The "Whole-Person" Approach in Math Assessment

Mary Jane Schmitt and Helen Jones 1

Math is not an isolated activity, something which adults do only when confronted with taking a test or demonstrating a competency. Mathematics is a dynamic process, one that is rich and diverse, one that involves gathering information, exploring ideas, discovering relationships, identifying patterns, and making connections. We believe that by talking about and teaching math in this way, adult learners will come to value mathematics, be confident in their ability to do math, become real-life problem solvers, and learn how to reason and communicate mathematically. 2

What's Wrong with this Picture?

An adult learner walks tentatively into an ABE math classroom and is greeted warmly by the teacher. The other learners move over to make some room. The atmosphere is comfortable and accepting. After introductions, the teacher approaches the new arrival with a basic math assessment (computation and word problems), and asks the learner to try some of the problems. She explains that her goal here is to find out what the adult learner remembers and where she needs to start reviewing.

What's wrong with this picture? Nothing at all, unless this is all you do to assess your students' knowledge and past experience with
math. Computational tests are helpful but they can't provide all the information you need. To plan the most effective learning activities and create the right kind of learning environment, consider taking a "whole-person" approach in the initial math assessment.

The following nine factors are important to consider when creating an individual's learning plan:

Factor 1
Emotions and Attitudes

Factor 2
Long- and Short-Term Goals

Factor 3
Everyday Math Experiences

Factor 4
Computational and Problem-solving Processes

Factor 5
Math Skill Level

Factor 6
Reading Level

Factor 7
Cultural Background

Factor 8
Learning Pace and Style

Factor 9
Perceptual Disabilities or Strengths

FACTOR 1: Emotions and Attitudes

Many learners have had negative experiences with math; it's important for you to recognize this and to open up your classroom for sharing "math memories—your students' and your own. Keeping a math journal is one way learners can record their thoughts and feelings about doing math, while also describing what they're learning in class.

Students who are math anxious often have developed coping mechanisms to deal with their fears: panicking when faced with a word problem, saying, "I hate math," or, " I can't do math," or hiding how they get an answer because they fear it's not the right way ." It's important to acknowledge this "emotional" information and to deal with it in your classroom.

Let students know that you are fully confident in their ability to do math, and encourage them to insist upon "getting it." They should be comfonable in telling you when they're confused. Agree upon a signal, like holding up a pencil, to let you know if something doesn't make sense. Ask questions along the way to check comprehension. Remember, keep the dialogue going.

Reflect on your feelings about math. If you are at all uncomfonable with math, think about how your own math anxiety plays out. What kind of messages do you give your students Do you go too much by the book because you're afraid to make a mistake? It's best to be honest and to learn with your students. (see Fig. 1)

FIGURE 1

FACTOR 2: Long- and Short-Term Goals

It is critical to know why a learner has come back to school. Knowing your students' goals will help you develop and guide the overall curriculum. This is information the teacher keeps in mind as s/he begins instructional planning.

Setting up a plan that enables students to achieve their long-term goals is a critical next step. Some outside research on your part may be necessary. If a student wants to go to nursing school, for example, get a sample of the entrance exam and learn about the entrance requirements. You can find copies of current nursing textbooks and get a feel for the content of the course work.

Be skeptical of exam preparation books. Go to the source, if you can. If the student wants to take the GED, get the Official Practice Tests
and teacher's guide that come directly from the GED T esting Service.
Don 't forget about short-term goals. They are critical benchmarks of progress. The learner who wants to be a nurse, for example, can work toward the short-term goal of learning the metric system. Also, students' goals may change over time, so be sure to check in periodically.

FACTOR 3: Everyday Math Experiences

Asking learners to think of ways they've used math in the past month is a good activity to initiate for many reasons. It opens up discussion, and allows learners to see the many ways they use math every day. A typical list might include:

• doubling a recipe
• figuring sales tax
• building a porch
• measuring baby formula
• grocery shopping
• catching a bus
• balancing a checkbook
• punching a time card
• analyzing a paycheck
• checking change
• measuring food for intake (in the case of a diabetic)
• looking for an apartment

Keep track of the information your students provide, and use it in your instruction. Mathematics is about making connections, and good lessons start with experiences students can relate to.

FACTOR 4: Computational and Problem-Solving Processes

Observing and listening to how students solve problems, and affirming their strategies is important. Students should know early on that there are many ways to reach a solution, and that the best way is that which makes most sense to them.

Acceptance of learners' calculating methods does not mean that you should accept all answers or off-the-wall thinking. First, find out how the learner arrived at that answer before you challenge or correct him or her. Try to understand the logic behind each learner's approach. The more you listen to and respect the particular way of reasoning, the easier the teaching and learning process will be. (see Fig. 2)

FIGURE 2

FACTOR 5: Math Skill Level

It's important to know if your students know the four operations on whole numbers, fractions, and decimals, and whether they can use these skills in context. That's why we usually start out with a computational math assessment.

Be skeptical of this assessment process, though; it is not an exact science. Even in your best attempts, you may underestimate or overestimate a learner's skill level or potential. A student who can't divide, for example, may be able to solve algebra problems.

FACTOR 6: Reading Level

Math will never make any sense if language gets in the way. It's important that word problems be within the learners vocabulary and comprehension level. Also, when integrating reading, writing, and math in your curriculum, be sure to consider the learners' abilities in all three areas. However, don't let low reading levels prevent you from teaching math. If you are working with new readers, present problems orally in groups, or tape-record problems for new readers to work with. There are ways to teach math successfully to learners who are at varying reading levels.

FIGURE 3

FACTOR 7: Cultural Background

Many approaches to doing basic math are fairly universal. However, some major cultural differences do exist. (see Fig. 3) For example, learners who attended schools in a Spanish-, French-, or Portuguese-speakirig country may write "two thousand" as "2.000," and write "two" as "2,000." Also, their method for subtraction may not involve the concept of "borrowing." In some countries, division is also
done differently. Measurement systems also vary by country. Many countries use the metric system, so you may need to use 12-inch rulers and yardsticks to show the customary units of measure in the United States. When working with students try to learn the methods they were taught. Have students from the same country tutor each other. In the classroom, build on the students' methods if you can. Don't insist on their learning new algorithms if their own methods work just as well.

If the students have children in American schools, talk about how math is taught in the United States. You can create interesting multi-cultural math lessons using this information.

FACTOR 8: Learning Pace and Style

People learn at different rates. That's a fact of life! So, many adult learning centers provide individualized instruction to ensure that learners have enough time to absorb the material.

Watch out for this. Instruction that is completely individualized can be isolating. By pairing students who learn at similar paces, or
by forming small work groups, you can provide for an enriching and cooperative learning experience.

Adults also have many different learning styles. In the ABE classroom, some learners are self-directed, whereas others need continual support from the teacher. Some learners prefer to work alone, just as others learn best in small groups. Observe your students, and learn how they work best.

Consider your own teaching style. Are you directive or facilitative? Does your teaching style match the learning styles of most of your students? These are some issues you ought to take into account.

FACTOR 9: Perceptual DisabilIties or Strengths

Many teachers are familiar with the following patterns: A learner has difficulty memorizing the times tables, is unable to pay attention to " + , -, x, + / "symbols, or can't line up decimal points. The list goes on. These may be symptoms of a visual perception disability.

If a learner has problems following oral directions, or has difficulty counting out loud, slhe may have an auditory deficit. Although they do not account for all problems, learning disabilities certainly do exist. It is well worth your time to learn more about this important issue.

Just as you should be aware of possible disabilities, it is equally important to build on students perceptual strengths. In your instruction, include the kinesthetic, visual, and auditory learning modalities.

Summary
Good teaching begins with good assessment and improves with appropriate and continuous evaluation. A whole-person approach to math assessment takes into account not only the learners' "pencil and paper" skills, but also their feelings about math and everyday approaches to problem-solving.

Notes
1. This article is excerpted from the viewer's guide which accompanies the training video, Changing the Rules: Teaching Math to Adult Learners, available from New Readers Press.

The video demonstrates four key ideas to improve adult basic mathematics instruction. These include using a whole-person approach to student assessment; integrating concrete learning activities into classroom instruction; using real-life math problems that have relevance to adults' daily lives; and finally, using a spiral approach to teach math content.

2. These goals are also outlined by the National Council of Teachers of Mathematics in Curriculum and Evaluation Standards for Mathematics, NCTM (March, 1989).

Originally published in Adventures in Assessment, Volume 3 (April 1992),
SABES/World Education, Boston, MA, Copyright 2003.

Funding support for the publication of this document on the Web provided in part by the Ohio State Literacy Resource Center as part of the LINCS Assessment Special Collection.