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COMPETENCE AND SELF-CONFIDENCE
The loss of self-confidence in math, the lack of understanding of particular math concepts, and the fear of math inhibits power. Many adults do not feel confident, competent, nor comfortable in math. Many adult learners are frustrated because they do not feel comfortable in math. Adults fear math. For some, frustration with math spreads to frustration in other areas of school as well.
Is this lack of confidence in math because people are limited or lack the ability to learn? No, the causes are more likely found in poor learning environments and lack of recognition of different learning styles and needs. Good learning environments, within the family, at work, or in school, produce different attitudes toward math and can help to overcome fear and lack of belief in one's ability. Confidence builds competence in math and competence builds confidence. Sometimes confidence in math comes after gaining self-esteem as an adult. Math skills may also be acquired on the job.
Those learners who feel comfortable with math have confidence in their ability and respect for the domain of math. Confidence in math increases power, voice, and the ability to act. The more adults learn, the more confident they become, and the more enjoyable the experience of learning becomes.
IMPLICATIONS FOR LEARNING AND TEACHING
In recent years, more research has been done in the area of math learning. This research has revealed that individuals learn math differently than we thought. Some are comfortable with learning step by step while other learners tend to jump to the big picture and work forward and backward to solve problems. Teachers need to let go of the need to make all learners solve problems the same way that they were taught in school.
Success needs to be built into the adult education classroom. Adults need to have success early on and often when they begin a math class. This success enables them to develop confidence in their ability to do math, which in turn paves the way for further positive math learning experiences. All individuals benefit from positive feedback, but it is particularly important that adults who have experienced failure in math class previously now find success in the adult education classroom.
Math content skills need to be presented in the context of real-life situations. When learners can immediately apply what they have learned, the learning crystallizes and the learners gain confidence and competence in their math ability. The perception is that math is too hard and that perception must be changed.
Connecting to real-life situations and understanding the why behind math processes improves math ability. Adults use math in their daily lives but often do not connect to their real world math to the math in the classroom. When asked whether they use math, adults who are not confident in math will often say that they don't use math. Connecting math to their real-life situations helps adults understand that they do use math.
There needs to be a level of trust in the adult education classroom. The adult education teacher needs to build an environment that is comfortable for adults and one in which adults can be open. Adults need to feel comfortable sharing their frustrations and lack of math skills.
Group work is one technique that helps build confidence and competence. Isolating learners from each other is not helpful nor efficient. In our global economy, much of what we do is done in groups. By becoming more familiar with cooperative group learning, the teacher can maximize the potential of all his/her students.
MATH ANXIETY
Math is mainly arithmetic!
Have you said or asked these before? If so, you are experiencing math anxiety. Math anxiety is not a myth. Approximately 50% of the adult population in any occupation suffer from this very real condition. Math anxiety is a state of uncertainty; disturbance of the mind regarding the subject of mathematics.
HOW IT HAPPENS
No one is born with math anxiety. It is a learned process. This barrier of learning is usually not found in elementary school. Most people say it started for them in fraction, algebra or geometry. An unsafe environment took place either at school, home or at both places. The process of math anxiety always involves another person besides the victim.
For example: In the book Math Anxiety Reduction by R. Hackworth, math teachers were questioned about their subjects. A large majority stated, "These subjects were far higher than basic math levels, and only the exceptional minds can grasp this knowledge." It was later discovered that these teachers,themselves , suffered from math anxiety. The attitude that only the most intelligent could do these tasks reached the students' minds and there it started to grow. This made these teachers unknowing helpers for math anxiety.
WHO IS A GOOD VICTIM FOR MATH ANXIETY?
According to Fear Of Math by C. Zaslavsky, in the 1970's females were more of a target than males. Today that has switched around. Males are more likely to suffer from math anxiety than females. The American culture has general expectations of the male and female roles. Males are seen as the breadwinners of the family. They think they should make all the decisions, handle everything on their own and never have to ask for help. The male ego says if you ask for help you have failed as a man. Our culture makes people who fail feel weak,stupid and sometimes incompetent. Females, today know they are just as smart as males. Yet they are still seen as the group gossip hostesses who talk to anyone about anything. Math anxiety must hate this. If a female is feeling uncomfortable with a math question they are more likely to admit the problem and ask for help, this decreases the chance for math anxiety. As teachers we need to be alerted to pride, it seems to be math anxiety's best friend.
SYMPTOMS
Math anxiety can have internal and external symptoms- heart throbs, sweaty palms and mind blanks along with severe fear of the subject and a total avoidance of math in general. To reduce the stress level of your students Fear Of Math and Math Anxiety Reduction suggest the following:
Check the learning styles of your studentsTry the relaxation Technique
For best results do these exercises 20 minutes before starting any math work.
Give more control to the student in helping them devise realistic educational goals.
Have students keep a journal to monitor their own learning activities.
Use more real-life math
an example: Draw a map from work to your house with the use of landmarks. Here the students are doing something familiar to them not realizing they are using geometry, algebra, measurement and problem solving.Try more estimation problems. Students become more relaxed when they know there is more than one correct answer.
Stress clue words for story problems.
Show students how to check their own work.
Encourage group work.
These stress reducers can help raise self-esteem and the drive to try again. Remember, there is no quick easy cure for math anxiety. For some there may be no cure at all, just the ability to cope.
BIBLIOGRAPHY
Math Anxiety Reduction
Robert D. Hackworth
H ~ H Publishing Company, Inc.
United States 1985
SMALL GROUP LEARNING
In the March/April, 1996 issue of Adult Learning in an article by Victoria J. Marsick and Karen E. Watkins, "Adult Educators and the challenge of the Learning Organization," we find out what an important concept working as a group or team is:
"Dechant, Marsick, and Kasl (1993) and Brooks (1994) in separate studies show that teams mutually create new knowledge through continuous cycles of thinking and acting. Teams use new ideas and information to challenge their current understanding, and to then test new insights through trial-and-error and experimentation, which leads them back through a similar cycle. Dialogue and inquiry enhance team learning."
Other benefits derived from group learning include:
OPTIMUM INTERACTION--interaction is an integral part of the learning process.This is not the type of group work that needs to be led by an instructor or volunteer. We have learned that students work best leading their own groups with teacher guidance and guidelines. Students often fall into small groups on their own: whom they sit by daily, whom they are friends with, or whom they know is "good at" what they are working on. These small groups will work but it may be more advantageous for the teacher to group students according to their abilities and work styles. Once these groups are established is best to keep them together for a number of lessons because the students learn to work with one another and feel more secure being more familiar with one another. These groups would probably change according to subject area or activity. Six students would be the maximum number of students that should work together.AVOIDING ISOLATION--learning does not take place in isolation.
ORAL LANGUAGE DEVELOPMENT/NOISE LEVEL--oral language development plays an important role in learning.
A SUPPORTIVE ENVIRONMENT.
EMPHASIZING THE PROCESS--emphasis must be on the process, not the answer.
STUDENT/TEACHER ADVANTAGES--
-social interactions
-opportunities to be teacher and student
-solving problems together is more efficient and enjoyable than working by one's self
-reduces teacher effort
-immediate feedback
-teacher can be learner also
-it works.
Several guidelines are suggested for small group work: 1) everyone should know everyone else's name; 2) no question should be asked of the teacher unless everyone in the group has the same question; 3) each person must be responsible for their own behavior; and 4) each member must be willing to help every other member of the group.
Students have repeatedly told us that they not only enjoy working in small group situations, but they feel they gain much more than working on their own. They learn from the other members of the group and they learn by explaining what they already understand. They share ideas and come up with more ideas than they would have been able to by themselves. They don't feel "so dumb", because they see other people struggle as well as themselves.
Many activities can be used in the small groups. Problem solving is probably one of the best concepts to with. Many cooperative learning books, such as GET IT TOGETHER SPACES, and Make It Simpler are all books that will help get both teacher and student started.
Waving the White Flag
Surrendering our traditional approaches to Mathematics in Adult Education
The battle to arm our adult learners with solid mathematics skills is often lost at the most fundamental level. The way instructors introduce specific mathematics concepts sets the stage for the success, or lack of it, that students have in mastery. We must approach mathematics with concrete strategies that not only show the learner how specific functions of mathematics work, but why they work.
Students will readily admit that the subject they disliked most in school when they were young was math. Often, they lack a fundamental understanding of basic concepts such as division and multiplication. Many students will say that they have no trouble with these skills unless they have to determine which to use in a word problem. The reason for this is that word problems demand a far deeper conceptual understanding. Rote memorization is a very small part of mathematics. Mathematical operations have to be understood in a fundamental way, as do all aspects of math, so that the student can withstand the tests of logic and critical thinking that come with every day of life.
If we approach math as a sort of laboratory science, we can experience the same moments of discovery that our mathematical forefathers did. Why is a base ten system so helpful in counting, adding, or subtracting? Why does it make so much sense to quickly add groups of numbers and call it multiplication? How can we use division to lead into the concept of fractions and then later on prove that fractions can't be divided? Because they are adults, teachers are often uncomfortable working with such primary concepts. The fact that they are 'primary' is all the more reason to make sure we approach them as a necessary function of being a successful mathematician. Accordingly, we must approach each element of mathematics in the same fundamental way, as if we have to prove it before it can be true.
The members of our team were in agreement that manipulatives and real life situations are the best way to generate interest in new concepts. Any physical entity that students can hang on to works as a kind of security blanket for temporary support. The goal is to outgrow our 'blankies' at some point in time and move on to something else. Games are certainly one way to conceal mathematical objectives. A spoonful of sugar really does help the medicine go down. Variations on Bingo can be used regularly to check student understanding for any subject, but first there has to be understanding. It was our goal to consider some of the most important objectives for instructors to successfully approach mathematical concepts. These are:
None of us find it easy to surrender our weapons. Paper and pencil just seem to be the traditional tools of mathematics, and we can't help but grasp for them when we teach. What we all realize is that this route did not work for our students the first time around, and chances are it will only fail again. The discomfort we all feel is that manipulatives seem so juvenile. The last thing we want to do is insult these adults. However, by dissecting concepts as if they were biology experiments, teachers as well as students learn to appreciate the remarkable world of mathematics as less of a battlefield and more of a field of discovery.
APPROACHING MATHEMATICS
What is multiplication? Most students do not think of multiplication as anything more than memorized facts. Provide groups of pennies, nickels, dimes, and quarters, then have them discuss how they calculated totals. Explore different ways to calculate totals, such as groups with 2 quarter, 3 dimes, and 4 nickels. Graph paper cut into assorted shapes works well also.
When is division really division? Thinking of division as an inverse operation has little meaning once we begin to go deeper into math. Division must be understood as cutting things into equal parts. This is quickly associated with fractions. Have students cut up paper or cookies, or split a restaurant tab. Use specific numbers of cards or candy and have them divide things up fairly.
Do you understand a fraction of this math? Look for fractions every-where with students see that they are not just book work. Measuring spoons, screws and nails, telling time, etc. Give students an 1/8 cup and tell them you need 3/4 cup of water. Have students prove that the second fraction must be inverted in division.
What is the point of a decimal? Money is everyone's favorite decimal number. Work with place value and make reference cards for students to place numbers on. Use less than a dollar in change and have students write the amount they have. Why do we write it that way? What if we didn't use a base 10 system? Use circles cut in 10 pieces, having them write decimal equivalents.
What does this symbol (%) really mean? Most of us spend so much time teaching how to find a percent that students rarely understand what a percent actually is. Spend time cutting up apples or cheese and discussing parts of the whole and percents of the whole. Always start with 100%. Use 10% to approximate answers (30% is three 10%s) Lots of real life application.
Do you believe everything you hear? Geometry is the most terrific area in math. . It is visual to begin with and can always be proven The three angles of a triangle always equal 180*. Mark each vertex, then cut them off and put side by side. Pi is the diameter of a circle placed around the outside edges 3.14 times. Let students do it. Pythagorean Theorem helps use check for perfect corners when building. They call it a 3-4-5 corner; measure 3 inches, 4 inches on the other side, your mark s should be 5 inches apart across the corner.
Do you speak Algebraic? It's a foreign language to many student so do everyone a favor. Teach them the basics-signed numbers and the order of operations. Then work on translating English into Algebraic using simple equations, then real life situations. Use thermometers and number lines, let students move physically through addition of signed numbers. Stay away from long equations that only your college- bound students need to digest. Try to avoid the word algebra if possible.
Teaching Math With the Use of Computers
An educational computer software program that addresses the needs discussed is WICAT. WICAT is designed for adult users with reading and math levels from 1st through 12th grade. It addresses math concepts beginning with whole numbers, and moves through fractions, decimals, and percents. It then moves into geometry, algebra, trigonometry, and basic beginning calculus. WICAT also addresses job skills and life skills, including money management activities. In addition, GED® science and social studies activities are available. WICAT will soon update its software by adding such topics as drug and alcohol rehabilitation.
The program is extremely effective in educating students. It provides immediate positive feedback by instantly presenting the score correct to the student completing the activity. It provides positive comments for work well done, as well as immediate intervention when problems arise. If a student does poorly on an activity, a screen appears telling the student to call his/her teacher. If a student gets a 70% or below, the "call your teacher" screen appears. This allows the teacher to step in and assist the student with whatever problems he/she may be having. The teacher must then type in a password to delete the screen and allow the student to get back to work.
The software is quite detailed in its explanations of topics and concepts. For example, when doing a long division problem, the students are required to type in the steps, one at a time, to the problem. This allows the students to work out the problem just as they would on paper. The only difference is that the students receive some type of indication of whether or not the problems were right or wrong. They also would get an idea of where they made their mistakes, if in fact they did.
Another effective use of computers in education is through the use of a touch station. Touch stations can operate through the use of laser discs. However, they are now currently being updated to a C.D. ROM system. The touch station is specifically geared to low level math and reading students. The station is a tactile, or hands-on, way to learn. Students touch the screen to indicate their choices. The instructions are read to the students in case they have trouble reading in any way. This multi-sensory approach helps learners develop confidence and avoid frustration. Students accomplish more because they don't have to concentrate as much on figuring out the words, just the concepts. It really is quite effective and rewarding for the students.
There are quite a few other software programs on the market now that are effective in teaching math. When teaching adults, it is important to look for programs that are age appropriate. Many of the programs available now for adults in math instruction have a video game feel but aren't too juvenile, therefore allowing students to learn without feeling as if the computer is too immature for them. The programs tend to not actually teach the concepts, but merely reinforce concepts already learned. A list follows with various computer math instruction programs. The prices of the list vary from approximately $10 to $40. So, the programs can be purchased for a fairly inexpensive amount of money.
Computers are rapidly changing the face of society as we know it. It is imperative that learning, along with other facets of society, enter the technological age of computers. By allowing students to explore educational activities through the use of a computer, students will in turn learn more than purely academics. They will become familiar with a computer keyboard while learning and reinforcing newly acquired math concepts. This approach helps to boost self-esteem while teaching concepts. Computers are proving to be an extremely effective form of teaching instruction and learning.Multi-Media Fractions
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