This Tips for Parents article is authored by Ann Lupkowski-Shoplik from a seminar she hosted for Young Scholar families. She discusses the many aspects of parenting a math-talented child, including: finding mentors, above-level testing, online math programs and the benefits & drawbacks of math acceleration.
The Diagnostic Testing -> Prescriptive Instruction model is useful for tailoring instruction to exceptionally math-talented students. This includes aptitude testing (using above-level tests such as EXPLORE or the SAT), and achievement testing to determine what the student has already learned. The mentor uses the information provided by the testing to design instruction and spend the majority of time working on new material rather than reviewing concepts the student has already mastered. After instruction, the student is again tested with an alternate form of the pretests to determine mastery. Then, the student can move to the next level and the process can begin again.
The DT-PI process has been used extensively in the summer programs offered by university-based talent searches. In these programs, talented young people can complete one or more years of mathematics in a few weeks. This process can be applied during the school year as well, so that students are able to move through curriculum they have already mastered and spend their time studying new information. Sometimes mentors work one-on-one with a student outside of school, and sometimes mentors are assigned to work with small groups of students as part of a school-sponsored program.
We recommend that the student work one-on-one with the mentor (or in small groups with other talented students with the mentor) a total of 2 hours per week. During math time, while other students in the regular classroom are doing their seatwork, the accelerated student can work on mentor-assigned homework.
Finding a mentor
Certified teachers, retired engineers, and college students pursuing education degrees have made excellent mentors. The first requirement is that the mentor should know the math and be good at communicating that to students. It seems to work best if the mentor is a certified teacher. School personnel tend to accept certified teachers’ recommendations more readily and would therefore be more likely to give credit for work completed with that mentor. Parents can locate mentors by looking within their local school district as well as contacting the math department or math education department in local colleges.
Benefits of Math Acceleration
Bright students who are accelerated in math experience a curriculum that is more closely matched to their academic needs and abilities. They also benefit from being placed with other students who have similar abilities. Accelerated students who are placed in a regular class at a higher grade level are more likely to receive credit for work completed (compared to students participating in an outside-of-school program such as independent tutoring). Subject-matter acceleration is a relatively easy, inexpensive way for a school to provide instruction at an appropriate level for math-talented students. This has long-term positive effects as well: students who accelerate in math tend to take more math, study higher levels of math, and pursue careers that use their mathematical abilities compared to equally able students who do not accelerate.
Drawbacks of Math Acceleration
Accelerated students may not have a lot in common with the older students in the classroom. Steps should be taken to ease the transition for the young student. If the receiving teacher is not in favor of the acceleration, the transition can be difficult. Other challenges include scheduling (if the math class is at the same time as another important subject) and transportation (if the desired class is in another building).
What should we consider when accelerating young students in mathematics?
- Students need to be challenged in mathematics throughout their school years.
- Students should have a strong mathematical base. They need to have a good number sense and a good understanding of arithmetic before plunging into advanced mathematics.
- Rather than randomly presenting interesting math problems at the students, it’s better to provide a systematic process for them, so they study mathematics in an organized fashion and ideas are allowed (and encouraged) to build upon each other.
- Some children are ready for algebra in 5th grade or 4th grade, maybe even younger. We do have to satisfy ourselves that they have a good understanding of pre-algebra concepts. The Diagnostic Testing-Prescriptive Instruction model is very useful here.
- Two useful tools that were specifically designed to measure students’ readiness for algebra are the Iowa Algebra Aptitude Test (Riverside) and the Orleans-Hanna Algebra Prognosis Test (Harcourt Brace Educational Measurement). Both of these tests have been used successfully to measure young student’s readiness for algebra. Either test can be administered by a teacher.
Writing Down Your Thinking
Math-talented students need to learn this important skill. If the work is too easy, the students are likely to continue solving the problems in their heads and develop poor study strategies. When students are given more challenging work, they are more motivated to write down their thinking. To continue encouraging this type of behavior, offer to be a scribe for your child (some — not all — the time!), have a discussion about how he approached solving the problem, ask her to record how she solved it on a tape recorder, or have him write it on a blackboard or whiteboard rather than on paper.
For talented students, above-level testing is critical. This means using a test that was designed for older students. For example, the EXPLORE test, which was developed for 8th graders, is used for academically talented 3rd – 6th graders because it raises the “ceiling.” It allows us to have a long-enough yardstick to measure their math talent. Above-level tests also allow us to differentiate talented students from exceptionally talented students, which is useful in tailoring advice to a specific child’s abilities and needs.
We also need to measure math achievement. Although an aptitude test (such as EXPLORE) tells us a lot about a student’s abilities, it doesn’t give us enough specific information about topics the student has mastered or has not mastered. Achievement tests are designed to gather this information. Examples of achievement tests include the Stanford Diagnostic Math Test, the Sequential Tests of Educational Progress (STEP), and the Comprehensive Testing Program (Educational Records Bureau).
Online Math Programs
One of the major benefits of studying math via an online mathematics program is the opportunity to study a subject at the right level of challenge. The student can work at his or her own pace and at the right level. One of the most difficult aspects of online math programs is that the student should be highly self-motivated and an independent learner. Some students thrive in this atmosphere, others feel isolated and find that they prefer being in a classroom setting. To give a student participating in an online program more opportunities to interact with others concerning mathematics, consider joining a math club or participating in math competitions. Participating in a summer program offered by one of the university-based talent searches provides the appropriate level and pacing while also keeping the student with a true peer group.
Some Final Thoughts
- Objective information about your child’s abilities and achievements in mathematics is critical. Have your child tested (in school or privately) using above-level tests. Take the time to understand your child’s test results. Objective information obtained as a result of the testing is much more powerful to school personnel than opinions of parents or others. However, parents’ observations of the kinds of things your child enjoys doing, a portfolio of math projects, and a list of math programs that he or she has enjoyed combine with objective test results to give a more complete ‘picture’ of the student’s abilities and needs.
- Parents may need to educate school personnel, if the school personnel have not had the opportunity to learn about gifted students, specifically math-talented students. Some useful resources are included below.
- Assouline, S. G., & Lupkowski-Shoplik, A. (2005). Developing Math Talent: A Guide for Educating Gifted and Advanced Learners in Math. Waco, TX: Prufrock Press.
- A Nation Deceived: http://www.accelerationinstitute.org/nation_deceived/ summarizes the current reseach on acceleration. Please share this information with school personnel!
- George Lenchner’s Creative Problem Solving in School Mathematics (available from www.moems.org).
- Ed Zaccaro’s Challenge Math (https://www.hickorygrovepress.com)
- Talent Search programs (such as those offered by Johns Hopkins, Carnegie Mellon, Northwestern, Duke, the University of Denver, and the University of Iowa) provide testing as well as classes for exceptionally talented students.
- Distance learning programs such as the University of Nebraska-Lincoln online high school (https://highschool.nebraska.edu/).
- Another excellent website is Math Forum (https://www.nctm.org/mathforum/).
- www.hoagiesgifted.org/math.htm contains links to other sites your child might enjoy.
- The SOMA cube: https://www.fam-bundgaard.dk/SOMA/HISTORY.HTM
- The Math Olympiads for Elementary and Middle School Students (www.moems.org) provide challenging problems for students but do not require an understanding of algebra.