Episode 113 - Knowledge Needed for Teaching Mathematics

Growing up I thought doing Mental Math meant doing the algorithm in my head.  Times have changed and now many educators have kids solve math in different ways but during Mental Math it’s still only having kids to do math in their head.  That’s not exactly what Mental Math should be about.  In this episode we explore what doing Mental Math really should be like. Get any links mentioned in this video at BuildMathMinds.com/167 

If you’ve ever watched a child during a counting collection and thought “Ugh! Why are you grouping the items like that?!?”  Well, there’s probably a reason.  There is a progression kids go through when organizing items they are counting.  Now even though this information comes from a book about Early Childhood Education, it still applies to those of you in 3rd-5th as you work to help them group items in ways that lead to multiplicative thinking. Watch this week’s video about The Progression of Grouping to help you understand why kids might be grouping items a certain way and how to help them.  Get any links mentioned in this video at BuildMathMinds.com/166 

It is commonly thought that Geometry in the early grades is just about getting kids to name and identify shapes.  There are actually 4 big ideas talked about in the Navigating Through Geometry book.  One of which is the work around two- and three-dimensional shapes but it is so much more than just naming & identifying shapes.   In this episode we take a look at what knowledge kids in PreK-2 should be developing around shapes and the types of experiences you can provide to help them develop it. Get any links mentioned in this video at BuildMathMinds.com/165   

There are 4 main strategies children tend to use to solve addition, subtraction, multiplication, and division problems.  These math strategies are not tricks.  Their foundations are built on number relationships and properties of operations.  In the Math Strategy Sessions we have already explored 3 of the strategies and our next session is focused on helping kids use and understand the Inverse Operation Strategy (https://buildmathminds.com/strategy-sessions to register).  This is more than just helping kids know Fact Families, it’s about helping them understand the meanings of the operations and the connections between Addition-Subtraction and Multiplication-Division.  Helping your students develop the Inverse Operation Strategy will last them the rest of their lives.  In this episode I’m sharing the first books I read that highlighted the importance of helping kids develop the strategy.  I never learned I could solve a subtraction problem with addition (or division with multiplication) until I was an adult.  Kids should be building this understanding way before I did.  Get any links mentioned in this video at BuildMathMinds.com/164 

There are lots of Problems of Teaching when you are helping young kids learn mathematics.  One of the hardest ones is helping your students to be successful learners, constantly trying to manage a large classroom of students who often are not very productive. In the book Teaching Problems and the Problems of Teaching by Dr. Magdalene Lampert, there was a line in the chapter Teaching Students to Be People Who Study in School, that still has me thinking: “...if we view students’ productive or unproductive actions in the classroom as expressions of who they think they are, then classroom management merges with something that might be called ‘academic character education.’”  That whole section of the book got me thinking of things you could do in your classroom to help your students be students who study mathematics, which in turn helps them to be successful learners.  Listen for my 4 ways to help your students be successful learners of mathematics.   Get any links mentioned in this video at BuildMathMinds.com/163 

In this video I’m sharing a part of a book that made me go “Hmm, I’ve never really thought about that!”  It has to do with just how precise we can actually be when measuring items. One of the Standards of Mathematical Practice is “Attend to Precision” which is about being precise in all mathematical vocabulary and content, but just how precise should we make students be when it comes to measurement?  Get any links mentioned in this video at BuildMathMinds.com/162  

I love pies, Pecan Pie especially, but I don’t love them during math time.  Pies, well circles in general, are an overused visual when it comes to the teaching of fractions.  In this video we take a look at visual fraction models that are much better to use and will be helpful to your students as they progress into other mathematical concepts like percentages, ratios, etc.  Get any links mentioned in this video at BuildMathMinds.com/161 

After the 2024 Virtual Math Summit, there was so much mention of using Sentence Stems I wanted to dig a bit deeper into them.  In my research I stumbled upon an old blog post by one of my favorite Math-y people, Sara Van Der Werf.  In this podcast episode I’m sharing a piece of her blog post that talks about one tweak you can make to Think/Pair/Share (or Turn & Talk) to help get your students more engaged in the math discussion.  Take a listen and go to buildmathminds.com/160 for any links mentioned in the episode.

Cathy Fosnot and Pam Harris are The Queens of Number Strings (or Problem Strings as Pam would call them).  I’m way too excited about the fact they are teaming up to do a one-day workshop all about using Problem Strings for Automaticity, Fluency, and Beyond.  If you’ve been doing number strings and want to go more in depth on how to use them in your classroom, I highly recommend going to this workshop.  Go to https://buildmathminds.com/159  to get links to items mentioned in the episode.  

Before the 2024 Virtual Math Summit starts next week, enjoy this preview of a Pre-Summit Session by Rosalba Serrano on Preventing Teacher Burnout.  Rosalba shares a ton of information and ideas to help you with burnout but I specifically picked this clip because one of the ideas she shared is one that my family uses a lot: Control the Controllables.   Get registered so you can watch Rosalba’s full session before the summit starts: VirtualMathSummit.com/register.