Welcome fellow Recovering Traditionalists to Episode 105.  Today we are looking at the 3rd-5th grade sessions at the 2021 Virtual Math Summit.

Welcome to Build Math Minds the podcast, where fidelity to your students is greater than fidelity to your textbook. I’m your host, Christina Tondevold, the recovering traditionalist and BuildMathMinds.com Founder, where my mission is to change the way we teach elementary math to our kiddos. Are you ready to start building math minds and not just creating calculators? Let’s get started.

The sessions at the Virtual Math Summit are for all elementary grades PreK through 5th, but some are specific to PreK-2nd and some are 3rd-5th.  In this week’s podcast I’d like to highlight two sessions that are focused on content that 3rd-5th graders are building.

Both of the presenters I’m sharing today are going to be a part of the Speaker Panel Q & As so if you want to participate in those make sure you are registered for the VIP access or become a member of the Build Math Minds PD site. You can see the options for the summit registration at VirtualMathSummit.com/Register.

Up first is Emily Kappel and her session on using Number Lines.

Emily has sixteen years of experience in the classroom and an enthusiasm for teaching math.    Having taught two years of Algebra I at the high school level and 14 years of math​ at the elementary level​, she knows the progression​ of the math standards across grade levels.​ When she does PD sessions, her emphasis is teaching audiences to make the shift from “How?” to “Why?” so students don’t just “do” math​ for procedural understanding​, but they show a deeper​ conceptual​ understanding ​which develops children to become mathematical thinkers.  This is definitely how she approaches her Virtual Math Summit session in which she helps us understand the “why” of using number lines, not just the “how.”

Emily Kappel:  When I think of my students, both in my classroom and the students that I work with in other schools, and the teachers that I work with, I’m thinking of them as a mathematician. I want to build students up, so they think of themselves as mathematicians. To do that, they need to be mathematical thinkers. When you’re looking at this diagram, our whole idea is to get our kids to be problem solvers. We want them to be doers. We want them to be thinkers.

Emily Kappel:  To do that, they need to do the big four ideas. They need to be able to communicate. They need to be able to communicate their connections. We’re constantly teaching connections when we teach ELA. Think about it. We’re reading a story. We’re asking our students to do text to text, text to self and text to the world. We need to be doing that same idea, when we’re teaching mathematics. Where do you know this concept from? Have you done it in your real life? Have you done it prior math classes? Here, as a teacher, it’s your responsibility to then make the connection to what they’re going to use this for down the road.

Emily Kappel:  Doing that vertical alignment is huge, when we’re talking about mathematical concepts. It also allows you as the teacher to know where you need to go back and maybe fill in gaps, when you’re having your students make those connections. Your students are going to be using reasoning and proof to solve problems. I’m always asking the questions. What do you notice? “What do you wonder and why, why did you choose that method?” “Why did you choose that tool?” “Is there another way that you could solve this?” And leave the kids thinking and they are able to then start to make connections as to, “Why did I use this tool,” “Well it’s my favorite tool,” “What am I comfortable with?” And they’re going to be able to communicate that with you.

Emily Kappel:  Lastly, the big hitter for today is the representations and models. Our number line that we’re going to walk today is a prime example of a model that students can use to do the bottom part there, reasoning and proof, show why their answer is what it is. It also allows students to make discovery, which I cannot wait to show you, how you can use the number line to have your students make different mathematical discoveries, instead of you telling them mathematical rules. It’s one of my favorite parts of using a number line in the math classroom.

Ok, onto Dina Mendola’s session about helping kids get out of the repeated addition & subtraction stages for multiplication & division and moving into multiplicative strategies.

Dina is an Instructional Coach with the US Math Recovery Council®.  Throughout her 26 years in education, she has assumed a variety of positions but in her role with the US Math Recovery Council®, Dina is committed to empowering teachers, districts and states to put mathematical research into practice. In her session she does just that.  She combines the research of how children develop multiplicative thinking along with practical ideas you can use in your classroom.

Dina Mendola:  In thinking about this, why are multiplicative strategies so important and why is it so critical to get students to take that leap? There is research out there by Dr. Leslie Steffe called the Reorganization Hypothesis. In this research, it shows that the way that students work with whole numbers directly influences the way they’re going to work with fractions.

Dina Mendola:  In fact, many of our students performed the same mental actions to make sense of actions that they do to make sense of their whole number knowledge. So thinking about this, additive strategies are a part of this journey. They’re an important part, but we know that they can become cumbersome. When numbers get so large and so complex, it becomes highly inefficient for our students to use these additive strategies. Thinking about that, that’s what makes this work in shifting students’ way of operating with whole numbers so critical.

Dina Mendola:  We need to continue to devote that time to learn and create those foundational knowledge and skills that they need to move from unitary strategies, those by ones into thinking about composite units, using composite strategies. This is what’s going to build that flexibility with their number relationship. So let’s take that journey.

Dina Mendola:  We’re about to start that journey. And really it’s all about units and coordinating those units. So discovering what the levels of unit coordination are, and how we can use that knowledge along with prioritizing numbers is going to help us to develop this strong network of relationships, that students can leverage to get to any of their multiplication and division packs, and also extend into multi-digit factors. This is where we’re going to go in our session, and we’re about to dig deeper here.

Are you excited to learn more from these ladies?!?!  Head on over to VirtualMathSummit.com/register to get registered.  On that page you will see three options.  The FREE option is there, of course, but there is also the VIP access and the option to become a member of the Build Math Minds PD site.  Both of those options give you extended access to the summit sessions along with extra interaction with these two presenters (and many others) by participating in the Speaker Panel Q & As.


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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.