Common Problems in Math InterventionsTypically, middle school and high school math intervention students have the math skill level of a 3rd to 5th grader. They struggle with fraction manipulation, long division, and often basic math facts. Many of these students do not believe they will ever succeed in math, resulting in a huge lack of motivation. These students are not ready for Algebra I and are at risk of failing to graduate from high school.
In our opinion, there is no tougher task than to run a successful math intervention with high school students that are at risk of never graduating.
Credible Research-Based StrategiesIn 2009, the U.S. Department of Education released Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools, which is available here: http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=2 . One of their most important conclusions is that for math intervention students, there is not enough time to teach everything, so you must prioritize your curriculum for these students. The document makes 8 research-based recommendations. If you are serious about implementing a successful math intervention program, we suggest that you download and study it.
In 2008, the National Math Panel released Benchmarks for the Critical Foundations of Algebra, which highlighted the skills that they felt were by far the most important for future Algebra I success. These skills included math facts, decimals, fractions, negative numbers, percentages, and some geometry concepts. Given that you won't have time to teach everything, these guidelines should be taken very seriously for your math intervention program.
The full report can be found here: http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.
Computation Skills vs. Critical Thinking SkillsYou need a combination of both skills to truly be proficient. Start with a deep understanding of fundamental operations, such as the meaning of addition, multiplication, and place value concepts. Follow that with mastery of the math facts (and yes, we suggest drilling). The 2006 Curriculum Focal Points (by the National Council of Teachers of Mathematics) states that mastery of math facts is a prerequisite for acquiring deep critical thinking skills. The implication is that if your students fail to master their math facts, it is hopeless to attempt to teach them higher order critical thinking skills, so assessing that skill in particular is especially important.
There is no such thing as a student that relies on a calculator to compute 7 × 8 that manages to get an "A" in Algebra I, let alone AP Calculus!