A Student's Skill-Level Should be Private

A student's skill level should be a private matter, between him and the teacher, and students who are behind should be able to work comfortably, without embarrassment. "They know they should know more. They know they should not be working on tens and ones when their friends are doing division and fractions and all that, and there's no shame in working on it with the computer." Actually, the same principle applies to kids who are off-the-charts advanced: if they just want to relax and do high-...

 Children's Art Has Its Own Logic

Even simple scribbles are meaningful. While it was once thought that kids only scribbled to experience the physical sensation of moving their arm along the page, “now it’s been shown that when children are scribbling … they’re representing through action, not through pictures,” said Boston College’s Winner. “For example, a child might draw a truck by making a line fast across the page and going ‘zoom, zoom,’ and so it doesn’t look like a truck when the child is done, but if you watch the proc...

 Teacher Approval Ends Discussion

After years of classroom research, Dillon (1988) concluded that teacher interventions during student discussions tend to shut down student thinking and student talk. He found this to be particularly true of positive feedback or praise. The rationale, of course, is that when a teacher communicates agreement with one student’s thinking, both the speaker and other classmates conclude that there is no need for further thought because the teacher has gotten the answer he or she was after.

 Discussion Rhythm to Promote Student Participation

Teachers are partnering with students to establish a new rhythm in classroom questioning. This rhythm provides teachers and students with a silence for thinking at two crucial junctions in the questioning process: • Wait Time 1: After a question is posed but before a student is called on to answer. • Wait Time 2: Directly following that student’s response. Almost 50 years ago, Mary Budd Rowe (1969) famously discovered multiple benefits associated with intentionally pausing at these two poin...

 The Double Multiplicative Nature of Fraction or Ratio Equ...

Most real-world numbers aren’t always so nice and neat, with wholenumber multiples. If, say, Plant A grew from 2 to 3 feet, and Plant B grew from 6 to 8 feet, then we would say that Plant A grew 1/2 of its original height, whereas Plant B only grew 1/3 of its original height. Such reasoning exemplifies multiplicative thinking and necessarily involves rational numbers. Consider a final example. If you ask a rising 6th grader to compare 13/15 and 14/ 16, chances are that the student will say t...

 Constructivism

Jean Piaget’s work is the origin of Constructivism, which is the foundation of learning-centered classrooms (Bogost, 2007). Constructivism is a broad theory of learning that argues (quite unlike Essentialism) that what matters in learning is not the accumulation of facts, paradigms, and theories but rather the meaning making that comes from taking these disparate notions and integrating them to form new knowledge. What matters is not the received wisdom handed down from generation to generati...

 Teaching with Pokemon Go

Learning objectives that ask students to assemble and integrate data (like a language or math class) are well-suited to the capture and find aspects of Pokémon Go!. Imagine setting up a variety of PokéStops around your campus. Each one can be visited by students as they go about gathering the data they need to accomplish the learning objective you set. Perhaps after traveling about campus, they have to return to your classroom and use the data they’ve gathered like PokéBalls to solve more com...

 Why Did Everyone Draw that Fancy "S" in Grade School

"The reason kids go through this is probably because it's a Moebius strip," he said, referring to the sort of looped one-surface shapes Escher was fond of drawing. "It can't be drawn continuously, but it does have a perpetual flow." I think he was on to something. Most nine-year-olds can't draw, so when someone hands them a magical recipe to create something fairly cool, on demand—that'll go viral. Especially when the shape has the sophisticated, mathematical lineage of a Moebius strip. Yes...

 Math Exercise: Multiple Approaches to Problem-Solving

For example, if the problem was to fi nd the answer to 8 × 6, students may suggest three options: memorizing the multiplication table for 6, knowing that 8 × 5 = 40 and adding another 8 to equal 48, or adding a column of six 8s. Allowing students to personally choose among approaches all confi rmed as correct and to support their choice will increase their comfort levels. Th is process also builds math logic, intuition, and reasoning skills that extend into other academic subjects and real-li...

 Delay Method of Errorless Math Practice

Prepare a list of the calculations from the flash cards on a sheet of paper. These can be on a template, with multiplication facts at the appropriate level pulled and copied for the student. On these forms, include three columns next to each multiplication question, labeled “correct repeat,” “correct wait,” and “correct response.” Start with review and confi dence building. For example, show the question 3 × 4 = __ on the card and without any delay say the answer. Th e student repeats the que...