A while back I was asked a question about student acceleration and differentiation. The question related to different types of acceleration opportunities for students that master math content before others. This question is often at the heart of differentiation for high achieving students. I thought awhile about the question and started to brainstorm what opportunities truly exist or if acceleration is needed in those circumstances. In an education setting acceleration is often associated with a curriculum that is moving faster or happening at a quicker pace than the norm.
In math at the elementary level, concepts are usually built upon one another and acceleration seems to be valued. Similar to a lattice fence, once one concept has been mastered, teachers often move the student to the next row/concept. The goal is to continually move students in an upwards trajectory towards the next concept on the ladder.
When acceleration is the focus, students are asked to master and then move to the next numerical concept. For example, If student A has mastered 2.0A.A.1 they automatically move to the next concept, 2.0A.B.2. Keep in mind that mastery is often defined by the author of the assessment. Mastery could be correctly answering a few abstract problems in a row or answering 90% of the answers correctly. In the author’s mind, the faster this process occurs over time the more the student learns. This isn’t always the case and the perceived notion of learning might not actually be occurring. This is especially prevalent with online adaptive software programs. This type of philosophy often facilitates minimal understanding and can lead to problems down the road. Also, students that are accelerated are often asked to answer questions more on an abstract level rather then explore mathematics constructively. Creating a personal level of mathematical understanding is valuable. Focusing in on only the abstract doesn’t always lead to a learning experience or a better understanding of math.
I believe acceleration has a place in the elementary classroom, but I don’t think that it should be the default. Honestly, I feel like accelerating is easier than providing opportunities for enrichment. Instead of acceleration why not emphasize enrichment for students that have already demonstrated mastery? I think the word enrichment gets caught up in buzzword land, so here’s a formal definition:
Miram-Webster defines enrichment as the process that improves the usefulness or quality of (something) by adding something to it.
Enriching math instruction doesn’t necessarily mean that students quickly move from one concept to another, but instead it may focus on practical application and problem solving. Developing strong problem solving skills enhances the usefulness of mathematics. I find that students benefit when given opportunities to enrich their understanding of mathematics. In addition, enrichment provides opportunities for students to practice relevant skills that become immediately useful. Logical thinking, abstract reasoning, and problem solving can all be part of the enrichment process. All of the skills that are practiced through enrichment activities can be used cumulatively throughout a math curriculum sequence. The picture below is just one example.
Students often need to have a foundational understanding of mathematics to be successful at the middle and high school levels. Logical thinking and abstract reasoning skills tend to contribute to the background knowledge for algebra and geometry concepts. Problem solving is a skill that’s used throughout school and life. Enrichment opportunities encourage students to use the math learned and apply it to practical situations. It also enables students to solve problems using trial and error and find multiple solutions. Perseverance skills are also practiced during math enrichment opportunities. Instead of completely emphasizing the upward trajectory of concepts, students that experience enrichment opportunities develop skills laterally and may cement a more solid mathematical foundation in the process. It may also enable students to see mathematics in a new light, not just a lattice of concepts placed in chronological order. Feel free to review Mathwire, NRichMaths and Andrew Stadel’s Math Acts, for a few different examples of how to incorporate math enrichment opportunities.
There isn’t really one right answer to the question found at the beginning of this post. The solution includes a possible combination of acceleration and enrichment, but immediately leaping to acceleration might not be the best option.
How do you use math enrichment in the classroom?
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors
Enrichment. 2014. In Merriam-Webster.com.Retrieved July 21, 2014, from http://www.merriam-webster.com/dictionary/enrichment
photo credit: Filter Forge via photopin cc