Literacy Online
NCAL Brief

What Does "100% Juice" Mean?
Exploring Adult Learners' Informal Knowledge of Percent

Lynda Ginsburg
Iddo Gal
Alex Schuh
National Center on Adult Literacy
University of Pennsylvania
Based on NCAL Technical Report TR95-06, 44 pages, $8.00.

Key Findings:

  • Most adult students interviewed have developed some informal knowledge and skills involving percent but do not have formal computational skills; a few students have formal computational skills but cannot utilize these skills in everyday contexts.
  • Many adult students showed gaps in their knowledge of different facets of the use of 100% as the basis of the percent system, with different students showing gaps on different facets.
  • Almost all adult students displayed some knowledge of the percent system as it is used in everyday contexts and while many were able to explain and use the benchmark percents "100%" and "50%" effectively, fewer were able to explain and use "25%."

Key Recommendations:
  • Assessments should explore adult students' informal knowledge and skills to identify knowledge gaps or misunderstandings that might hinder or distort further learning.
  • Real world tasks should be integrated into instruction to provide a meaningful instructional context and to facilitate transfer between tasks; development of interpretive skills, conceptual understanding, and informal computation should be emphasized over context-free computational skill.
  • Instruction should be designed to build on adult students' informal knowledge so that they will be able to integrate new ideas and skills with knowledge that is already meaningful and useful to them.

Introduction
Although percents are central to many everyday aspects of adults' lives, little is known about what adults with limited formal mathematical skills know about the percent system or how they approach common percents when they encounter them while shopping or as information presented by the media. National surveys suggest that many adults leave school with incomplete knowledge of percents. However, in order to cope with everyday demands, they may informally develop some percent-related ideas, skills, and strategies. Information about self-developed, context-bound informal knowledge is important for the design of effective instruction that builds on students' strengths, tries to ameliorate knowledge gaps or misunderstandings, and aims to enhance students' ability and willingness to put new learning to use in their lives.

Methodology
Interviews were conducted with 60 adults studying in 7 urban and suburban adult education programs. The 57 women and 3 men ranged in age from 18 to 53 years (mean=27.5) and had completed a mean of 10.6 years of schooling. While all interviewees were studying mathematics, none had begun working with percents in their present programs.

The adults were presented with explanatory, shopping, visual, and computation tasks involving the benchmark percents, 100%, 50%, and 25%. Questioning centered around the adults' interpretations of the meaning and use of the percents as embedded in everyday percent-laden stimuli such as newspaper articles and advertising flyers. For the computation task, interviewees completed a school-like series of percent exercises.

Analyses looked at individual adults' patterns of responses and patterns within groupings of those whose pre-instruction scores on standardized tests were below 7th grade, between 7th and 8th grade, and above 8th grade.

Implications
Adult students bring to their studies a patchwork of knowledge of the percent system and formal and informal percent computational skills. For effective instruction, teachers must take this and other informal knowledge into account when interacting with students or when planning activities. Teachers should help students integrate new instruction into their existing frameworks, establishing and reinforcing connections between concepts.

Students' knowledge is often limited in depth and tied to the context(s) in which it was developed, whether those contexts were specific everyday situations or earlier school-based, context-free computational skill instruction. Teachers need to be concerned with transfer of existing and new knowledge to an expanded range of situations. Towards this end, instruction should develop students' conceptual understanding, interpretation skills, and informal computation, as well as formal computational skills within realistic problem contexts. Similarly, assessments should not be limited to evaluation of decontextualized computational skills, but should explore performance on realistic tasks and evaluate depth of understanding by requiring that students justify or explain responses.

Further Reading
Gal, I. (1993). Issues and challenges in adult numeracy (Tech. Rep. No. TR93-15). Philadelphia: University of Pennsylvania, National Center on Adult Literacy.

Leinhardt, G. (1988). Getting to know: Tracing students' mathematical knowledge from intuition to competence. Educational Psychologist, 23(2), 119-144.

Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street Mathematics and School Mathematics. Cambridge: Cambridge University Press.


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