Designing Instruction with the Components of Numeracy in Mind
The article, "Designing Instruction with the Components of Numeracy in Mind," discusses the importance of using the components and subcomponents of numeracy when planning math instruction. The article first examines the "risky practices" that teachers often use when teaching adult students math. These five practices: primarily emphasizing calculation skills; focusing on the language aspects of word problems; attempting to dissipate math anxiety; primarily dividing math content into distinct, non-overlapping topics; and only embedding instruction within real-life contexts are discussed in detail.
The discussion of each "risky practice" includes two parts. First, each "risky practice" is clearly explained using instructional examples, and numeracy instructors will likely find at least one example of a risky practice they have used. The discussion of each "risky practice" also includes research and detailed observations explaining why teaching using that strategy does not work.
With the previous groundwork laid, the article examines the importance of using the numeracy components when planning instruction. The article does not provide a formal discussion of the components and subcompontents of numeracy. The author provides a chart and web source for this information. Instead the author discusses how these components can be integrated into the numeracy classroom.
As each component is discussed, detailed examples are provided so teachers understand how the strategy can be used in their classroom. Key components discussed in the article include: teaching several skills at once, not in succession; making sure students talk about the meaning of the math they are doing; teaching problem solving strategies; relating instruction to the goals of the students; teaching estimation skills; building productive dispositions towards mathematics (teaching students to "engage, use and persevere in mathematical thinking"); and encouraging group problem solving. The author's knowledge and understanding of teaching mathematics to adults is evident in this discussion.
Finally, the author challenges the reader to reflect on their instruction. Asking the question, "What will happen if I…" If teachers do this, their numeracy instruction will definitely improve and our adult learners will benefit.
This resource is invaluable to the field of adult education. Many teachers are uncomfortable teaching numeracy and lack ideas on how to proceed. Many teach numeracy as they were once taught. This article provides a guideline on how numeracy topics should be presented and emphasizes the importance of cognitive aspects in teaching as well.
This highly useful article provides practical tools for the adult education instructor who is interested in improving numeracy instruction. The article provides specific examples of the ways in which an instructor can put into classroom practice the components of numeracy as described in the previously-published paper, Ginsburg, L., Manly, M., & Schmitt, M.J. (2006).The Components of Numeracy. [NCSALL Occasional Paper]. (The article includes an excellent summary description of these components and subcomponents of numeracy.)
The author uses very diplomatic language to describe the five "risky' practices currently in use in many ABE programs. She describes the limitations of these practices carefully, so that instructors might recognize themselves and their instructional programs, yet not get defensive about the need for change. This is quite important, obviously, in laying the groundwork for instructor openness and flexibility to try new things.
Of significance, also, is the author's reminder to "…encourage and celebrate the use of alternative strategies to solve problems…" by asking students if anyone can do a math problem another way. As the author states, this is …"not only asking for alternative thinking but is sending the message that there is always more than one way to approach a problem or computation", which leads to greater understanding.
The author is clear in stating that there is not a rigid sequence of topics that must be followed in math instruction. Rather, she suggests that instructors start with what students already know and what they want to know and be able to do. This is advice that will resonate with instructors who do this and see its great value. It is also a very concrete example of how instructors can begin to reform instruction in numeracy.
There is an excellent discussion of the repertoire of strategies to use in dealing with the natural frustrations student encounter with math problem-solving practices.