the group.” Counting-on is an efficient way to add and we want children to count-on. Yet, many young children begin by counting-all. For example: Teacher [placing… Continue Reading

### What Did I Learn?

Now that the school year has ended, our research team has been gathering our data from time spent working with students and analyzing it to answer the question: “what have you learned this year?” More importantly, I wanted to figure out what I have learned that will actually enable us to help kids. After completing… Continue Reading

### Who Benefits From the Demo?

I will never be the strongest woman in the room. I don’t mean that in any kind of cognitive or social-emotional way. I mean that I am physically not a very strong person. Nevertheless, I work out as often as I can and I have spent most of my life in physical therapy. A few… Continue Reading

### Composite Units in Learning Math

The term composite unit is important in understanding how children come to know math. When a student builds math concepts with a composite unit as part of the foundation, there is a real perceivable difference in what the student can do compared to students who learn math simply as a set of procedures. One of… Continue Reading