Students and teachers often approach math with a single goal in mind: to get the right answer. But teachers must resist the urge to simply teach a procedure, writes educator LauraMarie Coleman. Instead, they should make a conscious decision to facilitate a discussion that leads to deeper student learning.

When professional learning is interdependent, a teacher's individual success hinges on the efforts of the entire team. Leadership experts Jenni Donohoo and Ann Mausbach explain why that's a good thing.

The author presented a math task asking all his 3rd graders to find ways to count seven sets of eight donuts, arranged in grids of two-by-four. He hoped this task would lead students toward fluency in single-digit multiplication, albeit in a manner that was inherently personalized learning, with students choosing their own methods to reach an…

Pre-assessments at the start of teaching new content yielded information on what her students knew and might need, this math teacher found, but led many students to get nervous at a unit's beginning. To gauge students' understandings about math in a more inviting, stress-free way, she simply gave them drawings of protractors and asked "What…

One day a teacher writes 12 = ___ + ___ on the board. "You wrote it wrong," says one of the 1st graders. "You can't write the answer first!" exclaims another. As teachers in classrooms across the United States put the new mathematics standards into practice, they'll face countless examples like this one. When teachers…

Learning progressions detail the incremental steps that students take as they learn to master a skill. These progressions are based on developmental research about how students learn and how their thinking develops as a result of instruction. A typical progression not only describes the stages that students must master, but it also shows what…

In some math classrooms, students are taught to follow and memorize procedures to arrive at the correct solution to problems. In this article, author Mike Flynn suggests a way to move beyond answer-getting to true problem solving. He describes an instructional approach called three-act tasks in which students solve an engaging math problem in…

Teachers often express to Marulyn Burns their worry about the need to "cover the curriculum." In response, she draws on one of her favorite quotes: "You don't want to cover a subject; you want to uncover it." This quote is from "The Having of Wonderful Ideas and Other Essays on Teaching and Learning" by Eleanor…

By simply asking students how they got the answer to a problem, math teachers can open the door to stimulating discussions in class. But how can they make sure those discussions promote mathematical understanding? Allison Hintz and Elham Kazemi explain that teachers need to know what the goal is for a discussion and plan accordingly. The authors…

The traditional method of teaching math--showing students how to do a procedure, then assigning problems that require them to use that exact procedure--leads to adults who don't know how to approach problems that don't look like those in their math book. Seeley describes an alternative teaching method (upside-down teaching) in which teachers give…

Being able to find the correct answer to a math problem does not always indicate solid mathematics mastery. A student who knows how to apply the basic algorithms can correctly solve problems without understanding the relationships between numbers or why the algorithms work. The Common Core standards require that students actually understand…

The Common Core standards distinguish between domain-specific vocabulary (topic, point on a graph) and general academic vocabulary (consist of, analyze), but is this a false dichotomy, the authors ask? Analyzing character development, they point out, is not the same as analyzing data. This has implications for vocabulary instruction in the areas…

Considering the nature of the complex prose that K-12 students today must learn from, in light of the Common Core State Standards, students need to read informational texts on a meaningful level-and with enthusiasm. Teachers, Brozo says, need to achieve three goals: motivate students to read informational texts, expand students' background…

Graphic novels (book-length fiction or nonfiction narratives told using the conventions of a comic book) bring together text and image in a way that seems to capture students' imaginations. Right now, there is little more than anecdotal research about how graphic novels can be used within specific middle school and high school disciplines. As…

Summit San Jose is part of the Summit Public Schools network, a group of charter schools in California's Bay Area. In 2011, when Summit San Jose first opened its new high school with a cohort of 9th graders, the teachers decided to pilot Khan Academy. At the time, they had piloted their math resources and platform with five classrooms in Los…