Meeting the Needs of High-Level Learners in Mathematics

Presented by Mary M. CundyNSU Center for Statewide E-learning

2009 TIE Conference

Students at the greatest risk of learning the least in the classrooms may be those at the top range of ability. The needs of these students are often neglected because these students achieve acceptable standards on state assessments. High-level learners can create multiple connections and organize those connections in many different ways: they learn differently from their classmates.

Some myths about high-level learnersThey are like cream that rises to the top of a

classroom.They are always high achievers.They are so smart they do fine with or

without special programs.They are a homogeneous group and need

only one curriculum.

Common Blunders Asking a high-level learner to serve as a tutor for students

who are struggling “Research indicates that a learner is more likely to

successfully model a peer who is slightly more advanced in performance level than one who differs greatly” (Callahan, 2001)

Giving high-level learners more work when they finish early

“This is counter intuitive . . . if the student is completing his/her work in an efficient manner, it is likely that the work is too easy” (Davidson Institute, 2003)

Allowing high-level learners to move ahead only when they can demonstrate 100% accuracy

In 1980, the National Council of Teachers of Mathematics (NCTM) made a bold statement, “The student most neglected in terms of realizing full potential is the gifted student of mathematics” (“The STEM Promise,” 2008).

According to “The STEM Promise,” (2008):

A number of recent studies have shown that U.S.students scoring above the 90th percentile inmathematics and science are among those makingthe least progress in school.

Sixty-five percent of the top math students in theU.S. are children of immigrants.

Who are the high-level mathematics learners?

Characteristics of High-Level Learners They demonstrate an ability to think

abstractly, an ability to learn and process complex information very rapidly, and a need to explore subjects in depth.

They remember what they have learned, so spiral curriculums and reviewing may be boring

They perceive ideas and concepts at more abstract and complex levels

They may be passionately interested in specific topics and have difficulty moving on until they feel satisfied whey have learned as much as possible.

The teacher:

a powerful player in the indentifying process.

Designing Content“Challenge and frustration are a part of learning

and life. Limiting mathematics to an intellectual box where there is no struggle or frustration is not healthy”(Zaccaro, 2006)

A favorite article: “Finding the Glory in the Struggle: Helping Our Students Thrive When Math Gets Tough” (Suzanne Sutton in “Bulletin” (Feb. 1997) – a periodical for the National Association of Secondary School Principals)

The mastery of complex concepts is dependent on hard work.

Designing ContentShare the wonders of math!Math can be gorgeous – even elegant.A finely done mathematics problem is a work

of art.“Math is often taught as all scales and no

music. Children must have the opportunity to see the exciting and interesting parts of mathematics” (Zaccaro, 2006)

Designing ContentContinually emphasize the interesting

connections between math and the real world: mathematics concepts are all around us.

“Math and science are not like referees and umpires that you can argue with if you don’t like what they tell you. Math and science are coldly and cruelly indifferent to your hopes, dreams, and wishes. They give you an honest and objective look at a situation. Don’t ignore their message!” (Zaccaro, 2006)

Designing Content High-level mathematics learners need

materials that “truly challenge them and appropriately challenge them” (Zaccaro, 2006).

The instructional balancing act: creating appropriate challenges while reinforcing basic skills.

The practice of offering extra credit should be replaced with approaches that can motivate students to become enthusiastic learners (Winebrenner, 2000).

Designing Learning ExperiencesLet go of normal! You will not harm a

student by offering opportunities for advanced work.

Opportunities and materials for learning high-level, innovative mathematics should be readily available where students can work with peers of similar interests and abilities.

Designing the Learning Environment“Highly able children must have the opportunity to work

with children with similar abilities” (Zaccaro, 2006).Consider distance learning opportunities: “online high

school and college courses, including online AP classes, are a great way to substitute more challenging curriculum for students who demonstrate proficiency with grade level material.

“Every high school should offer high-level Science Technology Engineering and Mathematics classes such as Advanced Placement . . .” (The STEM Promise, 2008).

Vertical teams of teachers should work together to prepare students for these classes.

Managing Learning ProductsAudience can be a powerful factor in the

learning experience of high-level mathematics students.

Use Web 2.0 tools and electronic learning environments to give students the opportunity to share their work with an audience of their peers.

“Writing is an excellent tools for extending and deepening student understanding, especially in math class” (Brandenburg, 2002).

Managing Learning Products“When children see that an area in which

they excel is valued by those around them, their interest and passion for the subject can increase dramatically” (Zaccaro, 2006)

The teacher can make students feel that they have a gift that is to be treasured and shared!

Designing Assessment“Formative assessment contributes to student

ownership of learning more than any other classroom-based practice” (Brookhart, Moss and Long, 2008).

Break the cycle – break the mold!Give high-level mathematics learners control

of their own learning.

According to “The STEM Promise,” (2008):

“Many of our students with the greatest aptitudes are underachieving, languishing in repetitive, unchallenging classes.”

“Students need access to a systematic, timely, continuous progression through a high-level, challenging, creative curriculum.”

“State and national content standards and assessment must lift the ceiling and provide opportunities to go beyond the level of proficiency.”

Teacher as talent scout!

“Come to the edge.We can’t. We’re afraid.We can’t. We will fall.

Come to the edge.And they came.

And he pushed them.And they flew.”

-Guillaume Apollinaire

“Come to the edge.We can’t. We’re afraid.We can’t. We will fall.

Come to the edge.And they came.

And he pushed them.And they flew.”

-Guillaume Apollinaire

References

Brandenburg, M. L. (2002). Advanced math? Write!. Educational Leadership, 60(3), 67-68.

Brookhart, S., Moss, C., & Long, B. (2008). Formative assessment that empowers. Educational Leadership, 66(3), 52-57.

Callahan, C. M. (2001). Beyond the gifted stereotype. Educational Leadership, 59(3), 42-46.

Characteristics and behaviors of the gifted. The Rhode Island State Advisory Committee on Gifted and Talented Education. Retrieved April 14, 2009, from http://ri.net/gifted_talented/character.html.

Davidson Institute for Talent Development (2003). Tips for teachers: Successful strategies for teaching gifted learners. Retrieved April 14, 2009, from http//www.davidsongifted.org/db/Articles_print_id-10075.aspx.

Levy, S. (2008). The power of audience. Educational Leadership, 66(3), 75-79.

ReferencesThe STEM promise: Recognizing and developing talent and expanding opportunities for promising students of science, technology, engineering and mathematics. National Association for Gifted Children Task Force. Retrieved April 14, 2009, from http://nagc.org/index.aspx?id=4454.

Winebrenner, S. (2000). Gifted students need an education, too. Educational Leadership, 58(1), 52-56.

Zaccaro, E. (2006). The seven components of successful programs for mathematically gifted children. National Association for Gifted Children. Retrieved April 14, 2009, from http://www.nagc.org/index.aspx?id=1457.