Edutopia on Facebook
Edutopia on Twitter
Edutopia on Google+
Edutopia on Pinterest Follow Me on Pinterest
WHAT WORKS IN EDUCATION The George Lucas Educational Foundation

Today's guest blogger is Judy Willis. A former neurologist, Judy is now is an elementary and middle school teacher as well as the author of numerous books on the brain and learning. This post is an excerpt from her latest,

Learning to Love Math.

Before children can become interested in math, they have to be comfortable with it. They must perceive their environment as physically and psychologically safe before learning can occur. Students build resilience and coping strategies when they learn how to use their academic strengths to build math skills and strategies. Your intervention helps them strengthen the networks that carry information through their brains' emotional filters to the area where higher-order thinking skills are concentrated, the prefrontal cortex (PFC). With practice, they will be able to use the highest-level analytical networks in the PFC to evaluate incoming information and discover creative solutions to math problems (in addition to problems in all subject areas). To better understand how your students learn, it is important to first learn how to propel information through those filters and begin building math positivity.

STRATEGY: Arrange Family Conferences

No one wants to add to student pressure, especially when you suspect that a student will suffer emotional or even physical abuse if he or she does not meet certain parental expectations in math. Parents with extremely high expectations for their children are usually motivated by a desire to see their children have more than they have themselves. Unfortunately, when children internalize these expectations and don't fulfill them, they can suffer depression, anxiety, physical illnesses (high levels of cortisol associated with chronic stress lowers the immune response), or psychosomatic illnesses, or they may even inflict physical injury on themselves and others. Family conferences can help parents learn some of the scientific evidence linking the effects of stress to academic success. These interventions will also allow you to explain that the first step to math success is a positive attitude toward the subject matter, not just to the grades associated with it.

You can also suggest ways for these parents to be involved in a positive way. Explain that the brain is most receptive to learning about a topic when there is a clear link between that topic and something the child values. Parents can act as "math allies" if they find ways to integrate real-world math into their child's hobbies and interests. For example, they can encourage their children to calculate how long it will be until their special television show begins if it is currently 3:00 and the show starts at 5:30. They can also help their children compare the costs of things they like (e.g., bicycles, toys, computers) in newspaper ads that offer various percentage discounts off different base prices.

STRATEGY: Retest to De-stress

Reassure all students that if they want to achieve high grades, they will have opportunities that will allow them to regain some sense of control, such as retests. Because progress in math is so strongly based on foundational knowledge, students need to achieve mastery in each topic?which forms the basis from which students can extend their neural networks of patterns and concepts?before they move to the next level. Retests provide opportunities to reevaluate answers and make corrections, as necessary. To ensure mastery, I require that students take a retest when they score under 85 percent. My primary goal is to have students learn the appropriate material so they can move forward with an adequate background for success.

Incorporating accountability into retesting allows students to build skills related to self-reliance, goal planning, and independent learning. Parents or colleagues may voice concerns that students might not act responsibly or seriously once they realize that they'll have a second chance. Accountability increases when you require students to provide evidence of corrective action, such as participating in tutoring, doing skill reviews, or finding textual examples that correctly demonstrate how the type of problem is solved. If the original test and retest scores are averaged together, students understand that they remain accountable for that first test grade. Compared with cheating (an unfortunate response to grade pressure that further decreases confidence and self-esteem), the option of taking retests is a more positive approach to low grades. Retesting takes time on your part, but it shows your students that you respect their capacity to be responsible, successful learners.

STRATEGY: Demonstrate the Value of Math

Key to developing students' interest in math is to capture their imaginations. Instead of allowing them to think of math as an isolated subject, show the extended values of math in ways they find inspiring. If you teach elementary school, find opportunities throughout the day to show students the ways they benefit from mathematics and how it is applicable to their areas of interest. For example, students can use math to determine the number of absent students by counting the students present and then "counting back" to subtract.

In upper grades, cross-curricular planning is a way to achieve this goal. Older students, for example, can solve meaningful problems related to the quantity and price of tickets they need to sell in order to cover their expenses for an upcoming field trip. When you increase your students' positive feelings toward mathematics, you unlock their brains' math-blocking filters, promote long-term memory, and foster greater understanding beyond rote memorization.

What are some techniques you've used to build positivity in your students in math or other subjects?


Comments (49)Sign in or register to postSubscribe to comments via RSS

Erik Bell's picture
Erik Bell
HS mathematics and AP Statistics teacher

I don't think grades are a problem as much as people's perception of grades. For example, thinking that a poor grade is a "punishment." A poor grade is an indicator of your current level of knowledge and application. It is not a means of "control", nor is it an indicator of one who is "abdicating responsibility for their students' learning."
Granted, the above method of learning would be fine in a utopian environment. We, however, must deal in the real world. And, no tradesman would allow his apprentice unlimited time to learn the trade. The time will come when the apprentice must be able to do it or find something else.
One final comment: It would seem to me that someone who would allow his students to "choose how well they'd like to do and be graded on the segment based on their own decisions" is the one who is "abdicating responsibility for their students' learning.

Mrs. Aston's picture

I am an Elementary school teacher who never had a positive experience in a math class and never learned to do math. Now that I am teaching, I work very hard to create positive experiences for my students so that they will not have to experience the same frustration and anxiety I have over math.
I would like suggestions from others on positive approaches to teaching hard subjects that might help out for my 4th Grade class.
Any suggestions?

beth kosiorek's picture

Retesting is a touchy subject in my district. Several years ago our past school board instituted a "success at all costs" policy. Basically they told us that we had to allow students to retest and retest and retest until they got a passing grade. What a mess that was!! It got to the point that students would walk into a room and ask (before they even saw the test) when they could come back and retest. The students saw no reason to study-they just figured they'd retake the test until they got the grade that they wanted. Thank goodness that only lasted one school year.

We now have the ability to make our own decision about retesting in the classroom. As a general rule, I do not; however, that doesn't mean I never would. I teach high school math (Honors Geometry and Algebra II) to middle school students who get the high school credit for it. For the most part, they are the brightest of the bright and take their studies seriously. On occasion they do slip and I will let them take another quiz or test on the topic. I also will allow test corrections for partial credit.

Petrich's picture
Elementary Special Education Teacher, Grad Student

I agree that students should be able to retake a test to mastery. Our students are allowed to retake a test on math concepts up to three times; each time if they master a portion, they do not have to retake that portion. The students feel that they are involved in the process of learning and feel valued. As mastery learning has been implemented in math classes, the understanding of the concepts have increased from the students.

Harry Keller's picture
Harry Keller
President at Smart Science Education Inc.

There's an essential tension between the concept of learning to mastery and the potential for students to attempt to game the system. Are teachers wardens or mentors?

The concept of limited number of retests can help, but doesn't eliminate attempts to game the system.

I have to admit that when I took my two languages exams for my PhD in chemistry, I did not study for either. I had three chances to pass. I had nicely categorized them into "no study," "study," and study as if your life depends on it." I had no way ahead of time to gauge the difficulty of the tests or the strictness of the grading. With limited time, I decided to put my efforts where they'd do the most good and not to try for perfection the first time. It worked because I did pass both, barely, on the first attempt.

I couldn't have passed if I didn't have a knowledge of basic vocabulary and grammar for both French and German. That was apparently the criterion being tested for.

Note that I would have been justified in asking for the dates of the two retests so that I'd know how much time I'd have for "study" and for "study as if your life depends on it."

I know that graduate school is hardly eighth or ninth grade. However, some principles apply widely. If students are familiar with nature of tests given by their teachers, then they can judge how to handle the situation. If not, can you blame them for going into the first test with only cursory studying.

However, all of this discussion misses the most important point. Why do we give tests? I aver that the answer is not obvious. If it's to measure accomplishment, to what end -- to provide remediation or to provide reward and punishment? If it's to motivate students, do you really think that works with all or even most children? If it's to satisfy some requirement from the system, do you think that's a valid reason? If it's to let students know how well they're doing, does the test really measure subject mastery or test-taking ability? Probably both, but how much of the grade is just knowing how to take a test? And how important are test taking skills in life?

I've asked these questions in a challenging manner, but I'm not so wise as to know that answers. I'd like to see less testing, or, rather, I'd like to see testing every single day, but not such formal testing.

Here again, I'm not saying that this is THE answer, just that it might help a bit. Of course, as currently run, you'd have a hard time doing as I suggest and having students answer one or two penetrating questions every day of class so that you and the students can gauge progress.

However, a new era of education is slowly dawning. Students who are online while learning can have a question pop up on their monitors, answer it quickly, and move on. Or the question could be embedded in the highly interactive materials they are working on. If "test" questions could be minimally intrusive (I believe they can), then schools can do it all: measure progress, provide JIT remediation, adjust materials to the individual student, allow mentors to support learning, make learning to mastery a reality, and more. If a student is doing poorly in a subject, then easily move that student into a less challenging version of the subject and let them get their A/B in the alternate course. We should not be giving any grades, IMO, to students except for A and B -- mastered and mastered excellently (in reverse order) -- and incomplete if they've reached the lowest level without success. Students with incomplete would receive some counseling.

We do have to live with a rather imperfect system now. I hope that it's not long before we have an only slightly imperfect system.

I definitely welcome comments because I don't KNOW that I have the right answer. I hope I'm heading in the right direction.

Kristina H.'s picture
Kristina H.
5th Grade Teacher

Mrs. Aston,
I agree that it can be difficult to develop a positive mindset in students, especially for math. I have been teaching fifth grade for eight years, and math has always been my favorite subject. In my opinion, the biggest obstacles are the parents' and students' attitudes about math, as well as their low expectations. I cannot count the number of times I would talk to a parent and hear, "Oh...I was never good at math, so Johnny isn't either." I always find this unbelievably frustrating because the parents do not even realize how much their negativity is affecting the students. Here are some things that I do that seem to help. At Back to School Night, I always address the issue of the "power of suggestion." I show the parents how passionate I am about math. I do the same for the students. I always start off the year reading "Math Curse" by Jon Scieszka and Lane Smith. This is a wonderful and entertaining book that shows how math is all around us. Our first project is always researching everywhere we can find math. I do use many other story books throughout the year, as well. I try to make the lessons meaningful to the students, even if it is only using something that their age group is interested in as the topic for a word problem. I purposely allow them to see me make mistakes, and we talk about how making a mistake is part of the learning process. I never want them to feel "stupid" for doing something incorrectly. Some students may not have confidence in their ability and will be afraid to ask questions, so I have a question box in my classroom. Students can drop in a question for me to address without anyone knowing who asked. I also do a lot of group work. Students learn so much in a collaborative environment, and besides that, they have fun. Recently, we were working on the different methods of multiplication: traditional, lattice, and area model. Most parents only had experience with the traditional method, so for homework, the students were required to teach a parent one of the other methods. They could not stop talking about that homework assignment. I even allowed them to create their own quizzes to bring home. I hope some of this is helpful. Good luck!

Harry Keller's picture
Harry Keller
President at Smart Science Education Inc.

Kristina H.

Have you considered suggesting that students text their question to you. That would me more natural for today's students.

Cossondra George's picture

In a recent article in Teacher Magazine, I described several concrete ways to improve math instruction. You can read the article here: http://www.edweek.org/tm/articles/2010/08/18/tln_george_mathmeaningfulfo...

Until we, as educators, parents, and a nation, make the ability to "do math" as much a part of our culture as reading and writing, no longer accepting the stereo-types of "I don't do math", our children, as a whole, will continue to lag behind other countries. Retesting, reassessing, requiring mastery is just one small component of the paradigm shift that must occur. However, this is a critical component. For too long, failure HAS been an option in our schools. It remains there as a viable option for too many students. They don't do the work, fail the test, do not master the concepts, but just move along the continuum of education, never really growing/maturing mathematically. Until mastery is required as part of the 'curriculum', we are setting them up for failure.

Grades, overall, are a deterrent to learning. School should be able moving forward, gaining knowledge and the ability to think, create and problem solve.

Felicia Johnson's picture

This statement is key in math education. At our school we use a program that spirals concepts throughout the program. Often enough practice is not provided. We supplement with other resources to give students experience and reach mastery. The integration of mathematics throughout the day in meaningful settings spurs the students to try harder. The students know that they will use math concepts beyond the classroom and that it will be useful. I often share stories of how I have used mathematics in the real world and encourage the students to share stories. They smile and beam with accomplishment when they have found a way to integrate our learning into the home life.

Harry Keller's picture
Harry Keller
President at Smart Science Education Inc.

That's a great approach, and I'd like to see even more so that students can also see the value of mathematics in their science classes, for example. They should know that even a carpenter must use mathematics.

Mathematics is a valuable tool that is often taught as an abstract set of ideas.

Sign in to comment. Not a member? Register.