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Studying the Mathematical Knowledge Needed for Teaching: The Case of Teachers’ Knowledge of Reasoning and Proof Andreas J. Stylianides and Deborah L. Ball

Welcome fellow Recovering Traditionalists to Episode 113.  Today we are taking a look at The Knowledge Needed for Teaching Mathematics.

When I was getting my endorsement in mathematics added to my Elementary Education teaching license I had to take a certain number of math courses at the college level.  Not math education courses, but just plain math courses. 

While I was sitting in my Pre-Calculus class all I could think was “how in the heck is this supposed to make me a better 6th grade teacher?!?!?”  I had such a bad attitude about having to take that course that the only thing I remember from that course was that singular thought that constantly ran through my head while I was sitting in class.

I took, and passed, the course but only as a hoop to jump through.  It didn’t provide any value to me in doing a better job helping my students to understand math.  I tried to tell myself that it’s good to understand the higher-level math that kids will encounter one day…but seriously that’s like telling a kid they need to learn to add and subtract so they can balance their checkbook one day.  What’s the value in learning it right now??  How will this help me right now, with the problems my students are currently having??

I had a hard time understanding why I needed to take it and still to this day I have a hard time with it.  I really don’t get why we make elementary teachers take math classes…we need classes that actually help us learn how to teach math and deal with the struggles kids have building their understanding.

I remember when I was first introduced to the research of Deborah Loewenberg Ball.  It solidified what I had been feeling about my lack of knowledge for teaching mathematics and my thoughts on why it was useless to take that darn Pre-Calculus class.

Deborah Ball has written a lot of articles about the knowledge needed for teaching mathematics so if you aren’t familiar with her work then go Google her, but one of her articles that she wrote with Andreas J. Stylianides in 2004 is available fully online and I’d like to share a part of it with you today.  

I’m sharing one of the smallest snippets I’ve ever shared but it’s so powerful and had a major impact on the information and learning I have pursued.  

In the introduction, on page 3 they write:

“Despite the focus on understanding what teachers need to know about mathematics, the field of mathematics education still knows too little about the mathematical knowledge needed for teaching.”

So what they are saying is that for whatever concept you are teaching, yes you do need the mathematical knowledge for doing the math, but as teachers we also have to know the mathematical knowledge needed for teaching that concept.

It isn’t enough to just know how to add or multiply or find equivalent fractions…there’s so much knowledge we need in order to teach that concept to children…to help them build their understanding of the concepts.

That’s what I was missing.  

When I first started teaching, all I had was the math knowledge.  I knew how to DO the math.  I thought that was enough to be able to teach it.  Boy was I wrong.  I knew I was wrong and that’s why I wanted to learn more and get my endorsement in math.  But the courses I had to take to get that endorsement just felt wrong…like I already had the knowledge of math, I needed that missing piece of the knowledge for teaching math.

I’ve been on a journey to improve my knowledge needed for teaching math for the past 18 years.  I don’t know it all.  

I’m still constantly learning.  But thanks to the work of Deborah L. Ball I’ve learned that it isn’t about learning how to do more math, there’s so much more to building the knowledge I need to teach math.

That’s one of the things I love about doing this podcast and my weekly videos over at is that I get to share what I’ve learned and what I’m currently learning with you.

If you’ve ever sat through a course or a PD meeting and thought “how in the heck is this supposed to help me help my students?!?!?” then I’ve got something for you in addition to the podcast and videos.  I’ve got some webinars coming up that will actually help you help your students to build their math understanding….and they are completely free.

I’m doing a webinar about The Missing Piece to Elementary Math Fluency.  No matter what grade, all elementary kids are working on developing their fluency.  But being fluent is more than just getting correct answers fast.  Come join me on this live, free training to learn the missing piece to developing fact fluency and increase your knowledge needed for teaching addition and multiplication facts. Just go to to sign up for free.

If you work with younger kids, I’m also hosting Sue Looney’s webinars about The Power of Counting.  In The Power of Counting webinar, you will learn the 3 reasons why counting is so powerful, and how you can use this information to help your students build a strong foundation in number sense. You will learn a step by step approach that leads to mathematical understanding and deep number sense. It begins with building your knowledge for teaching counting.  Go to to sign up for Sue’s webinar.

I’ll link up the article I shared so that you can learn more about the knowledge needed for teaching mathematics.

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As you start off the school year, I want you to keep in mind what is really important as we're trying to teach mathematics to our students.