Mar 25, 2019
Every Child has the Right to Learn Something New Every Day: Advocating for your Student with Exceptional Math Promise
If there were a Bill of Rights for students in our math classrooms, the right to learn something new every day might be at the top of the list. It is often assumed that our brightest mathematics students do not need specialized instruction in the same way as our most struggling learners, but that is far from the truth. Academically gifted students need coaching, mentoring and feedback as much as any other student in order to develop their unique gifts and talents. Take for example Albert Einstein, Michael Jordan, Marie Curie, Beethoven, Carl Sagan, Katherine Johnson: all examples of gifted individuals in their own right, all of whom benefited from the advice, guidance, and specialized instruction of a coach or teacher.
The National Council of Teachers of Mathematics (NCTM) in their October 2016 position paper titled, “Providing Opportunities for Students with Exceptional Math Promise” acknowledges that there are mathematically exceptional students who “demonstrate patterns of focused interest [in mathematics]; are eager to try more difficult problems or extensions or to solve problems in different, creative ways; are particularly good at explaining complex concepts to others or demonstrate in other ways that they understand materials deeply; and/or are strongly interested in the material.” NCTM carefully chooses to identify such students as “students who show exceptional promise” over the terms “gifted” and “talented” because historically those terms refer to students who were identified through a single-assessment that is often not math-specific. Also, historically the terms “gifted” and “talented can be associated with a fixed mindset as it relates to one’s innate abilities in mathematics (Boaler). While the National Council of Teachers of Mathematics (NCTM) is readily willing to acknowledge students that show exceptional mathematical promise, it also is quick to acknowledge that each and every student has mathematical promise.
So what can you do to advocate for services that meet your child’s unique math needs and what opportunities are there to extend their learning beyond their age-alike peers? It starts by knowing what differentiated options might be available to your student.
The key to flexible grouping is that it is indeed flexible. Students are placed in groups based on interests or targeted instructional needs. Students are receiving “just right” instruction at “just-in-time” moments to advance their mathematical learning. It allows for academic differentiation that meets the dynamic needs of students at all ability and interest levels. Unlike tracking, it does not hold students in a predetermined pathway but allows for constant adjustments based on their mathematical needs, understanding that students’ needs are not static and just because a student excels or struggles in a particular area, that does not mean that they will continue to excel and struggle in all areas.
While research has shown that heterogeneous-ability math groups are beneficial to students’ learning, especially those students who have traditionally been considered low-performers (Boaler, 2005), research has also shown that gifted math students benefit from being grouped with other gifted math students for at least part of their day. Successful teachers of the gifted realize that their gifted students make greater academic gains when interacting with intellectual peers than they do in mixed-ability groups (Croft, et. al.). Options for grouping might include self-contained gifted classrooms, pull-out programs, across-grade grouping, or within-class flexible grouping to name a few. Across-grade grouping involves sharing students across grades, grouping students according to their academic needs, giving gifted students an opportunity to learn with students in the grade(s) beyond their current grade. Within-class flexible grouping personalizes learning activities fluidly within the classroom according to student needs and does so without taking away from the sense of classroom community.
Grade or Content Acceleration
Acceleration in math instruction can take multiple forms. Perhaps the first form of acceleration that comes to mind is that of grade-based acceleration, more commonly known as “grade-skipping.” This is when highly-motivated students are placed in higher grade levels than than typical for their age. The other form of acceleration is content-based acceleration. In this scenario, the student may only join the next grade-level classroom for mathematics (or some other content area) and leaves their grade-alike classroom for only part of the school day. This type of acceleration sometimes has met opposition by those who say that students are not developmentally ready to interact with older students. However, many gifted students often feel bored or out of place with their same-age peers and naturally gravitate towards older student who are more similar as “intellectual peers.” One of the main causes of underachievement of the gifted is not that the work is too hard, but rather that the work is below what they are ready to learn (Stanley).
While grade or content acceleration is a viable option for select students demonstrating exceptional math promise, the National Council of Teachers of Mathematics reminds us that “care must be taken to ensure that opportunities are available to each and every student and that no critical concepts are rushed or skipped, that students have multiple opportunities to investigate topics of interest and depth, and that students continue to take mathematics courses while still in high school and beyond.” (NCTM, 2016) The Common Core State Standards are written on the basis of focus (fewer concepts, greater depth), rigor (balance of procedural and conceptual understanding as well as application), and coherence (the learning follows a clear learning progression pathway). What it means to know math today is beyond the strategies of rote memorization and answer-getting, so great care needs to be taken to identify mathematical readiness for grade or content acceleration. Assessments used to identify students for this type of accommodation should provide opportunities for students to demonstrate their deeper understandings of the mathematical knowledge at hand.
Perhaps the lesser-known option for acceleration is that of curriculum-compacting. Curriculum-compacting can be characterized as learning the expected math content at an accelerated pace with grade-alike peers. Because of the rigor of the Iowa Common Core Standards for Mathematics, it is recommended that curriculum-compacting does not exceed the pace of compacting 3 years into 2 (CCSSM, 2010). Although this type of curriculum-compacting in math can take many forms, it is probably most common in the middle grades when students have the option to complete the traditional 6th, 7th, and 8th grade math courses in Years 1 and 2 of middle school, with completion of a HS Algebra One course in Year 3. This type of compacting allows students to reach higher-level mathematics course in high school. It is important to note, however, that curriculum-compacting should not be seen as a pathway towards taking fewer advanced math courses in high school, opting out of math in later years once the course requirements are met, but rather as a gateway to accessing higher levels of mathematics in high school and beyond.
Academic acceleration in mathematics should only be for a select few that demonstrate readiness through a battery of appropriate academic assessments given by teachers appropriately trained to identify mathematics exceptionality. Critical concepts should not be inappropriately rushed or skipped, afterall mathematics learning is not a race. Acceleration should be appropriately paced to match the specific needs of the learner, but not at the expense of deep mathematical understanding.
Advanced Placement (AP) Math Courses
The Advanced Placement (AP) program has been offered by the College Board for decades. It gives able and motivated students an opportunity high school students the opportunity to study material for college-level courses, and depending on their AP examination scores, receive advance standing and/or course credit in college. The College Board currently offers mathematics courses in Calculus, Statistics, and Computer Science. Upon completion of the coursework, students have the option to participate in a 3 hour examination which is scored on a 5 point scale that determines the degree to which the student is qualified to receive college credit for their work:
5 - extremely well-qualified (or an A+ in a college course)
4 - well-qualified (or an A in a college course)
3 - qualified
2 - possibly qualified
1 - no recommendation
Each college has its own guidelines for how it will recognize a student’s work, but generally a score of 4 or 5 is accepted by even the most selective colleges, and usually a score of 3 is sufficient enough to obtain credit.
AP courses have been found to be one of the most effective means for meeting the academic needs of students who show exceptional promise in mathematics (Benbow). Students benefit when high schools offer courses that prepare them to take AP examinations and these courses provide the academic stimulation needed for advanced learners. However, it is often assumed that AP courses are only for seniors or that students can only take the exam if they have enrolled in the relevant AP course. These assumptions are not true. Students of any age can take the AP exams and students can study the material on their own and then take the examination. So inquire about the AP options for your student, and seek out other options if your local high school does not offer the coursework needed to prepare your student for the exam.
So far we have explored options that included flexible grouping and options for acceleration. This third option of accommodation for students demonstrating exceptional promise in mathematics is a more horizontal intervention referred to as enrichment. Enrichment activities allow students to expand their knowledge in mathematics while remaining with their grade-alike peers within the parameters of a normal sequence of the subject matter. It promotes opportunities for original mathematical investigations, advanced levels of analysis, and stimulates originality, initiative, and self-direction (Croft).
While enrichment opportunities can be infused into the school day to remove the ceiling of learning, they do not have to be limited to the four walls of a classroom. Enrichment opportunities can include after-school math clubs, contests and competitions, independent study, online activities, job-shadowing in STEM related fields, or summer programs to name a few. “These experiences deepen understanding in [math] and put students in contact with others who are their idea-mates rather than just their age-mates.” (Johnsen, 2012)
Parents can inquire with their students’ classroom or talented and gifted teacher to find out more about enrichment opportunities in the area. While some opportunities are free of charge, others may have an associated cost, and there may be funding and scholarships available for those in need of financial assistance. Here in our local area, such opportunities exist with the Belin Blank Center at the University of Iowa which specializes in teacher preparation, research, and student learning opportunities in the field of gifted education. Click here for more information from the Belin-Blank Center about upcoming opportunities for your exceptional math student.
Parents can also enrich their students social-emotional growth through the messages they convey about learning to their students. By valuing the learning process in mathematics over “getting the right answer” and by avoiding “est” words (brightest, smartest, best, etc.) we do not unintentionally project a mindset upon our students where failure or mistakes are not an option and their status as a gifted student feels constantly at-risk of disappearing. Click here or here for some easy tips to instill a growth mindset for your student.
We need to provide all students with an equal opportunity to learn and develop to their full potential. The quality of schooling is not determined by “time-on-task,” but rather “time well-spent.” (Sirotnik, 1983). The educational system is “not one that ignores individual differences but one that deals with them wisely and humanely.” (Gardner, 1984). Providing specialized services for our gifted mathematics learners should not be seen as a nefarious attempt at educational elitism, but rather as evidence of equitable access to an appropriate education.
Citations “Acceleration.” Best Practices in Gifted Education: an Evidence-Based Guide, by Ann Robinson et al., Prufrock Press, 2007. “Acceleration Works.” A Nation Empowered: Evidence Trumps the Excuses Holding Back America's Brightest Students, by Susan G. Assouline et al., Connie Belin & Jacqueline N. Blank International Center for Gifted Education and Talent Development, University of Iowa, 2015. AP College Board. “AP Students” https://apstudent.collegeboard.org/apcourse Boaler, J. “Twelve Steps to Increase Your Child's Math Achievement And Make Math Fun (for Parents).” YouCubed, www.youcubed.org/downloadable/twelve-steps-increase-childs-math-achievement-make-math-fun-parents/. CCSSM. “Common Core State Standards for Mathematics: Appendix A” Common Core State Standards for Mathematics, 2010. http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf “Grouping and Tracking.” Handbook of Gifted Education, by Nicholas Colangelo and Gary A. Davis, Allyn and Bacon, 2008. “Grouping Intellectually Advanced Students for Instruction.” Excellence in Educating Gifted and Talented Learners, by Joyce Van. Tassel-Baska, Love, 1998. “Implementing the Common Core State Standards with Various Program Models in Gifted Education.” Using the Common Core State Standards for Mathematics with Gifted and Advanced Learners, by Susan K. Johnsen and Linda Jensen Sheffield, Prufrock Press, 2013, pp. 50–53. NCTM. “Providing Opportunities for Students with Exceptional Promise.” National Council of Teachers of Mathematics, 2016, www.nctm.org/Standards-and-Positions/Position-Statements/Providing-Opportunities-for-Students-with-Exceptional-Promise/. “Philosophies and Policies to Guide Middle School Mathematics Instruction: Issues of Identification, Acceleration, and Grouping.” The Peak in the Middle: Developing Mathematically Gifted Students in the Middle Grades, by Mark E. Saul et al., NCTM, 2010, pp. 1–28. Roberts, Julia L. “Instructional Strategies for Differentiation within the Classroom.” NAGC Pre-K-Grade 12 Gifted Education Programming Standards: A Guide to Planning and Implementing High-Quality Services, by Susan K. Ed. Johnsen, NAGC, 2012, pp. 117–140. Siegle, D. “Tips for Parents: Promoting Achievement through a Growth Mindset.” Davidson Institute for Talent Development, 2013, www.davidsongifted.org/Search-Database/entry/A10791 “Teachers of the Gifted: Gifted Teachers.” Handbook of Gifted Education, by Nicholas Colangelo and Gary A. Davis, Allyn and Bacon, 2008. “What Do Students Need? Flexible Instructional Grouping.” Differentiating Instruction in the Regular Classroom: How to Reach and Teach All Learners, by Diane Heacox, Free Spirit, 2012.