This Tips for Parents article authored by Ann Lupkowski Shoplik, Ph.D is from a seminar she hosted for Young Scholar families. A number of topics were discussed in this seminar, including program options and opportunities for math-talented students.
In-School Options for Math-Talented Students:
- Enrichment in the regular classroom. This puts the ‘burden’ on the regular classroom teacher, who looks for math activities for the talented child to do. This is sometimes busywork. However, some capable teachers excuse students from certain assignments to allow time to work on more challenging mathematics. Susan Winebrenner’s book, Teaching Gifted Kids in the Regular Classroom (https://susanwinebrenner.com/), is a very useful tool for teachers who would like to structure their classrooms this way.
- Independent projects in mathematics.
- Allowing the student to work on his/her own in the back of the classroom. This can be a step up from not allowing the student to do anything different from the regular curriculum. However, it has the disadvantage of putting the burden on the child. He or she has to show enough initiative and focus to work in the back of a busy room while the other children are moving about and participating in other activities. This can be tough for a young student!
- Pulling the student out one or two periods a week to work on math with the gifted coordinator or some other individual. Advantages: individual attention, math may be more appropriately challenging. Disadvantages: what does the child do during the other 4 days of math?
- Grouping several math-talented students together to study mathematics in a separate class or grouping students within the regular classroom. This “ability grouping” has fallen out of favor with many school districts, in spite of the research that strongly supports this arrangement for gifted students.
- Grade-skipping or accelerating in mathematics.
- The DT-PI Model. This model was first developed by Dr. Julian Stanley at Johns Hopkins University. It is designed to match the level and pace of math instruction to the students’ abilities and achievements. Above-level aptitude tests measure the student’s abilities. Diagnostic pre-testing indicates what the student knows and does not know. During the prescriptive instruction phase of the model, the mentor works with the student on topics he or she has not yet learned. The focus is on new concepts rather than on material the student has already mastered. The mentor can work with one or more students at a time, as long as the students are on a similar level. Finally, the mentor administers a post-test to determine mastery. The DT-PI model is a powerful tool for working with math-talented students. It identifies the gaps in a student’s background and allows a process for the mentor to work with the student to fill in those gaps. It allows the student to study mathematics at an appropriate level and pace. The DT-PI model has been used both in and out of school.
Challenges of Math Acceleration
- “Mismatch” between your child’s age and social development and those of the older kids in the math class.
- Transportation to another building for math class may be difficult.
- Always missing certain activities due to scheduling
- Encountering teachers who are opposed to acceleration and try to interfere with a student’s success
- Long-term planning: the student needs to be consistently challenged in math every year. We want to make sure students get the right level of math each year and they don’t have to sit out of math for a whole year or even repeat the same math class.
- The perception that accelerated students might “run out” of math. The students will never run out of new math to study, but their school might not offer the right level of math for them. Students might need to go to a different building, have a tutor, or participate in a distance learning program. Although it is important to think about the long term, the possibility that a student might “run out” of math is no excuse to allow the student not to be challenged in math now.
Opportunities Provided by Math Acceleration
- When taking a “real” math class with older students, your child is more likely to receive credit for work completed. If he/she studies math with a mentor or outside of school, your school might not give credit for the work.
- Finding a more appropriate match between the students’ abilities and the curriculum
- A chance to interact with students of different ages
- Excitement about learning something new
- The chance for more opportunities because the student is already advanced
- 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 in math.
A lot of useful information can be gained from taking an above-level test. These students already do very well on achievement tests that compare them to age-mates. They get everything right or almost everything right on the test. The “yardstick” (the grade-level test) that measures their talent is too short. Above-level tests, designed for older students, make the yardstick longer so we can more accurately measure a student’s capabilities. Above-level tests also allow us to differentiate the talented students from the exceptionally talented students. This information helps us to tailor advice to your child’s abilities and needs
What should we consider when we’re thinking about giving our young student algebra?
- We want students to be challenged in mathematics throughout their school years.
- We want students to have a strong mathematical base. They need to have a good number sense and a good understanding of arithmetic before they go on to algebra.
- Rather than randomly throwing interesting math problems at kids, we need to set up 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 are the tests that were specifically designed to measure students’ readiness for algebra: 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.
Finding a mentor
If you are simply looking for a mentor who can help your child to have fun and explore math, then any responsible adult who is good at math and enjoys working with children might be a good mentor. If the primary purpose is to complete a course in math for school district credit, then it’s important to find a certified teacher who is also very good at math and enjoys working with children. Graduate students (math majors or math education majors), high school teachers, and retired engineers have all been good mentors.
Some Final Thoughts
- Parents know their children. They know their strengths, their likes and dislikes, and their history.
- Objective information is critical. Have your child tested (in school or privately). Use above-level testing information. Learn how to understand your child’s test results. This objective information is much more powerful to school personnel than opinions of parents or others. Along with the testing, parents’ observations are really important, including your observations of the kinds of things your child enjoys doing, a portfolio of math projects, or a list of math programs that he or she has enjoyed. All of this information together is important.
- 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.
- It’s always best to take the approach that “we’re on the same team” with school personnel. Try to avoid confrontations. “How do we solve this problem together,” not “You’re not doing enough for my child.”
- Know when you have to give up. It’s admirable to keep trying to make things better for your child. However, sometimes the situation can’t be improved. Can your child change to a different classroom? Can you just tolerate the situation in school but hire a mentor/tutor to work with your child at home? Do you need to change schools?
- Trust your instincts as a parent. It’s good to be informed about different options and opportunities, but don’t feel obligated to take advantage of every one. Your child is a child, and he or she needs time to play and be a kid, too. You parents also need time to kick back and relax.
- Assouline, S. G., & Lupkowski-Shoplik, A. (2005). Developing Math Talent: A Guide for Educating Gifted and Advanced Learners in Math. Waco, TX: Prufrock Press.
- Math clubs and competitions (such as MOEMS http://www.moems.org) give students the opportunity to interact with other students who enjoy mathematics.
- Talent Search programs (such as those offered by Johns Hopkins, Carnegie Mellon, Northwestern, Duke, and the University of Iowa) bring exceptionally talented students together with excellent teachers.
- Distance learning programs provide challenges to students outside of school.
- For books and other resources in mathematics, check http://www.hand2mind.com/, https://www.pearsonschool.com/), and https://www.prufrock.com/.
- Math Forum: https://www.nctm.org/mathforum/
- Hoagies’ Gifted Education Page – Math http://www.hoagiesgifted.org/math.htm contains links to other sites your child might enjoy.
- George Lenchner’s Creative Problem Solving in School Mathematics (available from http://www.moems.org).
- Ed Zaccaro’s Challenge Math: https://www.hickorygrovepress.com
- The Art of Problem Solving website: https://artofproblemsolving.com/
- The SOMA cube: https://www.fam-bundgaard.dk/SOMA/HISTORY.HTM