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Supporting Mathematical Thinking with Digital Portfolios

Mathematics is a word that strikes fear in the hearts of many children and adults. Most students enter school eager to learn. Much of their play is mathematical in nature, and they intuitively use and learn new mathematical skills every day. As students get older, many start to shy away from mathematics, saying they are not good at it. Yet, in reality, research tells us that there is no such thing as a math gene.

We live in an age where students are being asked to learn mathematics at very high levels while becoming critical thinkers and problem-solvers. Given this state of reality, how do we cultivate a love of mathematics and help all students learn mathematics at a deep, conceptual level?

Think, Capture, Explain

As educators and parents encourage student ownership of their mathematical learning, three actions are at the heart of the learning process: think, capture, and explain (Figure 1).


Rather than learn procedures taught by others, students need to engage with rich mathematical tasks requiring them to think and reflect. These tasks must rely on the learning students have done while requiring them to use that knowledge in a novel way. They need to think about what they know, what they are being asked to do, what they already know, what they might try, what has worked and what has not worked. This is a messy, yet productive process.

Rather than learn procedures taught by others, students need to engage with rich mathematical tasks requiring them to think and reflect.


As they think, students must represent their thinking. This is where “capture” comes into play. Students may use words, pictures, symbols, and tables, alone or in conjunction with each other to represent their thinking. Capturing helps to make thinking visible to students and to those who work with them.


As students think and capture, they have mathematical conversations with their peers. Students explain their own thinking and give feedback to their peers. This process of mathematical discussion creates a cycle of thinking, capturing, and explaining that helps students find answers to problems presented to them.

1703 Chart Math Thinking 1.3

In the process described above, students take ownership of their learning and are supported on the path toward success. As active learners, they develop positive attitudes about mathematics and become mathematical thinkers and problems solvers. FreshGrade is a partner in this think, capture, and explain process.

How FreshGrade Supports Mathematical Thinking


In FreshGrade, teachers can create rich math learning experiences that include a variety of resources to support student thinking including links to:

  • Explanation videos
  • Interactive math tools
  • Visual aids
  • Math exemplars.

Students can choose resources that best suit their learning needs, coming back to the activity to select additional resources to support or deepen their understanding.


In FreshGrade learners show their learning in a variety of ways. They can:

  • Take a picture of the math manipulatives they used to make their thinking visible
  • Take a photo of their equation, uploading new examples as their understanding grows
  • Use an app such as Screencast-O-Matic to capture their answer within an online interactive math tool
  • Capture their device’s screen while using a math app such as iSolveit: MathScaled or Photomath
  • Upload a PDF of their completed work


In FreshGrade, learners explain and document their learning in a variety of ways. They can:

  • Create an “explainer” video with a tool such as Explain Everything
  • Link to a Google doc that contains their answer and embedded comments that explain their thinking
  • Add comments and reflections to a video, image or document uploaded to their portfolio by their teacher
  • Working with a partner, share devices or comment in peers portfolio, providing feedback and ideas
  • Apply their mathematical learning at home by uploading and commenting on their results, and then receiving comments, feedback and questions from their parents.



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