The new math curriculum believes, among many things, that:
· Students learn by attaching meaning to what they do, and they need to construct their own meaning of mathematics.
· Students need to explore problem-solving situations in order to develop personal strategies and become mathematically literate. They must realize that it is acceptable to solve problems in a variety of ways and that a variety of solutions may be acceptable.
· Curiosity about mathematics is fostered when children are engaged in, and talking about, such activities as comparing quantities, searching for patterns, sorting objects, ordering objects, creating designs and building with blocks
Before I critique Anna’s arguments, we must realize that when someone talks about “meeting” or “raising standards”, they are usually referring to applying conventional, or traditional, instructional techniques in the classroom. Usually this really means, “Everything we are doing is OK, we just need to be harder on students”.
Anna Stokke, will have us believe that we have lowered standards in our math classes and we need to raise the standards back up. Her first argument about the new math curriculum is
“… practise and memorization of number facts are no longer a priority in our schools. Children are instructed to use overly complicated "horizontal" methods to work out simple arithmetic problems. Now, simply knowing how to produce an answer to a basic multiplication question, no matter how long it takes, is considered to be a sufficient indicator of fluency.”
The reality is that being told number facts, and forced to regurgitate these facts, will not create an environment which is conducive to deeper learning. The best way a student can understand, not just recite, mathematics is through discovering the facts on their own. For some, this discovery process can take seconds, while for others it may take an entire class. The role the teacher plays in this is by acting as a tour guide. By keeping the students on the “path” towards the discovery, it will ensure that all students create their own individual, and innovative, techniques in learning mathematics.
Next, she says that
“Kids are set up for failure if they are not required to memorize basic number facts. Without the memorized facts, they will become hung up on these simple numbers when they are trying to solve more difficult problems.”
I often ask myself, which skills do I want for my own children? Do I want them to be taught the skills to memorize, and ultimately be able to complete algorithmic tasks, or the ability to create and design which will lead them down a road towards a career with heuristic tasks?
The reality is that the age old saying that “Practice makes perfect”, does not apply to deep learning in mathematics. Traditionally, students have been given worksheets which have multiplication facts on them and are given a strict time limit to complete these (named Mad Minutes), but in actuality the mark given on these “Mad” sheets really do indicate to anyone as to knowledge of the student writing them.
The weak students truly suffer the most from this model of proficiency-driven, because they find these tasks dull, repetitive, and entirely unusable in the world outside the walls of the classroom. I would agree that sometimes, knowing facts as the days of the week are important, but these facts should be a by-product of use and application not out of necessity.
Another fact is, by spending time forcing these facts to be memorized is truly interfering with a child’s innovative and creative ability. Most of these worksheets require low level thinking and usually can lock the thought process of a student into understanding simple algorithms. Eleanor Duckworth summed it up the best,
“Knowing the right answer requires no decisions, carries no risk, and makes no demands. It is automatic. It is thoughtless.”
Is this the environment in which math students should be learning?
Last she makes the statement,
“…children need to practise arithmetic skills, without calculators, do an adequate amount of pencil-and-paper math, and memorize times tables in order to become proficient in math. Children need to be given time to do a reasonable amount of math daily at school and this needs to be a priority.”
This closely sounds like a case for homework at younger levels and there is not one shred of evidence that supports the idea of homework in elementary grades. Assuming this is not her argument, I will critique her argument for repetitive daily work in school.
When we teach math as “routine skills” students may get the correct answer, at an efficient rate, but they will most likely be clueless about the significance of their of their answer. The National Research Council calls it “Mindless mimicry mathematics” and can no longer be the norm in our classrooms. Another math educator, William Brownell, over 70 years ago explained “one needs a fund of meanings, not a myriad of ‘automatic responses..’ Drill does not develop meanings. Repetition does not lead to understanding.
There are many studies that support this view of thinking. If we look at an environment where students are not learning effectively, it is usually due to an overwhelming desire to maintain traditional beliefs and practices. Once again classrooms need to be aware that
It is important to realize that it is acceptable to solve problems in different ways and that solutions may vary depending upon how the problem is understood.