“It’s the Little Things”

Mardi Knudson

Sauk Rapids-Rice Public Schools

MCTM Region 6 Director

A . (decimal point), – (negative sign), or working with fractions – don’t get me started! It’s paying attention to the little things that makes a big difference. How do we get our students to see value in proof reading their work and answers? Such a critical step and yet so often overlooked. I cannot tell you how often a budding mathematician in my class would see their mistake after it was graded and said, “Oh yea, I just forgot to _______.” Insert any simple mistake in here …. notice the operation, move the decimal point, regroup . . .

As I was observing one of my student teachers teach math, I knew the problem as soon as she flashed it on the whiteboard. The hair on my head stood up. Because of my experience, I knew the road we were headed down with this answer.

Find the pattern, then figure out how many sides the 9^th polygon would have:

3 sides       5 sides        7 sides          9 sides

Sadly, I think math problems want to catch students making mistakes instead of showing us what they know. If the above problem was put on a test, you know, many students would just look at the last polygon, see the number 9 and  mark that answer. It would be one of the multiple choice answers. We just lay in wait for mistakes like this so we can pounce and further chip away at what little math confidence some of our vulnerable students have. Then we could say, “I told you you should check your work!”

Another strategy I have seen omitted, due to lack of knowledge or time is when a teacher is  moving around and helping students and saying,  “I see where you made your mistake.” Then pointing out their simple error. Or was it a simple error? If you tell a student they forgot that it was 60 minutes in an hour, did they really even know that? We need to remember the phrase, explain your thinking. Otherwise we miss the opportunity to understand where the student’s true understanding lies.

The little things… I did a presentation for paras on how to work in classrooms with math students. I told them to never have a pencil in their hand. I even saw math teachers do this and when I pointed it out, they didn’t realize they were doing it! The simple mistake was looking at the student’s problem, want to help, and erase their mistake and correct it for them while explaining what they were doing. I get it. There are 38 other students in your Algebra II class and you only have ten minutes left to get around to everyone and help them before they head out the door and you don’t want them practicing with wrong information. You know where I am going with this. A missed opportunity for you to truly understand what the young mathematician knows. How to correct this? Teach students how to work with partners. You could be strategic with pairs. You cannot be the only person in the room with correct strategies or reassuring words.

I observed a first grade classroom where when a student made a poor choice with behavior, the students would chime in, “ We know you’ll do better next time.” How reaffirming! The class had few discipline problems because they felt like there was hope they could be successful. Are you the only one during your math class that gives out affirmations? When I was teaching a class of struggling math students, I passed out  Post Its for each chapter in the math book to each student. They wrote their own affirmations, after we brainstormed them. Then they put one some place in each chapter and during the year they gave themselves a pat on the back when they came upon their positive note.

As a math teacher, you see all too often how little things end up becoming an issue if we don’t help students learn to check their work. For example are your math classes expected to write down the intermediate steps in working with fractions? This makes students slow down and compute more accurately. When correcting assignments, remember correcting by consensus, where students correct in pairs and compare answers.

Due to large class sizes, it is critical we teach and reteach students how to work with pairs and be reaffirming. A kindergarten example. Students move to stations to work independently while the teacher works on skills with small groups. Great concept, but is the learning in the stations really as effective as it can be? Simply taking time to teach the students your expectations for working in pairs will make an enormous difference. The station I am thinking of was using the plastic bears and pattern cards to continue patterns. Most of the time I watched students playing with the bears and often they would try and continue the pattern, but it was wrong. Even if there was a card to check, they couldn’t be bothered. Often students were working in these stations independently. Teach them to work in pairs and check each others’ work before they move on to the next card.

Little things come down to paying attention to details. It is sad to see the light bulb turn on after the results are in. True, better late than never, but let’s be more purposeful in helping students before the results come in.

You are coming to the end of your math school year, testing is complete. That doesn’t mean we stop the learning. I was appalled when a fifth grade cooperating teacher proudly told me she finished her whole math curriculum three months early and was looking for things to do. How is that even possible? What depth of understanding did she miss along the way? Take time to reinforce the little things as your year draws to a close. Honestly evaluate steps to incorporate next year that will help students with this whole idea of paying attention, mindfulness, in math. For the last part of your year, work on building math confidence in your students so you send them into the summer months with the knowledge that paying attention to the little things ends up making a big difference.