Thinking Mathematically

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Hello everyone and welcome to my blog. My name is Mark and I write about Mathematics education. I am a Teacher, Instructional Coach, and Life-long Learner. Passionately curious about education. As a classroom teacher, I have taught grades 5-8.

Thinking Mathematically

2y ago

Many teachers are comfortable allowing their students to read for pleasure at school and encourage reading at home for pleasure too. Writing is often seen as a creative activity. Our society appreciates Literacy as having both creative and purposeful aspects. Yet mathematics as a source of enjoyment or creativity is often not considered by many.
I want you to reflect on your own thinking here. How important do you see creativity in mathematics? What does creativity in mathematics even mean to you?
Marian Small might explain the notion of creativity in mathematics best. Take a look:
Mari ..read more

Thinking Mathematically

2y ago

Data management is becoming an increasingly important topic as our students try to make sense of news, social media posts, advertisements… Especially as more and more of these sources aim to try to convince you to believe something (intentionally or not).
Part of our job as math teachers needs to include helping our students THINK as they are collecting / organizing / analyzing data. For example, when looking at data we want our students to:
Notice the writer’s choice of scale(s)
Notice the decisions made for categories
Notice which data is NOT included
Notice the shape of the data and spatia ..read more

Thinking Mathematically

2y ago

TRU Math (Teaching for Robust Understanding) a few years ago shared their thoughts about what makes for a “Powerful Classroom”. Here are their 5 dimensions:
Looking through the dimensions here, it is obvious that some of these dimensions are discussed in detail in professional development sessions and in teacher resources. However, the dimension of Agency, Authority and Identity is often overlooked – maybe because it is much more complicated to discuss. Take a look at what this includes:
This dimension helps us as teachers consider our students’ perspectives. How are they experiencing each d ..read more

Thinking Mathematically

2y ago

A few weeks ago I was introduced to Jenna Laib‘s game “Number Boxes” and was very interested in using it as a dynamic game to help students learn a variety of new content — Jenna’s blog explaining the game can be found here: “One of My Favorite Games: Number Boxes“.
Basically the game involves students rolling dice (or spinning a spinner / drawing a card) to generate a random number and placing that number in one of their empty number boxes one-at-a-time. The game can progress in a variety of ways:
Rolling 1 number at a time, create the largest number you can.Rolling one number at a time, crea ..read more

Thinking Mathematically

4y ago

In 2001, the National Research Council, in their report Adding it up: Helping children learn mathematics, sought to address a concern expressed by many Americans: that too few students in our schools are successfully acquiring the mathematical knowledge, skill, and confidence they need to use the mathematics they have learned.
Developing Mathematical Proficiency
The potential of different types of tasks for student learning, 2017
As we start a new school year, I expect many teachers, schools and districts to begin conversations surrounding assessment and wondering how to start learning given ..read more

Thinking Mathematically

4y ago

A few years ago Tracy Zager wrote a wonderful article called “How Not to Start Math Class in the Fall” where she shared the pitfalls of starting the year with diagnostic tests and instead gave a more positive and productive path which included setting a positive tone for learning mathematics and gathering useful formative data. While the article was a powerful reminder about what we should value and how we can help start the year off on a positive note, the article might be more important this year than most for us to consider.
The ending of the 2020 school year was (is) not ideal for many stu ..read more

Thinking Mathematically

4y ago

An area of mathematics I wish more students had opportunities to explore is spatial/visualization. There are many studies that show just how important spatial/visual reasoning is for mathematical success (I discuss in more depth here), but often, we as teachers aren’t sure where to turn to help our students develop spatial reasoning, or now to make the mathematics our students are learning more spatial.
One such activity I’ve suggested before is Skyscraper Puzzles. I’ve shared these puzzles before (Skyscraper Puzzles and Skyscraper Templates – for relational rods). With the help of my ..read more

Thinking Mathematically

4y ago

Ask any teacher anywhere what some of the most pressing challenges are that they face as a teacher and likely you will hear examples of how difficult it can be to meet the various needs within a classroom. When conversations on the topic arise, there are often discussions from one of two extremes:
One one side you might hear about reasons why a teacher might believe that it is best to make sure that every student be expected to learn the same things. These beliefs often lead to practices where everyone receives the same instruction, followed by individual assistance for students who were ..read more

Thinking Mathematically

4y ago

Recently Lowrie et al. published an article in the Journal of Experimental Education where they looked at the effects of a spatial intervention program for grade 8 students. This study followed the 876 grade 8 students across 9 schools as they received 20 hours of spatial interventions (as well as other grade 8 students in schools that conducted “business as usual” mathematics classes). Their findings were quite interesting. They found students who received spatial intervention programs achieved:
significantly better on spatial tasks (13% higher)
significantly better on Geometry – Measur ..read more

Thinking Mathematically

4y ago

Many math resources attempt to share the difference between teaching FOR problem solving and teaching THROUGH problem solving. Cathy Seeley refers to teaching THROUGH problem solving as “Upside-Down Teaching” which is the opposite of a “gradual release of responsibility” model:
And instead calls for us to flip how our students learn to a more active model:
So, instead of starting a unit on Geometry with naming shapes or developing definitions together, we decided to start with a little problem:
Create as many polygons as possible using exactly 2 pattern block pieces. Sort your polyg ..read more