## Grouping Problems in 1st Grade

My wife (Josie) was showing me the work she is doing with her first grade students in math. They are talking about grouping tens and ones, ultimately looking to explore place value. Her activity was to have students imagine situations involving collecting groups of items, and then looking at the mathematical structure behind those groups. One wrote about how a thief had a container that could only carry 10 ice cream cones at a time, which meant that he had to leave some of the ice cream cones he was stealing from a house behind. Another talked about the Grinch stealing twenty Christmas trees at a time from a forest that had 255.

There are two things that I really like about the approach. One is that it doesn’t do the common backwards approach I have seen in elementary math programs where the math problem comes first. It seems off to asking students to add 3 + 4 = 7, and then ‘make up a story problem’ that matches this abstract idea. Here, the students are coming up with problems that matter to them, and creating organization (groups) that make sense to them. Going from abstract to concrete works marginally well at best at the high school level for developing understanding, let alone for six and seven year olds that are wrapping their heads around abstract ideas like place value.

I also really like that Josie didn’t push the students to consider only even groupings. (255 trees into groups of 20? There’s a remainder. THERE’S A REMAINDER!) Word problems are often contrived to have even numbers only to make them ‘easier to understand’ and consequently even less real world. I just thought it was neat to see that she is making her students manage that messiness from the beginning.

This is clearly different from the higher level courses that I usually concern myself with in high school, but the idea still transfers well, regardless of the level. It’s always great to see things being done right by the younger students as well.

## Why I’m thinking today about the Tufts class of 2012.

I had my first group of ninth grade students during my second year teaching in the Bronx. It’s a unique experience being an adult mentor to a group of students fresh out of middle school. I’ve always gotten a kick out of seeing them first test the rules in their new high school environment, and this group being my first, it was new to me as well.

It has been a while since I’ve heard from many of them. I’m proud to say that a number of students from this group will be donning caps and gowns over the next couple of weeks to celebrate their earning undergraduate degrees. There’s a whole list of superlatives that describe the magnitude of pride I feel for this group and their accomplishments. As a digital pack-rat, I’ve held on to the spreadsheets I used to keep track of grades. I took a look at them just before writing this, which prompted a slideshow of smiling faces as I went through the list, name by name. I think I could vaguely place them in their seats in the classroom, but in all likelihood, this was just as likely my brain coddling me in my hope that I could remember such minimal details.

One student in particular in this group is pushing me to assert my bragging rights.

As I’ve mentioned other times on my blog, I am a proud graduate of Tufts University, majoring in Mechanical Engineering as a member of the class of 2003. It was through my work as a resident tutor in math and physics that I discovered that I had an interest in teaching, and this prompted me to apply to alternative certification programs that would help me do this. I could have applied my engineering credentials to be one engineer in the working world. Another option was to teach students to become engineers too, in effect, multiplying my own influence on the field. Through the New York City Teaching Fellows , I joined the faculty at Herbert H. Lehman high school in the Bronx during the fall of 2003 to teach math.

The first year was a blur. It was the fastest I’ve ever needed to learn a multidimensional set of skills and the most agonizing; I knew when I wasn’t getting across to my students and had few tricks to use in managing a class. The one thing I figured out very quickly though was that the students in my classes were sharp. They were good at picking up on things presented in the right way. Their skills were not necessarily where they needed to be, but that is a work in progress that can be managed through classroom work. I saw there was tremendous opportunity to help those students that were interested to become engineers.

I’ve had a number of students follow this route through my courses in math, engineering, and AP Physics. They chime in from time to time to let me know what they are doing, and I am always really impressed with their work. I’ve also had the occasional graduate write me to ask if it’s alright with me to not study physics or engineering as they originally planned to do. I am, of course, fine with this! I am always telling my students to go where their passions are, and am always a bit amused when they are afraid they are letting me down with such an admission.

The special case that I am writing about today is a young man that not only followed the engineering path, but decided to go to Tufts himself after leaving Lehman. He was a member of my first group of ninth graders, and though he was quickly switched into another section that year, he joined me for physics during his senior year. He also frequently contributed to the robotics team, never shying away from tackling the big challenges of robot design or from the small tasks of sweeping the shop floor at the end of the day. He also honored me during his senior year by speaking at a ceremony at which I received an award for my work, and his very kind words have stuck with me ever since.

It isn’t a miracle that he will cross the stage to receive his Tufts diploma today. Far from it – he did the hard work to get where he is, and I can’t take credit for the great things he learned both in my presence and away from it. And his story is far from over – I hope he (like many other students I’ve told this) keeps me in mind if I ever need a job. His story, and those of the rest of his class earning degrees this month, make me incredibly proud to be a teacher.

That said, there is something special about our story. The unique way that Tufts now connects us is unlike any I’ve ever had with others, even with my own Tufts classmates in the class of 2003. I hope that he can look back fondly to his times on campus as I do from time to time. For whatever small part I served in getting him there, I am glad to have helped him out.

I have nothing but excitement and pride for the adventures that lay ahead of him and his classmates.

Congratulations, Class of 2012!