*Much is taught, but little is learned.*

**factual and procedural**

**knowledge (the basics)**to do well in mathematics. Long-term memory is the key component in learning math or any academic discipline. Also, drill-to-improve-skill (

**repeated practice**) is necessary. "

**To learn something is to remember it.**" If you can't instantly recall 6 x 7 = 42, then you haven't learned it. If you can't write and solve a proportion with an unknown, then you haven't learned it. All learning makes changes in long-term memory. Indeed,

**competency in math**or any discipline is built on practice-practice-practice. Also, "

**Our ability to think depends on memory**," explains

**William R. Klemm**in a journal article, "What Good Is Learning I You Don't Remember It?"). Knowledge and skills are gained through memory.

**William R. Klemm**(Texas A&M University) points out that kids lack memorization skills. He writes, "Teachers should emphasize the educational importance of understanding, but not at the expense of overlooking the importance of memorization skills. Currently, mainstream educational theory embraces such attributes as insight, creativity, inquiry learning, and self-expression. But such emphases lead to bias and under-appreciation of the role of memory in learning. Students cannot apply what they understand if they don’t remember it. In the process of educational reform, the reformers discount the importance of memory." They are dead wrong! "Society needs people with knowledge and skills, which are acquired through memory." Indeed, "Our ability to think depends on memory." You can't think about something that you do not remember.]

In math, the fundamentals should be memorized. You don't want to figure out (i.e., calculate) 7 x 4 in [limited] working memory every time you come across it. Also, attention and focus are critical in class. Writing notes is important. Furthermore, teachers should present content that is well organized. Moreover, students can learn something better when it is associated with something they already know.

The progressive idea of learning in groups without an organized, hierarchical curriculum (e.g., Piagetian learning) is vacuous.

**Klemm**observes, "Kids don't appreciate how extraordinary attentiveness is." We teach kids not to pay attention when they are seated facing each other in small groups of four. Apparently, in the progressive classrooms of today, "collaboration" supersedes attention and learning.

Often, teachers are required to teach to the test. Unfortunately, they miss the idea that learning should be cumulative and permanent, not merely test to test. Abstract symbols and structures learned in math, (e.g., y = mx + b, 3 + 8 = 11, a + 0 = a, or y = x^2, etc.) are the visual images. Even if students know that an equation is like a balance (visual), they often do not apply the idea. An equation can be visualized by the equation, itself, a table of values, and a graph.

Lastly, the attitude of the student plays a critical role in learning. "Too often students have a negative attitude about the academic subject matter, and this attitude is self-defeating," writes

**Klemm**. In short a negative attitude toward math, for example, interferes with learning math. The negative attitude is learned from teachers who hate math and from parents who tell their kids that they were not good at math. I do not think most students dislike math; they just find it harder to learn than other subjects.

April 8, 2017, LT/ThinkAlgebra