Geoffrey Lewis is a math coach in Sunnybrook S.D. 171 in Lansing, Illinois, and acknowledges input and support for this article from Bruce Christensen, principal at Heritage Middle School, and Joseph Majchrowicz, district superintendent.
Reaching Adequate Yearly Progress (AYP) targets in middle school math has no short-term, easy solutions. Yet goals for educational instruction fall into your lap as members of the school board.
As members of the school board, the community looks to you to provide the general direction of education in your district. If something is not working you don't need to take charge of day-to-day operations, but you do need to provide a vision and overarching goals for your administration and staff to attain.
To do that, you also need to understand what's happening in your district's classrooms.
To make AYP under No Child Left Behind, the state is telling many districts that they must change. Change in math instruction involves three major areas:
The Illinois Standards Achievement Test (ISAT) has changed over the last several years and, like it or not, each of these areas is being tested. ISAT testing in math is now a test of concepts and applications, not just computation. This is not to say that students no longer need to know their basic facts, but there has been a shift in the balance of memorization of facts versus the concepts and applications of these facts.
"If only those darn elementary teachers had taught the kids more we would not have this problem" is often offered as both a cause and solution. Don't believe it. High school teachers say almost the same thing: "If only those darn middle school teachers had done more, our school could make AYP."
Previously learned material can affect scores, but a low score in a single area is much more than a concept not being taught. It is a symptom of a much more serious problem that may require multiple solutions. The first symptom of lung cancer might be a cough, but this is an indicator of many more problems.
Example: a low score in measurement is not a low score in a single state goal, but also a reflection of a fundamental lack of understanding of fractions and numeration. Because measurement usually involves a kinesthetic activity and group work with communication and connections, these also are lacking.
If students are not being taught what, why and how to be able to understand higher level concepts, it may also reflect classroom management skills and type of instruction ... perhaps even building climate.
Do not expect "pull outs" to work. Other types of remediation also are doomed unless they incorporate a fundamental change in the method of delivery of instruction and the staff is willing to make change. All too often the students do the same worksheet each year in grades 5 thru 12 and still do not have a clue how to do the problems when they graduate.
Where to start
The change from a computation-based test to a concept/application-based test provides a place to start. A quick review and a report by your administration of the previous year's test scores should show the areas of weakness. Students may score well with Goal 6 problems involving estimations and measurements, but they might be unable to analyze data and predict probabilities as required in Goal 10.
Usually an area is weak because the teachers never got to the concept in their lesson plans. How can students possibly answer a question that they have never been exposed to?
The questions are not asked in great depth on the ISAT, nor are students exposed to questions that involve a great deal of computation to solve. However, many times classroom teachers will spend several days teaching the same concept over and over again with work sheets that make no connections to the student's world and with larger and larger computation problems.
In addition, the problems do not teach the concept in a way that is understandable to the student — they only provide more practice on computation using a calculator to crunch out meaningless answers to a problem that now has become just a memorized process.
Instead, the national math council recommends that students be taught why something works. Administrators should insist on having students do kinesics activities that help them understand how and why a process works. The administrators should check that staff is not spending too long on one goal and ignoring others. They should also have the instruction make connections to the learner's world, by asking that part of the evaluation process include this as a goal.
When test time comes, it should not be a shock to staff that they have only covered half or a third of the concepts tested and that students do not remember the material they did cover. Administrators should check to see that teachers "spiral" their review throughout the school year. "Spiraling" involves introduction of a concept that is then revisited throughout the year. Learning for the students must be a process that engages them and makes connections, not something that is introduced one day and expected to be mastered the next.
Time and direction must also be provided for principals to develop leadership and team building in your schools. Someone must check that goals are being covered and that individual students are mastering these goals. Staff and administration must follow up and see that a structure is in place for remediation for students who did not master a goal.
Making observations
A team of observers, using teachers or administrators from other buildings or even educationally informed community members, is an effective method to determine whether teaching methods involve the student and are not just convenient for the teacher. Teams should be built to teach mathematics across curriculum areas.
When teachers work as a team, they also provide a sprit of ownership in the test scores for all staff. Data from walk-through observations can provide feedback in all these areas.
Harry K. Wong, in his book The First Days of School, offers many helpful solutions: "The effective classroom is one where the students are actively engaged in meaningful work. The ineffective classroom is one where students are in their seats doing busy work or nothing. Students learn only when they are actively engaged."
Observers should watch the students and the lesson, not the teacher. Are students actively engaged in the lesson? Is the lesson one that is related to national or state standards?
One teacher I observed said the students were actively engaged with their pencil and paper doing the worksheet. Worksheets are not learning! However, used in moderation, they can provide some additional practice.
"If you increase the amount of time the student is working you increase the amount of learning," according to Wong. If the teacher is doing the doing and not the kids, something is wrong.
Two additional keys
In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics offers two additional keys to student learning: connections and communications.
"When students can connect mathematical ideas, their understanding is deeper and more lasting. They can see mathematical connections in the rich interplay among mathematical topics, in contexts that relate mathematics to other subjects, and in their own interests and experiences.
"Communications is an essential part of mathematics and mathematics understanding. It is a way of sharing ideas and clarifying understanding. Through communications, ideas become objects of reflection, refinement, discussion and amendment. The communication process also helps build meaning and permanence for ideas and makes them public."
Communications and connections also extend to teachers and the administration as to how they set the tone in the classroom and building. "The effective teacher has positive expectations for student success," Wong wrote in The First Days of School. "The effective teacher is an extremely good classroom manager. The effective teacher knows how to design lessons to help students reach mastery."
These are all skills that the teacher must have to relate to students. In its own way, the ISAT evaluates each of these keys. This is part of the change in school climate that is needed to meet ever-increasing AYP targets.
Bloom's taxonomy provides an appropriate evaluation tool for your administration. At level one, students are required to use only the simplest skills, essentially fill in the blanks on a worksheet. At level two — comprehension — students are asked to describe, explain and say things in their own words. Level three requires students to apply, conclude, demonstrate and illustrate. Higher levels use words like: classify, compare, contrast, compose, create and evaluate.
The current ISAT is one that asks for level two skills and beyond, so staff must teach this type of learning. Are teachers trained to teach higher level thinking skills? If not, your district should offer this training.
Making changes work
ISAT coach books have about 45 lessons at each grade level. Each of these reflects a state learning goal and can easily be taught in one or two days. Administrators should determine if your teachers are covering all of these before testing.
Low scores are a good indicator. The staff and administration should ask questions, such as:
Learners, especially in middle grades, need fun and involvement to change school climate. Instructors must also help students see connections between similar material such as fractions, decimals and percent by using techniques such as mind mapping.
A variety of brain-friendly techniques can be used to help students remember difficult, multiple-step problems. The use of problem solving blocks, the Asian method of solving story problems, fraction tiles, integer chips and algebra tiles all have been shown to be effective. However, teachers must be trained in such techniques for these tactics to be used effectively.
The final piece
The final piece of the puzzle is use of technology. Computers and appropriate use of interesting, interactive websites keyed to state standards can provide a connection to middle school students. Games involving practice on key mathematical concepts and on basic skills can involve students so that they will buy into working at home for hours learning mathematics, which also solves the problem of getting students to spend more time on math.
Material chosen to be used this way must satisfy two basic criteria: it must be fun for students and must relate to state or national goals and standards.
Student use of learning time in my district has greatly increased and the attitude toward math has changed. Because students are playing actual games, they are more than willing to think at higher levels to win. They read instructions and are involved. They now regard math as a fun activity they enjoy doing.
The better math websites provide instant student correction and response. They also have students using their creativity and thinking skills. Many are already correlated to standards.
Computers also provide students a chance to experience activities that would be very difficult for a classroom teacher to demonstrate, such as 3-D drawings, graphing and probability. Because computers are very visual and hands-on, there is no question of who is doing the doing and learning. Students do not sit staring at a blank computer screen as they can sit blankly in class.
No single answer exists for every school, but a combination of the above methods should provide an answer.
Play is work for children, and children must be empowered by their teachers to learn. Teachers must be empowered by the administration. Teachers, students, parents and administration must be a team where each feels ownership to not let the others down.
The board must support the direction for both the teaching style and curriculum material to be covered through training and follow up by teacher/administration teams. Training for staff requires a long-term, continuous goal that will take several years to accomplish. It is one that when used correctly has proven to change test scores.
References
National Council of Teachers of Mathematics, Principals and Standards for School Mathematics, 2000
Harry K. Wong and Rosemary T. Wong, The First Days of School, Harry K. Wong Publications Inc., 1998