October 1, 2025Learning, Manipulatives, Mathematicsby Math for All

Manipulatives: Not Just for Kids, Not Just for Strugglers

By 1953, scientists knew much about DNA, including its chemical components and how they related to each other. There was even X-ray crystallography of the molecule. However, the structure of DNA in three-dimensional space remained a mystery. James Watson and Francis Crick experimented with building wooden models, creating several until they found the one that fit all of what was already known. This work, which relied heavily on the use of physical models, earned them and their colleague, Maurice Wilkins, a Nobel Prize. Their discovery of the physical structure of the DNA molecule was a breakthrough that lead to massive advances in the understanding of genetics and in medicine.

September 1, 2025AI, Mathematicsby Math for All

AI: A Coaching Thought Partner

My husband is a data scientist, so I’ve been hearing about AI and ChatGPT a lot over the past year. When I listened to him share his experiences using this generative AI tool, I—like many other educators—wasn’t sure how we should be using it. Educator and researcher Donna Shrum was encouraged to try out AI in her teaching practice by her colleagues. She wrote about her positive experience using it to give immediate feedback during a writing workshop in an opinion piece in Education Week (Ferlazzo, 2025).

June 1, 2025Language, Mathematics, Neurodevelopmental Functionsby Math for All

Strategies for Math Intervention Can Benefit All Students

Every math classroom is filled with students who have different strengths, experiences, and learning needs. While research-based math intervention strategies are designed to support students who may struggle, these same practices can also strengthen learning for all students.

This blog post explores two powerful practices that can help students deepen their understanding of mathematical concepts: building mathematical language and using models and manipulatives (also known as representations). Language and representation might seem distinct at first, but in reality, they are constantly interacting. When students are explaining their ideas aloud or showing their thinking by using models, language and representations work together to help students make sense of math.

May 1, 2025Learning, Mathematics, Parentsby Math for All

Supporting Students with Limited or Interrupted Formal Education

Years ago, I worked in classrooms and in after-school settings with refugee youth at a school that was established specifically for students newly arrived in the U.S. The teachers who founded the school in the Bronx promoted literacy as a means to help students succeed in their world. They were skilled and reflective practitioners. They designed project-based curricula that allowed students to draw on their personal backgrounds, and understood how to integrate language and content in ways that were engaging for adolescents. Yet as rich and thoughtful as the curriculum was, a subset of students challenged their competence. These Multilingual Learners (MLLs) were designated as Students with Limited or Interrupted Formal Education (SLIFE).

December 1, 2024Language, Mathematics, Neurodevelopmental Functionsby Math for All

Mathematical Discourse & Our Students

[T]here is frequently more to be learned from the unexpected questions of a child than the discourses of men, who talk in a road, according to the notions they have borrowed and the prejudices of their education.

—John Locke, Some Thoughts Concerning Education, 1693

When John Locke wrote these words at the close of the seventeenth century, the world was in the midst of the Enlightenment and change was in the air. Mary and Edward Clarke, Locke’s friends and fellow aristocrats, began seeking his advice on educating their eldest son, who was not having much success with what was then considered a typical education for boys of his class. Locke’s advice was long and specific, but he elevated virtue, a love of learning, and practicality above all. He warned the Clarkes that any tutor they found for their son should “not so much to teach him all that is knowable, as to raise in him a love and esteem of knowledge.” Locke also spoke of a child’s curiosity and how to “keep it active and vigorous” through acknowledging and answering their questions and taking seriously that which interests them. By the end of the eighteenth century, Locke’s influence on educational theory was well known and well regarded.

May 1, 2024Learning, Mathematics, Parentsby Math for All

Parents and Teachers as Co-Constructors of Children’s Success as Mathematical Learners

Parents as advocates. Parents as allies. Parents as collaborators. Parents as their children’s first teacher and “top educator,” with the home as the “premiere” classroom. Make no mistake, teachers: Parents play an invaluable role in the lives of their children as learners. Parents’ close-up view of how their children learn is an essential piece of the metaphorical puzzle that gives a fuller picture of their children’s abilities when matched with the puzzle piece held by teachers. Undoubtedly, parents begin gathering information about their child during the formative years and that wealth of information continues to grow throughout their child’s journey at home and in school.

March 11, 2024Language, Mathematics, Neurodevelopmental Functionsby Math for All

The Problem with Word Problems

Word problems can be confusing. Period. They can be set in an unfamiliar context. They can include superfluous information. They can contain ambiguous language. They can be written to trick or confuse. They can be overly complex. Here’s an example that meets a few of these criteria:

The pet store sells crickets for lizards. They charge $3.65 per two-dozen crickets, but right now they are offering a 15% discount on any purchase over $40. What will be the total cost for 276 crickets if there is a 6% sales tax?

January 3, 2024Learning, Mathematics, Neurodevelopmental Functionsby Math for All

Looking at a Student at Work

Teachers look at student work often and for many purposes. Many look individually, as a way to better understand student thinking and to inform instructional choices. Other times, looking at student work may be collaborative, such as when co-teaching, during a professional learning meeting, or as part of an instructional, curricular, or school reform decision-making process. These types of collaboration often take place after student work is completed and when students are not present. The Math for All approach combines aspects of both individual and collaborative ways of looking at student work by including planning and debriefing with colleagues and an emphasis on an observation process for looking at a student at work—attending carefully in real time to one student and their ways of learning.

December 1, 2023AI, Learning, Math Classroom, Mathematicsby Math for All

AI, Oh My! A First Foray into ChatGPT and its Usefulness to Math Teachers

Recently, I’ve been reading a bit about AI—artificial intelligence—the technology that is supposed to change the world as we know it, including the world of teaching. The changes are anticipated to be so momentous that the President issued an executive order to make sure that the development of AI is “safe, secure, and trustworthy.” In the world of education, students are already using AI to do their homework. After all, it can write papers, analyze texts, and solve problems. Some even say that AI might eventually make teachers obsolete. That certainly hasn’t happened yet, and while AI tools can help students cheat, they also have the potential to help them learn and help their teachers develop better lessons that deepen learning.

November 2, 2023Learning, Mathematics, Visualizationby Math for All

Why is Visualization Important for Learning Mathematics?

How often do we ask students to show their mathematical thinking or explain an answer using words, pictures, or diagrams? If you’re like most of us, the answer to that question is probably “Very often”! But what does it mean to express mathematical ideas and processes through these modalities? What is our expectation that students’ work contains language that connects to diagrams and pictures? Are representations of thinking created after a solution is found, or are pictures, diagrams, and language part of developing a solution? To explore these questions, let’s first take a close look at four mathematical tasks, each requiring increasingly complex conceptual understandings, and the visual representations and language that can support understanding these tasks.

Mathematics