Soft Skills – Building From Strength

Recently I was in a classroom and I used the word “quantity” when speaking with a student. He said to me, “That’s a big word.” When I replied that at the end of this unit, “quantity” may be a word that he uses, he smiled.  I asked another student to explain to me how she figured out a missing value in a diagram.  Her reply was “I don’t know how to say it.” I asked her to try anyway, and she did.  She got some words out that allowed me to ask questions that helped her to built up her response.

The soft skills of teaching have to be paired with  high expectations that students can and will be able to meet the challenges set before them.  Soft skills without high expectations doesn’t help students learn.  This is what it looked like in my classroom back when I had my own classroom:

  1. I meet students where they are at in their learning and ask them to move forward in a meaningful way.
  2. I listen to students to hear what they are thinking and seek to find strength that they can build from and take the “next step” for them to move forward.
  3. I let them know where we are headed and that they can get there along with the rest of us.  

For over twenty years I worked at a junior high school with students that came from backgrounds that many people call disadvantaged, students that were still learning English although they entered our district in kindergarten, students that came from homes where many of their parents don’t have a high school education and their parents work hard at two or three jobs just to pay the bills.  

One group of students that intrigued me were the students that entered 7th grade math “knowing” that they were not good at math.   One such student,  Emmanuel, was a polite, organized young man who had beautiful handwriting.  His test scores showed that he had been “below basic” on state tests for multiple years in elementary school.  This data got him placed in the lowest math class in our school as he entered 7th grade.  He had the sense that he wasn’t good at math. As I came to know Emmanuel I found out that he was very good at solving the  3-D wooden puzzles and the puzzles like the Crazy Turtle Game that I had in my classroom.  His visualization skills that allowed him to solve puzzles were phenomenal! Over winter break, Emmanuel took home a puzzle that no one had  been able to solve in three years.  He returned with it solved.

I learned that Emanuel was a problem solver.  Although he was a willing student, memorizing a cookbook’s worth of mathematical procedures wasn’t his strength. Emmanuel helped me learn that I needed to turn problems into puzzles so I asked him to make sense of mathematics with diagrams or drawings.  He thrived as a student in my class because I got to know him and found strengths that he could build upon.

Emmanuel is a high school senior this year. I have not seen him since junior high. When he left junior high, his math skills were approaching grade level while his reading skills still lagged behind. In junior high he wanted to be a landscape architect or drafts person.  He was just beginning to learn about careers in engineering.  Soft skill are about getting to know your students, and helping  them meet the goal that you have for them and that they have for themselves.

My Favorite Math Practice

My Favorite Math Practice

Common Core Standards for Mathematical Practice:

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

When I was first learning about the Common Core Standards for Mathematical Practice, I gravitated toward Math Practice 1 – Make sense of problems and persevere in solving them and Math Practice 3 – Construct a viable argument and persevere in solving them.  These two practices seemed clearly understandable to both me and my students, and they made sense from a practical, everyday point of view.  Who wouldn’t want to learn to make sense of things, persevere in the face of challenge and to be able to engage in well reasoned conversations built around evidence? As I worked with my students, we talked about these two math practices a lot, along with paying attention to the math practices that were already, to some degree, a part of my regular classroom instruction: MP 4 – Model with mathematics, and MP 5 – Use appropriate tools strategically and MP 6 – Attend to precision.  

I gave myself permission to not engage in Math Practice 7 – Look for and make use of structure and Math Practice 8 – Look for and express regularity in reasoning.  I didn’t readily know what this thing called “structure” was, let alone how you might see it or use it.  When I made an attempt at defining structure, my ideas came out more like repeated reasoning.  As  I continued to improve my understanding of all of the  math practices, MP 7 and MP 8 became clearer. And then, just recently, I heard someone speak at a math conference.  What the speaker said made so much sense that many of the separate pieces of information that I had come to understand shifted to create a more cohesive understanding of the math practices as a whole.

The speaker was Grace Kelemanik and her talk was on the math routine “Contemplate then Calculate” (#CthenC)  from the book Routines for Reasoning (#4RforR).  What she presented helped me understand that:

  1. Not all math practices are created equally. Each math practice plays a different role as students become mathematicians, yet they all work together.
  2. Math practices should be seen as an opportunity, not a hurdle for students that struggle with mathematics.  Many of the types of learning experiences that engage students in the math practices are similar to the types of learning that support students with learning disabilities and English learners.
  3. The three math practices that I left  until last to understand are vital avenues for thinking that can be taught through specific instructional routines. Check out this visual of the math practices that describe the avenues of thinking.

So, what is my favorite math practice today?  Math Practice 7:  Look for and make use of structure. For me, seeing structure is the ability to see complicated mathematical representations in chunks that can be worked with or rearranged to make problem solving easier.

For example, seeing and using structure can be found when you look at the problem 8 x 15.  If you can “see” this as 4 x 2 x 15, which can change into 4 x 30 then you are using mathematical structure. (By the way, this example is begging for a graphical representation to go along with it but that is not going to happen right now.)

MP 1 and 3 used to be my favorites, but for 2017 I have a new favorite… MP 7 Look for and make use of structure.  I still like you MP 1 and 3, but I am adding a new favorite to my list.  As long as I am calling out favorites, for those of you that are familiar with NCTM’s Principles to Action, the Mathematics Teaching Practice Use and connect mathematical representations is one of my favorite teaching practices because these two favorites work so well together.