# Building Math Positivity

*Learning to Love Math.*

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,

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

Why do we need a system at all? Stamping students with a seal of quality assurance implies that all students who receive an A understand fully which is not always true. There is not going to be a way to measure a student's understanding with 100% assurance. There must be better ways of learning beyond cookie cutter carnegie credits.

[quote]Mastery learning has its merits as the article suggests. The whole point of school is to learn. We need to remember that the experience we have and what we learn and NOT the grade should be the focus. Grades merely direct us to areas of need in our students. I wish we could move towards a more useful and positive learning system where students' thoughts are valued over their grades.

Erika Burton, Ph.D.

Stepping Stones Together, Founder

http://www.steppingstonestogether.com[/quote]

Overall grades are only meant to be a generalization of the academic level of a student. They do not give specific information on how that student did in each of the standards assessed. Deciding what you want to communicate to parents and future teachers for that student should be the deciding factor for how you calculate grades. Notes or a rubric should accompany any letter grades to establish exactly what the letter represents.

Letter grades for only one objective assesed at a time should reflect the current mastery level of that student. The point of education is to help students gain the ability to locate information, use it to solve problems in a meaningful way, and make sure our children grow into productive, happy, self-supportive members of society. Let their grades reflect that.

Harry,

Thank you for your suggestion. Texting is absolutely more natural for the students. I always joke with them how I didn't have my first cell phone until I was 21. They can't fathom how I survived! Unfortunately, my school does not allow for teachers to give their phone numbers to students. However, your suggestion gave me the thought of utilizing my school-based email for the students' questions. Thank you!

I am a strong believer of teaching mathematics' value versus its content. Many of my students struggle with math, not because of a lack of understanding, but association or connection they gain from it. Showing them how its applications translate to real world experiences that they encounter on a regular basis how proven quite powerful, and blending this with other discipline, namely science and arts has vastly improved the engagement factor within my class. It is imperative for educators to continuously practice these methods to increase students understanding, thus gains.

The process of retest to distress brought home what it is that some of my veteran counter parts refuse to acknowledge. Not all students are excellent test takers, and many need that extra attempt to demonstrate mastery. Allowing students to explore alternative methods and self-correct gives them a greater confidence in their abilities, and in my experience produces phenomenal improvements on retest. Though extra time is required to undertake such endeavors, the commitment on behalf of students and the reward of mastery makes it well worth it.

This learning of mathematics should go both ways. I feel that it's incumbent on non-math instructors to bring math to bear in their classes just as math instructors should show applications to other areas of endeavor. The result will be much more powerful.

Retest is great, conceptually. Making it practical for those teachers who aren't so quick to sacrifice will take some effort. I have already incorporated retest in my software, which was the first online science lab system to have embedded assessments, and they were both formative and summative.

Now, we're beginning to research the potential of using our patented technology to help bring that real-world aspect to mathematics.

Harry Keller, founder and president

Paracomp, Inc.

Creators of Smart Science(r) Education.

As an elementary teacher, I feel like the most important thing we can do in the primary grades is to create an environment that encourages our students to participate in math. They have to learn that math is a good thing. So many times it is hard for them and they decide they don't like it and then it becomes more and more difficult.

We really need to create a culture of math in our classrooms.

It seems logical that students need to reach competency in each level of math. I know that is a very difficult thing for the teachers, but if our goal is for our students to learn to the best of their ability, why can we not figure out a way to start off by expecting them to reach competency in each subject all along the way.

I just wonder how this would possibly work in our schools.

The goal of testing is to demonstrate what a student knows. The best assessments evaluate student understanding when they can demonstrate knowledge in their most successful manner. Best understanding is rarely demonstrated (or truly tested) on multiple choice or similar standardized tests.

However, when students take written tests that are used as part of their final grade assignment, the test results can become learning tools. If students fail to demonstrate mastery on tests, the responsibility then falls to teacher and student to evaluate how that missing knowledge can be acquired. When metacognition is taught and practiced, the role of the teacher in the process of correcting knowledge gaps will decrease. One of the scaffolding for this metacognition is the use of test corrections sheets.

Below is a template from which sections would be used for test corrections my fifth students completed after failing to demonstrate mastery on a variety of assessments, predominantly the use of grammar in authentic written work, as well as on a formal grammar test. The successful completion of this "test correction sheet" was their "admission ticket" to the retest. Retests, and paper rewriting, were required until mastery was achieved so future learning could be constructed on a strong foundation. (Of course this is teacher time consuming, but if now us - who?)

The use of test correction sheets incorporates accountability into retesting. The reason for some type of accountability for the first test grade is to promote self-sufficient, independent learners, who prepare to their best ability throughout the learning process and for test preparation. It is not necessary to average the two tests together on a 50/50 basis. The system I used in math was to bring any initial test grade up to a passing grade and then averaging the two. Another option was to set the maximum recorded grade for a retest at less than 100%, such as 90%. The student would be recognized for the mastery achievement, but also recognize the responsibility for improving the study habits needed for successful mastery (not just test score mastery) on an on-going basis.

The option of how much to weigh the results of the original test and the retest are many, and best determined by teachers depending on grade level, English language proficiency, and many other factors based on the students, the subject matter, and the weight of tests in final grade calculation.

If others have suggestions for how to promote study and acquisition of knowledge, with the option of retests as part of mastery progress, without students being tempted to minimize effort for the first test if there are no authentic consequences for taking a retest, that would be valuable insight to share with us.

Grammar Test Corrections Grade 5

Please complete the responses to the first 5 sections for each question missed. Your assessment will be based on the completeness and accuracy of your answers.

Question I missed: Write the question number and copy the question itself:

Name of textbook or worksheet and pages I can go to find information about this question:

The correct answer to this question is? Explain fully why that is the correct answer. How did you decide that your new answer is correct?

What could you have studied to be more prepared for this question?

What will you do differently to be more successful in the future?

What success are you proud regarding your learning in this topic (either on the test or in other work you did to demonstrate your understanding?

Perhaps, we should create cultures of history, English language arts, and science as well, but I'm not so sure. Give a person a tool, even a great one, and that person will not learn to use it unless some value to the use is apparent. I always loved math and so was and am an exception, but I understand that some people enjoy history. I did not in my youth. Others feel that way about mathematics.

I began to appreciate history long after I earned my PhD. Until then, it was an old recitation of names and dates, of little value to me -- so I thought. I've learned to appreciate it. Being a scientist, I especially like science history and have recently finished reading "Age of Wonders." I appreciate it because of the insights it provides and the ways it allows me to view my world.

I believe that something similar must take place for algebra, geometry, trigonometry, and calculus. Once people find a use for mathematics in their lives, then other possibilities for learning open up. It may be difficult for a mathematics teacher, most of whom like mathematics of course, to bridge that gap. As long as mathematics is just a bunch of symbols and rules, it will remain elusive for many students. It's the same with history being names and dates, or for science being words, formulas, and procedures. Teachers must somehow get beyond the "stuff" of their subjects into the meta-subject. In science, which I know best, the effort is to get students to understand that, in John Herschel's words, "[the scientist] walks in the midst of wonders." Or, as Shakespeare suggested, you can find "Tongues in trees - books in running brooks / Sermons in stones - and good in everything."

Whatever your subject, you'll have students who consider it dead and dull. Your job is not simply to build competence in the minutiae of your subject but make it come alive. Perhaps, that's too much to ask. Unfortunately, it's the only way that you can coax real learning from your students. (Maybe it's not so unfortunate after all.)

Convince the students that our math class consists of a series of opportunities to learn the math. The first one is the worked-out example in the book (in my-speak a dfu, done for you example). Next is a very similar example that they work out (a udo, you do example). Other opportunities are one-on-one explanations, direct instruction on the board, and homework.

It is very backward to use quizes and tests only for assessment. I make tests and quizes into more opportunities to learn by making them open book and open me (they can ask me questions). I do not allow students to help each other because they just tell the answer without teaching. I used to allow retests, but found an easier way to do it. Retests were too time consuming for the students (and me also). I mark wrong answers with a small red dot and return them. They get one more shot before I count their grade.

I like the concept that a student can try again on the missed questions before anyone has the worked-out solutions. There are many reasons for getting an answer wrong. In general, making a mistake is a learning process but only if you figure out what your mistake was. It's MUCH better to figure it out yourself than to have someone tell you.

If you can manage your class in such a way as to implement this process, then go for it. Notice that this method also will reduce "test tension" a bit.

Great suggestion, assuming that we must continue to give tests. Until there's a better way, I guess that test taking will continue. Designing them to be "open book" also improves learning. You have to work a bit harder to create this sort of test and should reap commensurate benefits.

These principles apply to any class, IMO, not just to mathematics.

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