Learning and Cognition
Cognition has to do with the ways in which humans gain knowledge about the world. Cognition can also be defined as some internal representation of the external world. Learning in these terms, therefore, demands for the individual to strive to find the most accurate representation possible. The individual can use these types of representations to solve problems.
Mathematics is perhaps the first academic subject that we immediately associate with intelligence. As the saying often goes, you’re either good at it, or you’re not. Unfortunately, many people avoid this subject like the plague. Why such an overwhelmingly negative reaction? There are so many reasons that it is almost impossible to provide an answer within the scope of a book, let alone a single chapter. The body of research on the very broad topic of mathematical avoidance is enormous and comprises a number of subtopics. Some of these subtopics include mathematics anxiety (Richardson & Suinn, 1972; Tobias, 1993), attitudes and conceptions about mathematics (Fennema & Sherman, 1976; Hembree, 1990), learning disabilities in mathematics (Geary, 2004; Macaruso & Sokol, 1998), and mathematics as the filter discipline for career success (Steen, 2004). Indeed, each one of these subtopics can be a single theme of an entire book in its own right.
But people make math out to be a terrifying subject when it is not. Math does not have to be such a dreadful area of study. In this chapter, we argue that with a little ingenuity and perseverance, your child, who you may have subconsciously believed was mediocre at best and below average at worst when it comes to calculation and computation, can actually succeed in math—and even enjoy the subject, too. To show the ease with which one can succeed in mathematics, we start by providing a general overview of the development of mathematical thinking and the emergent cognitive processes by which young children acquire mathematical ideas. We then discuss important math habits that will instill a sense of triumph when your child encounters mathematical topics. Although these habits are crucial during the early years of formal schooling (i.e., kindergarten through fourth grade ), it is never too late to practice them in later school years. We then explain the importance of pattern detection and identification as an indispensable activity in succeeding in math. We show this through examples that require thinking (i.e., cognitive) abilities as opposed to the more rote, mechanical pencil-and-paper procedures or algorithms. Without identifying and recognizing patterns and relationships in mathematical problems, it is difficult to inculcate the motivational component of the subject—something that usually demonstrates a challenge for most teachers and parents. We then outline and detail a selection of essential mathematical concepts for parents and students to consider during the school years. We argue that these concepts serve as necessary keys to understanding more complex mathematical topics. Some aspects of mathematics may not necessarily be easy, but it is surely a subject that nearly all students can understand, find useful, and learn to enjoy.
To help you consider ways in which your child can improve her or his mathematical ability, it is necessary to instill good mathematics habits. The following are only some of the specific mathematics habits that parents can instill in their children to help them to excel in the subject:
- Write Neatly and Legibly. It is true that famous poets, novelists, composers, mathematicians, and scientists were often sloppy when they put their work on paper, but that was the case for their initial drafts. For most of them, however, the final drafts of their work were scrupulously clear and legible when submitted for publication or used for teaching. In short, your child needs to get into the habit of good penmanship—whether it’s for writing an essay or writing a formula in a math problem.
- Don’t Jump into the Exercises. Time and time again, when we ask students what they do when they attempt to complete their math homework, nearly all of them say that they only try to solve the problems assigned for homework. In other words, they don’t even consider reading the lesson, examples, or chapter topic in the textbook. As a parent, you must encourage your child to read through the section that is being covered for each homework assignment. Diving into the homework problems is a mistake, especially if your child is rusty with the topic.
- Use math technology appropriately. Calculators and computer software for mathematics can be quite useful but only to a point. Children of any age should begin to use a calculator whenever they are interested in using it or exploring with it. They should not, however, use calculators to complete homework assignments that involve number facts and multi-digit problems that involve addition, subtraction, multiplication, and division.
- Make math connections to everyday life. As parents, it is essential to make connections between what your child is learning in math along with the everyday situations that require skills in math. For example, have your child determine what the tip should be for a restaurant bill. Or, have your child measure the dimensions of a new construction in your home.
In general, there are five objectives that are necessary to help teachers and parents foster science learning in young children. The first objective is to recognize the child’s natural propensities to learn science. The second objective is to bridge the conceptual learning of science with inquiry-related skills. Third, parents and teachers need to recognize the importance of the creative process that is not measured by standardized assessment. Fourth, it is necessary to provide students with ample time and repeated opportunities to plan and conduct investigations that are directly related to their immediate interests whenever possible. And finally, it is critical to teach students the importance of cause-and-effect relationships that reinforce a level of internal control, allowing children to affect and predict events.