Long-View supports the learning of both our amazing student population, as well as the learning of schools from across the world. Through the number lab, our joint venture that is focused on teacher education, Long-View Micro School students and faculty share in the mission of helping other teachers meet the challenge of educating children at high levels in mathematics….
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At Long-View, we spend a significant amount of time investing in the learning culture of our school, with particular attention paid to how this translates within our mathematics classrooms. As Harvard educator Dr. Richard Elmore has so often made clear, the “default culture of American instruction” contains “certain robust patterns of instructional practice that are unique to the US and that are highly destructive to higher level student learning.” From our standpoint, these highly destructive instructional patterns are easily observed within American math classrooms and at Long-View we seek to disrupt these and nurture within Long-View math classrooms instructional practices that support high cognitive demand and high levels of learning among all students. This starts with deliberate work cultivating an environment that attends in an intentional manner to attitudes, beliefs, customs, and ways of interacting that resist the “default culture of schooling”….
Having been fortunate to observe a variety of math classrooms, especially within the independent school sector, we’ve come to learn a number of things, which we will write about across several blog posts. Today we are focused on the lack of metacognitive instruction and coaching within many math classrooms.
Metacognition research has assisted educators in changing the way we view learning. We know high achieving students usually apply metacognitive processes in their learning and problem solving. And students who apply metacognitive processes tend to be higher achievers. Recent studies have shown that even young children can apply metacognitive processes when the tasks fit their interests and capabilities. And any age-related development may likely be due to lack of appropriate exposure in school....
If you step into a Long-View mathematics class, you’re apt to hear students reading mathematics expressions using language that seems a little different.
In reading an addition expression such as 41 + 17, for example, you’d hear a Long-View student say “forty-one and seventeen” rather than “forty-one plus seventeen.” While this may seem like a subtle substitution, there is a great deal of deliberate thought underneath this use of language that supports our young mathematicians as they develop strong conceptual understandings that will transfer across all of arithmetic to Algebra. Language is actually one of the most under-utilized models in school mathematics. Not at Long-View....
This past week Long-View mathematicians were presented the following problem:
9 – 3 ÷1/3 + 1
Do you know the correct answer?
This expression went viral in Japan a few years ago and only 60% of Japanese 20-year-olds could solve it correctly.
So why is it that most of the Long-View students solved this problem correctly (during the 6th week of school, no less)? Long-View kids know to look at a complex expression and....