Reflection on the 13 Rules That Expire

Reflection on the 13 Rules That Expire 13 Rules That Expire is written by a group of women aiming to tell the misconceptions of the rules that young students memorize during their early years of education. The authors of the text are Karen Karp, Sarah Bush, and Barbara Dougherty. This article is written for teachers and offers different rules that teachers apply to mathematics and are often not applicable to students as they further their education. As a future educator, I think this article is very important to read and study because before the Common Core standards were introduced in 2010, many educators had been teaching students the ways they were taught as children, which can often times can feel mysterious and somewhat magical to young children. The new standards state that the Educators should hold children to a higher standard of understanding the material, instead of just memorizing mathematic rules. The article states “Mathematically proficient students try to communicate precisely to others.... use clear definitions... and carefully formulated explanations...”. This is a big change in previous teaching strategies, and specifically my experiences when learning math in my elementary school days. There are a total of thirteen rules that the articles thoroughly talks about and the first major rule I think is important is rule number two. Rule two states that students should use key words to solve word problems. Word problems are often very intimidating for students of all ages, much less young students. Many teaching strategies suggest key words such as altogether, sum, and left over are often used to find the answer to these word problems. The problem with taking key words out and not reading the context of the question is that many words in our vocabulary can be confusing and misleading often leading to the wrong formula being used to get the correct answer. The main point here is that although it may be useful for children while they are in the first years of learning how to deal with word problems, as they get older and more vocabulary is integrated into the questions, it may be misleading and produce the incorrect answer without reading the whole problem. Another big rule that we are taught as young students is increasing in numbers, addition and multiplication always produces larger numbers than the addends. This is rule number four in the article. When learning the basic orders of fact families, it is a good way to explain to children when using positive whole numbers. However, when students get older, they will be introduced in negative numbers and will have to use addition and multiplication to find the sum of two numbers. In this instance, multiplying two negative numbers equals a positive number. And on the opposite side of the spectrum, multiplying a negative number and positive number will not equal a larger sum. Another good example of this rule expiring with children is when they begin to multiply fractions and decimals. As far as the inverse of multiplication and addition we also learn a rule to math is that when using division and subtraction we must always get a smaller number than the addends. This rule is often introduced in the third grade and is known as rule number five in the text. When the two numbers are positive or whole numbers this rule is accurate and can be correct. However, if the two numbers the student is computing are negative we get a contradiction to the rule. When dividing two fractions or decimals we may actually get a larger number. This also applies when dividing two negative numbers. For example, if you divide -16 and -4 you will get 4 which is a larger number. Rule number seven states that two negatives always make a positive. Usually, when taught to students, this rule is used in the context of multiplication and division. While the rules work for both multiplication and division, it is not true when adding or subtracting. I believe this one is very important to realize the effects it can have on young children. When learning these rules or tricks when young, children often get used to the rules and are set on that rule. It is difficult to break them of that rule when talking about multiplication and division. As a teaching assistant teaching third grade students, when they see a teacher give a rule like this they will have a hard time differentiating when to use the rule. Instead of a teacher saying two negatives always make a positive, we should explain that when multiplying and dividing this rule applies, but when adding and subtraction the numbers this rule cannot be counted on. The last rule I want to focus on is that the longer the number the larger the number. This is rule number eleven, and it can also be confusing for young students. When talking about whole numbers, we can use this strategy to explain to children that yes, the bigger the number the larger the number. This rule focuses on the place value of each number in the question. A good way to explain this to children is that when using whole positive numbers, we can use this rule and that the longer the number is in fact a larger number. On the contrary, when educators introduce decimals and negative numbers, we need to explain that this rule no longer applies. A good example of this is if you explain that .5 is larger number than .250 we must use the place values of the decimals to teach students that just because the number is longer the place values are different than positive whole numbers. As a whole, I thought this article is very useful to change our methodical ways of teaching tricks and rules to students. Instead of teaching students the rules of mathematics, we should focus on the students understanding of each rule. If they students grasp the ideas behind the rules and can differentiate positive, negative, fractions, and decimal numbers the rules can be very effective and useful for the students’ future of mathematics. I think the overall tone of this article was quite negative towards the rules that we are teaching the young students. I think there are both positives and negatives in this article, as I stated before I think it’s important for a future educator to read and study article like this so we can start early to teach kids the correct ways of computing and solving problems. These Rules explained in the article are very effective while students are first learning the basic computing ways, teachers need to explain to students that these rules do not always pertain to each problem as they continue their education. From my personal experiences, it is hard to learn a different way of understanding math and to curb the old magical ways of solving problems. We’ve talked about many of these rules in our course this semester and have seen firsthand that we need to be teaching young students to fully grasp the information instead of just memorizing rules. When memorizing rules or tricks of mathematics students do not learn the correct information behind the rules. Although I think the rules need to be clarified, I also think that the rules we have been taught and continue to teach students help when they are just beginning to learn the ways of computing mathematical problems. I believe they are a good building block for teaching kids the intimidating and often frustrating subject of mathematics.