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Why Did They Change The Way They Teach Math?!
Sep 21, 2018
Look at the history of math reform in U.S. education and you will see that math instruction changes more significantly than reading instruction over the same period of time. You might wonder why math instruction changes from one year to the next. After all, 2+2 has equaled 4 since the beginning of time. While the literacy standards from the Common Core Standards Initiative get implemented without much backlash, the math standards have created shockwaves throughout Littleton and Colorado. Why? The answer may lie in the track record of math education in general.
At Mathnasium of Littleton we understand your frustrations with the changes in math curriculum. We hear from Littleton area partents daily how they find the new standards and the ways they're being implemented confusing and frustrating.
We are helping Littleton parents understand how and why the way the Common Core Standards are taught is different from the math instruction most of us received as a child through a series of articles. You may want to read two of our previous articles about the topic. I Don’t Understand the New Common Core Math My Kid is Learning and Are You Frustrated with Common Dore Math Standards?
This article on Quora is also interesting.
Math Reform Reflects Society’s Values
Teachers have been trying to figure out the best way to teach children math since the beginning of public school education. The history of math reforms is fascinating because it gives a snapshot into the values and beliefs of the day.
A Timeline of Math Education
1600’s and 1700’s
Colonial Americans were mostly concerned about preparing children for reading the Bible and training for a trade. Formal education was mainly restricted to children from the upper class. Children attending school learned to read and were instructed in ancient languages. Even for them, math was rarely taught beyond simple arithmetic. Arithmetic instruction was typically reserved for boys twelve and older.
America began expanding its view of education to include all children, regardless of class or gender. As business opportunities expanded, families saw education as a way for children to improve their economic status.
Harvard began requiring math skills for entering freshman. The secondary schools recognized that they should begin teaching math. However, teaching math proved difficult in the early days. There were no textbooks to use and most school teachers did not have any training in mathematics. In 1821, Warren Colburn produced a textbook called First Lessons in Arithmetic. For the first time, there was a resource for teaching math to very young children.
The College Entrance Examination Board was founded. The purpose of the CEEB was to standardize college entrance requirements. This was the predecessor to the ACT and SAT tests college-bound students take today. As subjects such as algebra, geometry, and trigonometry were increasingly expected as prerequisites for entering college, high schools began offering more advanced math topics to their students. Still these topics were reserved for the few who were expected to go to college. In 1914, less than 50% of U.S. high school students took algebra.
The National Council of Teachers of Mathematics (NCTM) was formed. This was the first time a group of math educators sought to improve math instruction and unify the approach. Their mission was, and continues to be, to provide leadership for all math teachers. This helps all students get a quality math education. Wow! Compare this to children in school just 100 years previously who might get a teacher who had never even taken math. Finally, an organizing body existed to improve math instruction for EVERY child.
The field of mathematics saw significant gains and it was being applied more and more to the advancement of technology. Mathematicians got interested in education. Some of their ideas about advanced mathematics began to make their way to the NCTM and to school teachers.
October 4th 1957
The Soviet Union launched Sputnik at the height of the Cold War. Having an enemy satellite flying overhead was a wake-up call to the American public about the state of math, science, and technology education in the U.S. Suddenly, politicians, educators, and parents were scrambling to catch up to the Soviet Union.
As a reaction to Sputnik “New Math” was introduced. New Math centered around the idea that a student should be able to prove a theorem before advancing to another topic. Children started learning more difficult math in earlier grades. Topics such as Boolean algebra and symbolic logic were also introduced.
1970’s and 1980’s
The New Math reform was considered a failure, even though Boolean logic helped the computer revolution get started. Most parents felt the topics were not practical. Teachers also felt poorly trained for many of the topics they were expected to teach. The backlash from New Math led to “Back to Basics.” Back to Basics focused on computation, algorithms, and facts. Many teachers and parents of high school children today were educated in the Back to Basics era. In 1983, the NCTM published A Nation at Risk which stated math education in the U.S. was mediocre, at best. Then in 1989 it published An Agenda for Action, which was the first attempt at making national standards.
California demanded textbook publishers to write math textbooks with a constructivist methodology. Constructivism is the idea that children need to experience math concepts, rather than be lectured on math concepts. It uses “manipulatives”, such as counting tools, to help children construct their own ideas about math. Much of the nation followed California’s example.
Scores from the 2012 Program for International Student Assessment (PISA) which was first conducted in 2000 and is administered every three years show the U.S. is still trailing other nations in math. The gap was particularly pronounced in problem solving and for low-income and minority students. Girls also face a learning gap in math and science.
In 2009, the National Governors Association hired a team of educators to write the Common Core Standards for math and literacy. The idea was to create a consistent and clear curriculum using best practices for schools to follow. The educational department in each state had the right to choose to adopt the standards in whole or in part. The Colorado Department of Education adopted all of them in 2010. Fourty-five states, the Department of Defense Education Activity, Washington D.C., Guam, the Northern Mariana Islands and the U.S. Virgin Islands have adopted the CCSS in ELA/literacy and math. They are now in the process of implementing the standards locally. Colorado's Department of Education adopted the CCSS in 2014.
The Common Core State Standards put more emphasis on mathematical reasoning and complex problem solving than what was emphasized in the past. A well-known mathematics educator, Douglas Gouws, described how societies’ understanding of what math is shapes instruction. Those who see math as a set of skills focus on teaching by drill, without any thought to mathematical reasoning. The more a person sees math as a way to understand the world, the more the math instruction is geared towards analytical and creative thought.
The Standards are intended to improve student achievement by having a “common” set of standards nationwide. The thinking is this: If students are able to achieve these standards, they will be much more prepared for college and/or their careers. Also, if students are taught and assessed by the same standards at each grade level or subject, the gap between underperforming and high-performing students should narrow.
The Common Core Standards are designed to help students master: Eight Mathematical Practices. While these practices are currently in use in many high-performing classrooms, their widespread use is expected to bring more focus to mathematics instruction.
- Make sense of problems and persevere in solving them
- Reason abstractly and quantitatively
- Construct viable arguments and critique the reasoning of others
- Model with mathematics
- Use appropriate tools strategically
- Attend to precision
- Look for and make use of structure
- Look for and express regularity in repeated reasoning
Change takes Time
Even when society demands a math reform, it is hard to make those changes happen quickly. Think of all the resources that must change in order to implement shift math education.
1. Mathematicians and policy makers must come to some consensus about the importance of certain strands of math and the order they should be taught. For example, why teach geometry instead of accounting? And does algebra have to precede geometry?
2. Current teachers must change their methodologies. This requires training and buy-in from the educational community.
3. Publishers must create new textbooks that focus on the new ideas.
4. Teacher colleges must start training future educators to implement the reformed ideas.
Mathnasium of Littleton is committed to helping parents and students navigate their math instruction. We know that understanding certain foundational concepts such as counting, wholes and parts, and proportional thinking form a solid foundation for students to be able to conquer more advanced math topics. Call us today 303-979-9077 or contact us using the form above to find out more information!