I was chatting with my friend Michelle about learning mathematics. Integers came up and the discussion led to the use of language when introducing a new mathematical concept to someone. The difficulty we were discussing was in relation to integers; why do educators sometimes use the terms 'minus 3' when referring to -3? When students …

### Mixed Numbers – why do they exist?

We recently had Monica Neagoy visit our school to do workshops with our junior and middle school teachers. During the PD session, the conversation turned to mixed numbers and the fact that they tend to only exist in English speaking countries. I teach with a colleague from Italy and have had discussions about different mathematical …

### The Start of Integers

Here is a problem I use to introduce integers. I never tell my students what we are learning, I just give them the problem and see what they can find. (we sing itsy, bitsy spider first) If a spider climbs 3 metres up a waterspout during the day, then slides back down 2 metres every …

### Multiplying Fractions

My journey of fractions continues. This post is focusing on multiplication of fractions, again using students previous understanding of whole numbers. Whole number by a whole number I love the area model for multiplication. We start with a simple problem such as (2)(3) Whole number by a fraction I have been using Alice in Wonderland …

### Dividing Fractions

When I did my Masters of Education, I wrote a paper on fractions and explored the research surrounding the challenges that students have with fractions. Since that time, I have grown in my own understanding of how best to guide students in their understanding of fractions. To start, I am going to focus on division …

### The Starting Line

This is my attempt at sharing ideas of teaching mathematics conceptually, building on student's previous understandings. My focus is on proof and reasoning and my students know that my favourite question to ask them is "WHY"? I have been teaching mathematics for a long time. Some of my ideas I have been using, and tweaking, …

### Math Autobiography

I have always had my students write a mathematics autobiography each year I've been teaching. I start by sharing my own mathematics autobiography and then have the students write their own to me. The purpose is for me to know what my students bring with them to the math classroom; math anxiety has a huge …