This is a guest post by Mark Webster, continuing his tradition of guest posting for me during Blogathon. He is a graduate of Purdue University from the School of Science in the field of Mathematics Education and is currently a High School Mathematics Teacher in Indiana.
Please note that the author is representing general trends and personal experiences of a trained educator combined with popular evidence-based practices. By no means is this exhaustive. Please do not be butthurt. If you have evidence-based practices that conflict with anything I have said, please feel free to leave a comment.
There has been a lot of discussion on the problems in education, in general, but never do you hear a bigger cry for change in any other subject than you do in Mathematics. Perhaps it is time to analyze the problem and line up some solutions.*
Who are the problems in Math Education?
Teachers are certainly not the only problem, but when deciding to figure out the problem, it’s always best to start inward. In this post, I will be looking at what teachers need to focus on.
In our schools, there is still a lot of passive learning going on. What is passive learning, you may ask? Let me answer your question with another question:
When you imagine a math class, what do you think of?
Probably something like this:
A teacher, facing the board, not interacting with his students. Many of us, myself included, have had experiences like this. No teacher-student interaction. No checks for understanding. No eye contact. Perhaps, even more pernicious, there may not even be an analysis of the learning and long term progress of students.
Direct lecture-style math classrooms create an environment of passive learning. The teacher says a bunch of words at the front of the board; maybe, if he is a more dynamic teacher, waves his arms around a little bit; and then throws quizzes and tests at you. (Multiple, if you’re lucky-on the college level, there is rarely regular assessment…but that is neither here nor there.)
Even worse, the math classroom suffers from a lack of student metacognition and critical thinking-an ailment in a math classroom that baffles me to no end, particularly because that is, more often than not, the go-to excuse that teachers trot out when a student asks them “When are we going to use this?”
Rarely is the question asked, “Is our children learning?”, the answer to which is, more often than not, either “No.” or “Not well enough.” Now it is time to move beyond that question to “How can we help them to learn?” For example, if you’re trying to teach the orthogonal matrix, which method would help the children learn best? Teaching on a whiteboard or by actively trying the methods themselves?
How will the Common Core Standards help?
One of the country-wide initiatives that will be taking hold in the coming years, the transition to which will be complete in 2015, is called the Common Core Standards. While there are standards for Math and English, for obvious reasons (Hint: I’m a math teacher) I will be only talking about the Math standards.
1. Stricter Math standards for the USA.
If you look on the national report cards, you might notice grades for the states are changing. Of the 50 states, only six of them have not bought into the common core standards. If you or your children are students in any state besides Washington, Alaska, Texas, North Dakota, Nebraska, or Virginia, you will have (hopefully) heard of the change. A common set of standards across the country will mean that students are learning with the same level of rigor and relevance in Indiana as they are in New York or Mississippi.
2. Increased focus on Critical Thinking
In my professional development and my own personal research on the PARCC exams, I’ve come across the same thing over and over: The standardized tests of the past will not go away, but they will be refocused. Instead of fifty “Math Problems” on a test, the student may be given five or six “Math Tasks.” These tasks may involve, on the elementary school end, explaining the purpose of a step within a problem that they have completed for you, finding errors in simplifying a problem down and explaining what the error is, or even taking a newspaper article and analyzing it to take a position, using evidence. Instead of focusing on finding an answer, the test will be concerned with how they can apply math to that answer. How wild!
3. Broader, more targeted learning objectives
Most state standards and assessments have, in the past, been far more focused on students simply demonstrating their knowledge of a process, i.e. “Plot these two points and determine whether the slope is positive or negative.” Common Core standards are far more broad and far more targeted. Much like the National Counsel of Teachers of Mathematics standards, the Common Core standards concern themselves with specific domains of learning and applying them to metacognitive tasks.
Now, instead of plotting those points on the exam; they may, instead, be given a question that asks them to analyze, display, and track profit margins for a company and take a position on whether or not they will be able to afford to stay open in five years.
The accountability is changing from teaching mathematical processes to teaching thought processes. I approve of this, but does this really address the problems that we have seen above? I don’t think so.
So…How Do We Do This?
There are many champions of new processes within the Math Education community. Many of you have heard of Salman Khan and his famous Khan Academy, fewer of you have probably heard of Dan Meyer***-some Math teachers even haven’t (A fact which breaks my heart.), and I’m sure even less of you know about the conflict of pedagogical styles that lies between them.
Let’s break them down:
Dan Meyer’s pedagogical philosophy, a project that began as WCYDWT? or What Can You Do With This? and has slowly morphed into something he calls Any Questions? is designed as a student-centered, inquiry-based, generally collaborative effort to force students to lead the discussion and gain ownership of the material by creating the payoff in the medium used to teach the material; and, instead of spoon feeding them concepts, force them to push through a mathematical task and create the demand for the material.
Salman Khan’s pedagogical philosophy, a project that began as a series of youtube videos, has become a website, and some might say a school, of its own. The Khan Academy allows students to develop on their own, facilitates continuous improvement for the students at their own pace and on their own terms, and allows for constant pedagogical moderation.
Math teachers and parents alike have raised concerns about the methodologies that these two men have created. Dan Meyer critics fight him because they believe his philosophy creates a lack of rigor. Salman Khan critics fight him because his videos do just as much lecturing as one might see in a classroom, and do nothing to enrich and create ownership of the material.
Even with the miles of space between their two philosophies, it is worth the time to compare them and see a similarity:
These philosophies depend on a consistent foundation of what has come before. The genius of Dan Meyer’s method lies in the students being able to work through the tasks because they are absolutely prepared to tackle it. The utility of Sal Khan’s method is that because students get to a topic on their own terms, they are prepared to see it and they can meet it head on.
Without constant analysis and moderation of our students’ learning, we cannot teach to our fullest potential. If we leave students by the wayside because we don’t know where they are, we have put a student in a hole that they may not be able to escape from.
*I’m by no means the first nor am I the most qualified person to look at this. We’ve been overhauling since before I started teaching, but one more eye on the problem can’t hurt. Even if I’m not saying anything new, informing new people can’t hurt. Right?
**http://www.canyonville.net/wp-content/uploads/2011/07/Math-Class-620×270.jpg Disclaimer: This picture is not necessarily an indictment of this teacher. It is a photo that I found on the internet with a teacher that had his back to the classroom. The fact that it took me about five minutes to find one is encouraging to me.
***Full Disclosure: I worship the ground upon which this man walks. The classroom ideal he has created is my personal mission.
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