“They can assure themselves and don’t have to wait for the teacher to come around and say, ‘yeah, you got it.'” Saul said of the approach. She makes sure students have time to work independently before they share their strategies with one another, a time when they practice using math language and explaining their thinking. Meanwhile, Saul is rotating around the room, supporting students and pushing their thinking along. One of the most important parts, she says, is when she invites students to come to the front and share their solutions. This student-led solution time reinforces the class culture and helps students see one another as experts.

Algebra is another important area of math and is often seen as the gateway subject to higher math. While students may see algebra as a time to memorize equations, strong teachers know this is an incredibly important time to make sure students’ math reasoning is solid. In the video below, math coach Audra McPhillips explains how she leads eighth graders through the process of developing a conjecture about functions. She asks them to look for patterns and has intentionally given them three examples that have something in common (the rate of change) and a point of difference (the y-intercept), meant to push student thinking a little further.

McPhillips does very little telling students how to think, instead she lets them develop a conjecture that they believe to be true beyond the examples in front of them and requires them to explain why. Note, she doesn’t expect all students to write a conjecture by the end of the lesson, but she does have them fill out exit slips to record what they learned and how far they got as a quick reflection before they head to their next class.

Education researchers are beginning to validate what many teachers have long known — connecting learning to student interests helps the information stick. This seems to work particularly well with math, a subject many students say they dislike because they can’t see its relevance to their lives.

“When I started spending time in classrooms I realized the math wasn’t being applied to the students’ world in a meaningful way,” said Candace Walkington, assistant professor in the department of teaching and learning at Southern Methodist University. She conducted a year-long study on 141 ninth graders at a Pennsylvania high school to see whether tailoring questions to individual student interests could help students learn difficult and often abstract algebra concepts.

Researchers studied a classroom using Carnegie Learning software called Cognitive Tutor, a program that has been studied frequently. In the study, half of the students chose one of several categories that interested them — things like music, movies, sports, social media — and were given an algebra curriculum based on those topics. The other half received no interest-based personalization. All the problems had the same underlying structure and were meant to teach the same concept.

Walkington found that students who had received interest-based personalization mastered concepts faster. What’s more, in order to ensure that learning was robust, retained over time, and would accelerate future learning, she also looked at student performance in a later unit that had no interest-based personalization for any of the students. “Students that had previously received personalization, even though it was gone, were doing better on these more difficult problems as well,” said Walkington.

**[RELATED: Nine Tenents of Passion Based Learning]**

She also found that struggling students improved the most when their interests were taken into account. “We picked out the students who seemed to be struggling the most in Algebra I and we found that for this sub-group of students that were way behind the personalization was more effective,” Walkington said. Specifically, the study tested students’ ability to turn story problems into algebraic equations — what’s called algebraic expression writing.

“That’s one of the most challenging skills to teach students because it’s a very abstract skill,” Walkington said. She hypothesizes that the abstract nature of the concepts actually allowed students to more easily generalize and apply the same knowledge to a wide variety of situations and to more difficult problems in later units.

Walkington is working to expand her study to all the ninth graders in a school district of 9,000 students. “The bigger, you make it the harder it is to tap into the interests of students,” Walkington said. But she’s confident that there are some general-interest categories that many students share, like sports and movies.

**WITHOUT TECHNOLOGY**

But can this tactic help a teacher with a class of 30 students that doesn’t use this particular math software? Teachers in the studied school asked this question, so Walkington developed a practical guide for them to use. She chose to conduct the study using the Carnegie blended learning curriculum because it was easy to layer on the interest-based personalization to the existing program. It also provided her with a wealth of data about how students approached the problems. That said, a teacher could use interest-driven questions without any math software.

From her guide:

Two Examples of PersonalizationPersonalization can be accomplished on simple mathematics story problems. For example, a typical algebra problem might read: “A particular assembly line in an automobile company plant can produce thirteen cars every hour.” Based on this scenario, students might be asked to write an expression or solve for how many cars are produced after certain numbers of hours. Below are some examples of how this problem could be personalized:ShoppingThe website of your favorite clothing store, Hot Topic, sells thirteen superhero t-shirts every hour.:Computers: A recent video blog you posted about your life on YouTube gets thirteen hits every hour.Food:Your favorite restaurant “Steak ‘n Shake” sells thirteen caramel pretzel shakes every hour.Music:Pandora Internet radio plays thirteen of your favorite pop songs every hour.Cell Phones:On your new iPhone 5 you send your best friend thirteen texts every hour.While these problems involve relatively simple modifications, our research has shown that this type of personalization is effective for improving student learning.

**[RELATED: How the Power of Interest Drives Learning]**

Helping students see algebra in their daily lives is one way to apply this technique. In the same way, video games have point systems that allow players to level up after they’ve won a certain number of points. Students understand these systems intimately, but aren’t often asked to think about them through the lens of algebra. Similarly, students have a sense of how often they text and how their texting habits compare to others, but they aren’t often asked to express that relationship in an equation. Helping students to see the math in their own lives could get them thinking differently.

Another way teachers can personalize algebra would be to ask questions that are likely to appeal to student interests. Walkington found that students find story problems that deal with social issues of communicating with family and friends accessible. Concepts of work and business were less accessible, as were problems that dealt with physics concepts like motion, time, and space. Problems based on home references like pets were more interesting to students and garnered better results. Using these broad guidelines, teachers can try to write questions that appeal to more students.

Walkington has also experimented with having students personalize their own math instruction, writing, sharing and solving story problems in small groups. She’s found that even students with relatively little math knowledge can create complex story problems and express them with algebra if there’s interest in the topic. This is a great way to have students construct their own knowledge while applying it to their passions.

A great time to use this tactic is when introducing an abstract idea or foundational topic in algebra. That’s when educators will see the most benefit of grounding the topic in student interests, Walkington said. It’s important to elicit student interest in the math concepts, however, and not just the question’s topic. This intervention could work well with struggling students too.

“We have to layer the algebra onto those relationships that already exist,” Walkington said. “And that’s not an obvious thing because it doesn’t look anything like algebra at first. It just looks like a relationship.” She’s confident from her own experience of learning to love math that when students see its applicability to things they care about, they learn more easily and deeply.

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– John Sipe, Jr. Senior Vice President, National Sales Manager, Houghton Mifflin Harcourt, on the company’s year-long pilot program with the iPad algebra curriculum. I’ll be posting the interview in its entirety over the next couple of days.

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