Follow up to Friday
Last week, I wrote about my disdain for the multiplication table and its use in the classroom. Today, I want to follow up with more information about the taped problems and cover, copy, and compare interventions. I also want to take the opportunity to discuss a few other things that I have seen in the math classroom that can be modified or improved.
The cover, copy, and compare method was adapted from spelling for use in mathematics. It has been used quite well in spelling and vocabulary in the past. In last week’s post, I focused on alternatives to the multiplication table, but it should be noted that these are not limited to multiplication alone. Taped problems and C, C, & C can be used for other math facts that need to be memorized for automatic recall. These activities can also be used for division facts or for younger students trying to learn their basic addition and subtraction facts.
In last week’s post, I wrote about using the term, multiplication, instead of using times. It is important to use precise mathematical language as much as possible. I think the biggest issue I see with this is how teachers and others refer to three digit numbers. The number 124, should be pronounced one hundred twenty-four and not one hundred and twenty-four. In math, the word “and” denotes a decimal point, so saying one hundred and 24 one-hundredths would be correct. Misusing the word “and” becomes confusing to students, and the use of precise language can help to prevent this.
Flexibility in Math Procedures:
I am sure we have all seen an instance where a student gets her answers correct, but has used a different method than the teacher. The student hears, “You got the right answer, but you did not do it the way I showed you. Therefore, it is incorrect. You have to do it the ‘right’ way.” This is very frustrating for students and often stems from the fact that the teacher does not possess a strong understanding of math and its concepts. There are numerous paths to the same answer in math and some methods can make more sense than others for students. However, many teachers force the student to learn the one way that makes the teacher most comfortable. Yet, teachers should be willing and able to meet students where they are, and must be flexible in how they approach problems. In order to do this, teachers need to improve their math abilities and knowledge. When I wrote my master’s capstone, I found at least 13 different algorithms to solve multiplication problems. Teachers are not limited to a single method for solving problems and should be able to employ a variety of tools to help all students understand math.
To appreciate math, people need to feel that it applies to them in some manner. Students need to see that math can be used in a variety of real-world scenarios. The story problems in most textbooks do not come close to being authentic problems. In fact, they are often so arbitrary that no one really takes them seriously. In addition, many schools have outdated textbooks that include problems with objects that do not exist any longer. For example, I have seen problems talking about a student going to purchase their favorite cassette. Students today have never even heard of a cassette and this makes the problem that much more frustrating and useless. It will take more work, but teachers need to consider writing their own story or word problems that reflect real world issues that students may face. Additionally, teachers should consider using the names of the students in class to write their problems. This gives students ownership and helps to make solving these problems more fun. Here is one example:
Maria, Abdu, and Laa’iq were tired of playing basketball on a dirt field. They found a donor that has agreed to pay for a concrete basketball court. However, the three students must determine how much concrete is needed, what local companies charge to pour concrete, and how much the project will cost, as a condition of the donation. Abdu has played basketball since he was very little and knows that a youth basketball court is 74 feet long by 42 feet wide. Use this information to help Maria, Abdu, and Laa’iq get their new basketball court.
This problem will require students to solve math problems for area, volume, and cost. In addition, they will need to use the internet or local resources to determine what concrete companies charge and what the total cost will be. This problem is a real-world issue that integrates math, technology, and finances. It is more robust and more authentic than most textbook problems. My students have really enjoyed being able to do these types of problems. I have used many similar problems in the 4th and 5th grade and found that students were able to calculate everything quite well if they were given enough time. Moreover, they had ideas like asking volunteers to donate their labor and making a half-court to lower costs.
Stay tuned, in tomorrow’s post I will tackle climate change and Christianity. Have a productive and joyful day.
I recently completed my PhD in Education (Curriculum and Instruction) at the University of Wyoming. I have published multiple articles in peer reviewed journals and have a book chapter coming early next year. I aim to explore issues of privilege and equity of education, especially as they pertain to STEM education.