A Digital Toolkit for Making Sense of Math

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Explore and create : Creation lab

Beth Chinderle  
Tod Johnston  

Deepen learning in your K-5 math classroom with The Math Learning Center apps, a versatile and free suite of virtual manipulatives. Develop your fluency with the apps through a series of hands-on activities that you can use with students in your classroom, school and district.

Audience: Curriculum/district specialists, Teachers, Technology coordinators/facilitators
Skill level: Beginner
Attendee devices: Devices required
Attendee device specification: Laptop: Chromebook, Mac, PC
Tablet: iOS, Windows
Topic: Online tools, apps & resources
Grade level: 3-5
Subject area: Math
ISTE Standards: For Educators:
  • Model and nurture creativity and creative expression to communicate ideas, knowledge or connections.
For Students:
Innovative Designer
  • Students exhibit a tolerance for ambiguity, perseverance and the capacity to work with open-ended problems.
Creative Communicator
  • Students choose the appropriate platforms and tools for meeting the desired objectives of their creation or communication.
Additional detail: ISTE author presentation
Disclosure: The submitter of this session has been supported by a company whose product is being included in the session
Influencer Disclosure: This session includes a presenter that indicated a “material connection” to a brand that includes a personal, family or employment relationship, or a financial relationship. See individual speaker menu for disclosure information.

Proposal summary

Purpose & objective

In the session, participants will develop their fluency with The Math Learning Center apps ( in a series of hands-on, interactive activities. The virtual manipulatives—available as both iOS apps and web apps—parallel the most common physical manipulatives and models in elementary mathematics. Unlike other elementary math technology that guides students through predefined learning pathways and can feel formulaic, the MLC apps are entirely open-ended and can be used to model mathematics beyond their primary use cases.

Participants will be challenged to “do the math” with and apply the MLC apps towards problems from the Math at Home website ( By engaging in realistic classroom investigations, participants will gain ideas and resources that can immediately be put to use in their own classrooms and schools.

Participants will also learn through first-hand experience how to use the apps alongside other common K-5 tech tools including Google Slides and Padlet. Not only will this provide tangible classroom integration use cases, it will encourage participants to consider best practices for reviewing student work and extending math discourse with technology.

Evidence of success include well-received presentations at both math and technology conferences including the TCEA (2018), NCTM (2018), CMC-South (2018-19), and ISTE (2019). To gain a sense of the session content and instructional methods, view the Google Site used at ISTE 2019:


1. Warm-up (10 Minutes): Energize participants with a short Would You Rather activity that exemplifies the many ways to view a math problem and the power of the math apps.
2. MLC apps (20 minutes): In small groups, participants learn about the flexibility of the apps and begin to develop fluency with the features and functionality of the apps. Participants explore how sharing in the apps allows students and teachers to share math problems and thinking.
3. Apply Activity 1 (25 minutes): Working individually or with a partner, participants join a Seesaw class as a student and explore a learning activity that uses an MLC app share code to launch an investigation. Participants show their thinking in the app and then overlay Seesaw tools to further explain their thinking. As a whole group, we explore types of feedback for deepening thinking.
4. Apply Activity 2 (25 minutes): Working individually or with a partner, participants are invited into a shared Google Slide presentation and asked to use an app of their choice to show their thinking about a Math at Home activity. As a whole group, we discuss techniques for encouraging math discourse in a digital environment.
5. Closing (10 minutes): Connect to CCSS Math Practices and ISTE Standards for Students by asking participants to reflect on which standards they engaged in during the session.

Supporting research

1. Principles to Action: NCTM (
Guiding Principle #4, Tools and Technology, states, “An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking."
2. Children's Mathematics: Cognitively Guided Instruction: Carpenter et. al. (
This framework outlines the importance of visual representations in moving students from concrete to representational to abstract mathematical understandings.
3. Joint Position Paper on Technology and Interactive Media: NAEYC and Fred Rogers Center (
The position statement emphasizes the benefits of “appropriate and intentional” technology use with young children.
4. Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning: Jo Boaler (
This paper, along with other resources from YouCubed, showcase the value of visual mathematics.

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Beth Chinderle, The Math Learning Center
Tod Johnston, Independent