The Absurdity of Math Evaluations
We all know the rules in math often don’t make a lot of sense when standing alone. Can’t divide by zero. Why? My Mom told me. Any number raised to the zero, except zero, equals one. What? When you divide fractions, you flip and multiply. How about working with integers, when adding sometimes you add, sometimes you subtract and when you subtract integers you change the signs and add, but sometimes you subtract. Wow!
To ensure math makes sense, we need people teaching math who know, understand, can apply and teach math so it does make sense.
The shortage of qualified math teachers exposes deeper issues on why our students aren’t successful in mathematics. The shortage of very qualified math teachers, teachers with a degree in math, has led to classes taught by people entering the profession through alternative licensure programs, programs that suggest a degree in business qualifies a person to teach math and substitute teachers with little or no math backgrounds. Clearly, these teachers need assistance so they can help their students learn math more effectively, efficiently and with understanding.
These under-qualified teachers are being evaluated by building administrators who probably have less knowledge and understanding of math than the people they are supervising, that suggests their evaluations don’t do anything to improve math instruction.
Most math classroom observations result in suggestions, recommendations or directions that are “instructionally” based not “content” based strategies. In the vast majority of these observations, there does not appear to be any specific math content strategies. Strategies that would suggest how an arithmetic sequence could be introduced through skip counting learned in elementary school using multiples, then scaffolding to non-multiples. Identifying simple, straight-forward examples that clarify the topics so students are focused on learning the new concept or skill and not being bogged down or distracted by needless arithmetic.
Math is very repetitive, using linkages to connect the Pythagorean Theorem to the Distance Formula, Equation of Circle and Trig Identity, cos^2(x) + sin^2(x) = 1, which are all the same formula just written differently because they are used in different contexts, allows teachers to introduce new concepts in a familiar language, thus making the students more comfortable, to review and reinforce previously learned math or address deficiencies and teaching in a different context all promote increases in student achievement. If school administrators can’t make those kind of connections, then they surely won’t be communicated to teachers that actually improve the delivery of instruction that helps students learn.
Math is very often about decision-making, that means students have to be able to compare and contrast information they are learning so they can make the problem simpler. For instance, just finding a common denominator calls for deciding which method to use; multiplying, writing multiples, LCM or the reducing method. The method chosen should be based on the problem itself. Solving systems of linear equations; do we solve by graphing, substitution, linear combination or Cramer’s Rule. Again, that decision comes from comparing and contrasting the information in the problem. Quadratic equations, do we solve by factoring, the x^2 method, completing the square of the Quadratic Formula?
If we intend to improve student achievement in mathematics, then we must improve the quality of math instruction in the classroom. In order to accomplish that, school administrators must include not only instructional strategies in their observations, but also math content strategies. Administrators should be able to include the necessity of having good math definitions, using specific linkages, using simple, straight-forward examples that work, that clarify instruction and don’t bog students down in needless arithmetic. They need to address scaffolding, looking for patterns, thinking out loud as well as building models that results in math making more sense. Stressing vocabulary and notation are extremely important for success in math as teaching students to reduce the issues to a simpler problem and scaffolding for increased understanding.
Teaching students how to take notes using math language and shorthand (notation), how to read math and to write about the math they are learning are all important to student success.
Improvement in math instruction will not occur unless school administrators take professional development in evaluating and supervising math, a class that stresses important topics in math and emphasizes the need to include math content strategies with examples that can be used in their post observation conferences and their more formal evaluations.
The added emphasis on math content strategies might also change the way teacher observations are scheduled. Rather than a date certain based on an open date on a calendar, school administrators might choose dates based on when a particular topic will be introduced so they can use their new-found math knowledge and understanding to address math content strategies in post observation conferences and evaluations.