DMTI-1: Math Foundations - 5 Core Practices

If we want students to truly understand mathematics—not just memorize steps—they need opportunities to explore, question, and make connections between concepts. When instruction moves beyond the script of a teacher’s guide and invites students to spot patterns, use visual models, and explain their thinking, they develop authentic mathematical understanding.

In this course, you will be introduced to the experts at the Developing Mathematical Thinking Institute (DMTI). You will watch real workshop sessions and then see the strategies in action in real classrooms. The DMT framework is built upon five core practices:

• Taking students' ideas seriously
• Using models
• Moving from conceptual to procedural understanding
• Using the language of mathematics
• Anticipating and addressing misconceptions

DMTI-2: Six Predictors of Math Success

It’s not speed. It’s not memorizing facts. It’s not even number sense. The #1 predictor of math success is something far more powerful—visual-spatial reasoning. Students strong in this area can “see” math, making it easier to solve problems, understand patterns, and build lasting conceptual understanding. This course dives into six key predictors of mathematical success. Learn how these predictors influence learning and gain new strategies to strengthen them in your classroom.

DMTI-3: Number Sense, Counting and Place Value

Place value is a cornerstone of mathematics, yet research shows that many students struggle to move beyond rote procedures to truly understand. For generations, students have been taught place value and number sense through repetition and memorization. In this course, you’ll explore hands-on strategies, engaging counting routines, and visual models that help students—even the youngest ones—talk about math, reason flexibly, and truly see how numbers work. Step into the role of learner and experience hands-on activities and workshop-style lessons designed to model effective teaching strategies. Learn how concrete, visual, and symbolic representations will strengthen student understanding and build strong number sense from the start.

DMTI-4: Addition and Subtraction

Imagine a classroom where students don’t just memorize math facts, they understand them, see patterns, and explain their thinking. In this course, you’ll learn about model progression, subitizing, and precise math language to make addition and subtraction meaningful. You will explore strategies that focus on deep understanding, using enactive, iconic, and symbolic models, developing subitizing skills, and introducing precise mathematical language that strengthens students’ reasoning. Through real classroom examples, interactive problems, and workshop activities, you will actively practice the approaches students use to make sense of addition and subtraction, gaining insight into how to guide your own learners.

DMTI-5: Addition and Subtraction Word Problems

Have you ever wondered why some students can solve one word problem with ease but stumble on another that looks almost the same? The answer lies in understanding the types of word problems students encounter. Not all problems are created equal—each type requires different reasoning, strategies, and models. When teachers know how to recognize these differences, they can better anticipate student misconceptions, choose more effective examples, and guide students toward deeper mathematical understanding. In this course, we’ll break down the different types of word problems and learn how to help students make sense of problems, draw models, and develop lasting strategies.

DMTI-6: Multiplication and Division

What if teaching multiplication could move students beyond memorized facts and help students truly see how numbers work? In this hands-on course, you’ll step into your students’ shoes. You’ll practice drawing iconic models, using ratio tables, analyzing word problems, and guiding students toward multiplicative thinking that lasts far beyond a test. You’ll see real teachers in action as they demonstrate different multiplication strategies. By the end, you’ll have a toolkit of engaging approaches that make multiplication meaningful, visual, and connected.

DMTI-7: Multiplication and Division Word Problems

Have you ever noticed how quickly students memorize multiplication and division facts but struggle when the numbers are wrapped in a story problem? The real challenge isn’t the math. Rather, it’s helping students make sense of the situation. In this course, teachers will learn how to unpack multiplication and division problems, identify the underlying structures, and represent them with clear, visual models. Using iconic representations like bar models and ratio tables, you’ll explore how to make invisible math relationships visible, so students can see, not just solve, what’s happening in the problem. Learn about multiplication, measurement division and partitive division problems and how small shifts in wording change the math completely.

DMTI-8: Fractions

Fractions can feel tricky for students, but they’re some of the most fun to teach—because they connect to so many real-world experiences, from sharing pizza to measuring wood for a project. In this course, you’ll learn how to teach fractions by focusing on iteration, precise language, and visual models. Practice strategies to help students place fractions on number lines, build bar models, and solve word problems with confidence. Along the way, you’ll experience common student misconceptions firsthand and learn how to address them. Experience learning fractions just as your students would by solving problems, building models, and reasoning through tasks.

DMTI-9: Fluency

In mathematics, fluency means being able to use numbers flexibly, accurately, and efficiently to solve problems. It’s not just about knowing math facts by heart...it’s about understanding relationships between numbers and being able to choose the best strategy for the situation. A fluent mathematician doesn’t just recall facts quickly; they think with numbers—adjusting, decomposing, or combining them in smart ways. In this course, you’ll explore an approach to mathematical fluency which goes beyond mad minute speed drills and focuses on deep number sense and flexible thinking. You’ll learn how fluency develops through strategies like doubling, squaring, benchmarking, and compensation, and how these can be applied across addition, subtraction, multiplication, and division. When schools begin fluency work as early as kindergarten, the results by fifth grade are remarkable.

Backwards Teaching: Using 3 Part Lessons in Math

Have you ever heard of "teaching backwards?" We often hear about backwards design when it comes to instructional planning but this is different. A "three part lesson" uses the final phase for most of the teaching. In this practical course, learn how to engage your students in math by incorporating Activation, Problem-Solving, and Consolidation. See how teachers act as facilitators by coordinating the sharing of student solutions and the use of questioning to help students make connections between their own mathematical ideas and the ideas of others.

CCSS Instructional Shift 1: Focusing on “High Value” Math Concepts

This course will focus on the first shift in the Common Core for Math, which is Focus. Through taking the course, you will learn what is meant by “focus” in the Math curriculum and how it will change the content you teach. You will understand the importance of allowing students to delve more deeply into few topics so that they can scaffold their knowledge through out their education. Finally, you will be able to apply the information and ideas behind this shift into your classroom and help your students reach their greatest potential in math.The first unit will provide you with knowledge and information on what the shift is and the second unit will show you classroom application of the shift.

CCSS Instructional Shift 2: Math Coherence Across Grades

Studies conducted during the last few decades have demonstrated both the need for and the benefits of gifted education programs. Of special interest are the benefits that occur for ALL children when gifted education strategies are implemented effectively. In this course, you will explore the nature of giftedness and strategies to connect with high ability students.

CCSS Instructional Shift 3: Increasing Fluency with Core Math Functions

Through taking the course, you will learn what is meant by “fluency” in the Math curriculum and how it will affect your teaching practices. You will understand the importance of students' ability to efficiently and accurately perform foundational computational procedures without aid. This will allow students to gain insights to mathematical structure and apply a variety of appropriate procedures flexibly as they solve problems. Through this course, you will be able to apply the information and ideas behind this shift into your classroom and help your students reach their greatest potential in math..

CCSS Instructional Shift 4: Building Deeper Understanding of Math

This course will focus on an instructional shift needed to help students acquire deeper conceptual understanding. Through taking the course, you will learn what is meant by "conceptual understanding” in the Math curriculum and how it will change your teaching practices. You will understand the importance of students' understanding beyond isolated facts and methods of mathematical computation. You will understand the Standards for Mathematical Practice that describe the student expertise needed to develop a deep conceptual understanding of mathematics. Finally, you will be able to apply the information and ideas behind this shift into your classroom and help your students reach their greatest potential in math.

CCSS Instructional Shift 5: Application-Teaching the "Why" in Math

How do you engage your students math skills in real-world ways? Students are expected to use math and choose appropriate concepts for application even when they are not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. This course will focus on the fifth instructional shift for Math, which is Application.

Through taking the course, you will learn what is meant by "application” in the Math curriculum and how it will change your teaching practices. You will understand the importance of students' ability to use math flexibly for applications in real world situations.

CCSS Instructional Shift 6: Dual Intensity - Drills and Application

This course will focus on the sixth and final shift in Math, which is Dual Intensity.

Through taking the course, you will learn what is meant by "dual intensity” in the Math curriculum and how it will change your teaching practices. You will understand the importance of finding a balance between students' understanding and practice in math.