“What is it with this new math?”
How many of you have heard this question from parents as they try to help their kids with homework?
With the switch to rigorous college and career readiness standards, many parents feel that the math being taught in the classrooms today is different from the math they learned when they were in school.
As I studied the new mathematics standards, I could see what the parents were seeing. Back when I was in school, we would receive a worksheet with algorithms to solve, using a step-by-step process to complete the work. However, this approach missed the conceptual understanding of the why behind the algorithms.
College and career readiness standards move beyond simply understanding the procedures of math to address three aspects of rigor: conceptual, procedural/fluency, and application. For students to reach the full intent of the standard, lessons should be planned to include the aspect(s) of rigor.
Analyzing a standard
Let’s look at a standard from second grade:
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
The aspects of rigor that need to be taught from this standard are both conceptual and procedural/fluency.
The word fluency indicates that at the end of the year, students will be able to complete addition and subtraction problems quickly and accurately.
The conceptual part of the standard indicates that students will be able to complete addition and subtraction within 100 by using the strategies listed (place value, properties of operations, and/or the relationship between addition and subtraction).
The standard does not specifically call for application to be taught; however, if students do not master the conceptual and fluency with this standard, it will be difficult for them to use addition and subtraction in a real-world situation.
Closing the gap now for future learning
A math teacher’s first go-to resource is the textbook. As they use the textbook to drive instruction, they find multiple instruction and practice pages that will use the standard algorithm to teach this standard to students. If a teacher only uses the textbook to teach this standard, there will be gaps in the students’ understanding of the why behind adding and subtracting numbers.
For students to be successful in future years with math, the conceptual understanding of adding and subtracting numbers is critical. They need to understand why and how to regroup ones to tens and tens to hundreds. They also need to know the why behind “borrowing” in order to complete the subtraction.
Teachers need to be good consumers of their resources, keeping in mind that the standards drive instruction.
Building on prior learning
If a second-grade standard is not mastered, simple problems in later school years will be difficult. For example, 12.64 + 23.77 is challenging if students do not understand how to regroup the place values that equal more than 10. Even though second grade standards do not have students working with decimals, they’ll need to understand addition to solve this type of problem in later grades.
Students who learn to add using a step-by-step procedure will need to either write this problem down or use a calculator. In a real-life scenario, purchasing items using these same numbers ($12.64 + $23.77), and then determining if $40.00 is enough to make the purchase, will be difficult if only the procedure is understood, due to the lack of understanding when subtracting with zeros.
Not knowing the "why" is not okay
Thinking back to my own experience with addition and subtraction, I learned to line the numbers up, and then solve the problem with the step-by-step process. I was never taught the why behind the algorithms for each operation.
As I progressed through my school career and into my adult life, I struggled with math. If I was in a store purchasing items that were $12.64 and $23.77, and I only had $40.00, I needed a calculator to figure it out. I could not subtract across zeros without either writing it or using a calculator. I felt innumerate my entire life, which seemed okay because I knew how to use my paper and pencil (or calculator) to get the right answer.
But it was not and is not okay. We never say it is okay for our students to be illiterate. As Elizabeth Green states in her 2014 article, Why Do Americans Stink at Math?:
To cure our innumeracy, we will have to accept that the traditional approach we take to teaching math — the one that can be mind-numbing, but also comfortingly familiar — does not work. We will have to come to see math not as a list of rules to be memorized but as a way of looking at the world that really makes sense.
5 planning questions to ask
Armed with this new insight into college and career readiness standards, now is the time to help students to become numerate. During the planning, ask yourself:
- What is the standard I am teaching?
- What aspect(s) of rigor does the standard call for?
- How do I need to teach my students the concept(s) in this standard?
- What is the complexity of the standard?
- What resource(s) will help students to reach the full intent of the standard and incorporate the aspect(s) of rigor?
Help parents understand the "why" behind the math
Parents also need to understand the importance of the three aspects of rigor to help their children at home. Here is a small list of ideas:
- Provide resources to parents.
- Host a math night or math events during the day in the classroom.
- Send home short how-to guides with new concepts.
- Record a short how-to video and post it on your class website, blog, or wiki.
- Use social media or email to share how-to guides.
The more parents are educated on the why behind the math, the more they will be able to help their children at home.
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