Neurodevelopmental Functions

[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.

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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?

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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.
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Imagine two classrooms. In the first, a general education teacher and a special education teacher work separately. The general education teacher takes the lead on instruction and the special education teacher assists and provides additional support, focusing primarily on students with an Individualized Educational Plan (IEP). Communication between the teachers revolves around logistics such as time management. There is little common planning time; each teacher plans independently for their specific students.
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Games are fun. Games are also challenging. Developing a strategy, improving skills, the ups and downs of winning and learning—these all are important components of games. When students engage in mathematical games, many don’t necessarily realize they are doing or learning mathematics but when students practice or apply something they already know or understand, there is growth.
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Three-Act Tasks. Notice and Wonder. Estimation 180. Math Talk. We learn about these leading practices for mathematics education in publications, on social media, and during professional learning events. Many educators find that these strategies are transforming today’s classrooms through increased engagement, constructive risk-taking, and rigorous problem-solving. We may be curious: From a cognitive development viewpoint, why are these techniques so effective?
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Math anxiety is more than just being nervous about math. It is characterized by feelings of panic, tension, and helplessness aroused by doing math or even just thinking about it (Ashcraft & Kirk, 2001). Researchers think that about 20 percent of the population suffers from it. But having mathematical anxiety does not mean that a student is not good at math. Even accomplished mathematicians, such as Laurent Schwartz and Maryam Mirzakhani, reported having suffered from it. Math anxiety is not the result of doing poorly in mathematics; rather, a student may do poorly in mathematics because they feel anxious about it.
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