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.

Putting Students at the Center: Helping Teachers Make Decisions About Instructional Strategies to Ensure the Success of Diverse Learners in Math

As mathematics classrooms are becoming more and more diverse, teachers aiming to help all of their students learn are increasingly challenged. Pandemic-related learning gaps, the arrival of newcomers who may have experienced interrupted schooling, and the increase in the number of students with disabilities in general education classrooms have intensified performance differences among students. It is widely recognized that teachers require help and support to meet the varied needs of the different students they serve. There is less certainty, however, about the kind of support that will help teachers to make this happen.

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.

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?

Honoring Diversity: What, why, and how?

The Math for All team has been reading Carol Ann Tomlinson’s Everybody’s Classroom for the past few months. There are many connections between Tomlinson’s work and our work in Math for All, as well as some key takeaways that deepen our understanding of making math accessible to all students. In this blog post, we explore what honoring diversity means to us and, building on Tomlinson’s work, take a deep dive into a flexible mathematics classroom environment that can enhance our ability to honor students’ diversity as learners.

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.

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.

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.

Translanguaging & Math

October is designated as Celebrate the Bilingual Child Month, and we take this opportunity to recognize and celebrate all the strengths that multilingual children bring to the classroom and to highlight some practices that can support these students in math. In the United States, about 10% of school children are English Learners (ELs). It’s important to note that EL refers to students who are in the process of gaining English proficiency but does not include the millions of students who are bilingual or multilingual and have gained English proficiency, having formerly been classified as ELs. ELs are a diverse group of students, representing many different school experiences, languages, academic strengths, cultural norms, and more. In this blog, I will refer to multilingual learners in recognition of the many students who speak two or more languages and who may be current or former ELs.

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