65! Working in groups and developing tricks around barriers provides constructivist opportunity1. Where does math fit in this student's life ---for this year and as an ultimate destination.What the youth can do this year Potential math abilityShort term goals: fractions, place value, number sense Long term or overarching goal - functional math skillsNOW SOME DAY2. What is math and how does it help a student? It is not really multiplying, dividing, adding, subtracting and algebraic equations.It is the study of pattern and the use of patterns to solve problems. It is embedded in life - and in life skills. Independent living is dependent upon having or achieving "math sense." It is so much a part of our lives that we don't think about it until we see someone who is missing it. Perhaps a student can't make change for a dollar. Possibly the youth doesn't know what size of container to get for the leftovers, can't double a recipe. For that matter, perhaps the student doesn't know the difference between a fractional and metric wrench.3. What does math ability look like? Math success occurs when youngsters have the tools to:form and remember associations understand basic relationshipsmake simple generalizations see and use patternsFrom National Council of Supervisors of MathematicsMath is an important art of living an independent life. It is important for students to feel successful while taking math classes - and it is important for them to have success in preparing for the myriad of ways that numbers, relationships, using patterns and problems solving. These are critical steps for insuring math success.I. Assess the student's math skills.Placement scores from the district or State achievement tests are a good start. Once a general level of numeracy is established, it is important to work, one-on-one with the student. Set up tasks that will allow observation of the way the student approaches a problem, and when possible, have the youth talk about what s/he is thinking as a task is performed. At the fundamental levels, look for classification --Emily (our imaginary student for this discussion) classifies coins by size and cannot overcome the notion that dimes really are worth less than pennies.Ordering is difficult for many youngsters. It involves seeing a pattern and using it consistently, then being able to turn around and apply a different rule and rearrange materials to fit the changed rules. Emily can put clothes together by color, but she cannot make the leap to hot or cold climate apparel. She can match socks,66two by two, but cannot then put them in the drawer according to dressy or daily. She can make a row of X blocks or a row of O blocks, but putting them X O X O X O is too hard.One-to-one correspondence is emerging. She can count blocks for about five items, and then she begins to group blocks and say one number, skip a block while counting, or say two numbers before changing to a new block.It comes as no surprise when we check onconservation skills, to find that they are not yet present. Emily can be fooled into drinking a smaller amount of soda by offering her a tall thin glass instead of a low fat glass of liquid. Her sisters do it all the time. Since these are emerging skills, and Emily has not yet mastered them, our conference with her will focus on math readiness. We can insist that she learn addition and subtraction facts, use flash cards or jump rope games to get her to learn the drills, but we cannot hope to build a math castle without a foundation. Basic skills are still our focus, because that is the point where Emily can have success -- and it is the area where she is motivated to push and press and learn.The next areas for testing include the underpinnings for successfully completing and understanding operations -addition, subtraction, multiplication, division -- and basic axioms -- associative, commutative, distributive properties and inverse operations. These tap into the ability to recognize and use patterns and to generalize the patterns and associations from one set of experiences to another. Remember those basics for success in math?Computation adds another dimension. This is where rigor, drill, practice, and order fit into math. Many youngsters see relationships and make generalizations, but the way they process information makes math success uncertain. When a student repeatedly gets the same kind of problem wrong, it is often the result of not knowing HOW to do the problem. Listen to a Bob's discussion while he solves the problem. In this problem, 32 + 47, Bob says, "Three and two are five and four and seven are eleven, so the answer is 16." Bob does not see 32 as a distinct number and there is much work ahead, including teaching tens and units.On the other hand, Mark says, "Thirty-two and forty-seven, hmmm. In the first column, the sum is 12 - put down a two and carry the ten over. . ." Ask further and it becomes clear that Mark reversed the two in his mind and saw it as a five. Mark has the necessary mathematical understanding, but it won't show up until he finds the tools to recognize when reversals are occurring and sets up a system to prevent this from occurring.Both students get the problem wrong, but the reasons for errors are critical. We can see, by talking with the boys --using informal assessment and determining the thinking that is occurring, that what we do for Bob will be completely different from what we help Mark learn to do for himself.Assessment in MathAssessment is finding a way to tease out the background from the foreground. We know when a student is not understanding, but finding out why --- that is the piece that is so vital.Of course, we can use formal and informal assessments, but it will not give us as much insight as . . . Asking the student what is working and what is not --- it actually helps them to identify that. . . and listening to the student as s/he self talks (what are you thinking while you work) and works out a math problem.Steps in math assessment usually include: General readiness those basics - relationships, 1:1, conservation, ordering or sequencingUnderstanding of operations conservation, commutative, associative, distributive Specific skills knows math facts, recalls and uses steps in computation, understands the processes67Problem solving sees the relationships and