Beyond the Daily Application: Making Numeracy Teaching Meaningful to Adult Learners

This document provides practitioners with practical ideas to help make the teaching of numeracy effective. It also highlights the characteristics of struggling students, what students' preferences are for good math instruction, and what characteristics students want in their math teachers. A majority of the research provided proof of the importance of developing productive dispositions in math students and when this is done, how powerful the transformation is for students to value mathematics. Practitioners might even want to try some of the interview questions the researchers used with their own students. Of particular interest was the use of student's diaries to help teachers better understand the level of math understanding and application their students possessed.

The research question of this qualitative research study was, "What makes numeracy instruction meaningful for students?" Data was collected from 80 motivated students from 4 different numeracy classes taught by very good teachers at formal education sites in England. In general, the data suggested that the most important factor affecting meaningfulness seemed to be whether the mathematics was linked to the student's motivation or related to his/her own purposes and needs. In particular, the data said that making mathematics more applicable to one's daily life does not necessarily make it more meaningful or relevant to adults; that is, mathematics does not need to be presented only as functional to be meaningful. For example, the first few major findings state:

• Teaching becomes meaningful when it is linked to an individual's purpose; what makes math meaningful is the quality of an individual's engagement with a problem rather than its utility. The majority of students do not want to come to learn how to read their gas bills. Thus making math real for students does not necessarily mean using everyday math.
• Although students bring their life histories to the class, they are generally not interested in bringing specific mathematical contexts.
• Students' motivations are varied and complex but few come to study math because they feel they lack skills in their everyday lives. The main triggers are to prove that they can succeed in a subject where they have previously experienced failure; to help their children; for understanding, engagement and enjoyment; and to get a qualification for further study.

This study found that the most common motivation for students to study mathematics was a desire to prove that they can succeed. That finding is mirrored in a recent publication from the GEDTS which states that "personal satisfaction" was the reason most often chosen for taking the GED test. (p.10.http://www.acenet.edu/Content/NavigationMenu/ged/pubs/GEDTSpostsecfinal.pdf  )

The findings led the authors to list the following implications and recommendations for practitioners, found on p.10 of the summary:

Meaningful numeracy teaching should generally:

• involve teachers finding out as much as possible about their students;
• involve teachers having high expectations of their students' potential;
• build students' confidence in themselves and remove the fear of failure;
• make learning and engaging in math an enjoyable and satisfying social activity;
• inspire intellectual curiosity about math issues and topics;
• encourage students to talk about math and offer opportunities for interaction and collaborative learning, encouraging students to refer to and help each other;
• develop reflective thinking and reasoning;
• offer challenging problems;
• help students interpret mathematical situations and develop problem-solving strategies;
• emphasize that methods and reasoning are more important than just getting correct answers;
• encourage students to move away from rote memorization and drills and to develop understanding of concepts;
• help students see connections between different mathematical areas and concepts;
• motivate students to measure their success by reflecting on what they have learned and understood;
• encourage students to take responsibility for their learning and develop independent learning and study skills;
• use contexts which are interesting, relevant and appropriate to the students; and
• use appropriate resources and develop learning material which relates to the interests and contexts of the students.

The recommendations made for instruction (above) do not differ significantly from the recommendations that have been made by the NCTM in Principles and Standards for School Mathematics, the National Research Council in Adding it Up and in the ANN Principles.

They underscore how critical it is in adult education to get to know one's students and their purposes for coming to class and note that using context (both situational and biographical) as an introduction to teaching various topics is a valuable instructional strategy even though utilitarian mathematics is not the end goal.

Since the educational system in England involves stricter stratification into tracks than what is typical here, some may question how applicable the results of this study in England can be to the situation in the U.S. In the student interviews it appeared that many felt that they had been denied access to the kind of learning where intellectual engagement (using one's mind well) was emphasized. They had been deprived of the opportunity to study real mathematics (algebra, etc) in the past and felt cheated out of the opportunity to move up in social class. It would be rare to see that attitude here. Perhaps some of that resentment motivates our older learners, but many recent school leavers left school in part because they were required to take at least one algebra class. Even so, anecdotal evidence from good teachers in the US indicates that recognizing students' math fears and placing emphasis on understanding concepts rather than procedural rules have worked to effect positive changes in attitudes toward learning mathematics. Thus, although the original motivations of students may seem "foreign", the recommendations are universal.

• Semi-participant observation
• Individual and group interviews
• Student diaries
• Student photographs
• Classroom notes
• Session plans and assignments