Changing Mathematical Mindsets of Pre-service Teachers

In August, I began my 21st year of teaching in an elementary classroom. Over those 21 years I have taken advantage of as many opportunities as I can to continue to grow and learn about teaching literacy and mathematics. Those experiences have led me to an Adjunct Professor position at the University of Redlands. My first course, Curriculum and Methods I (Mathematics and Science) recently concluded. I was excited to have the opportunity to lead that course as I have spent a lot of time in the recent years learning more and more about teaching those content areas. I was able to create a syllabus that I felt would help students build a foundation for teaching in those areas. I pulled from resources from many well-respected mathematicians that I have met, read their books, heard present, or took part in a training facilitated by them. The list includes but is not limited to: Jo Boaler, Christina Tondevold, Graham Fletcher, Robert Kaplinsky, Tracy Zager, Cathy Fosnot, Kathy Richardson, Ruth Parker…

The messages from these mathematicians are important, research-based, and relevant.

I asked the students as we began the course to think about a mathematics classroom and as we finished the course I asked them to reflect on teaching mathematics. What follows are some of their thoughts on teaching mathematics. These are excerpts from some of the reflections. Their words will say it better than I could.

“At the beginning of this course, when asked to reflect on what a mathematics classroom looked like, I wrote “black and white, boring, right and wrong.” Now, my view of mathematics in the classroom looks much different. I remember a time in my early education when I enjoyed math and considered myself to be good at it. Sometime during high school, my view of math changed. I no longer felt interested or good at it. I have tended to confess, “I’m not a math person.” However, since taking this course, my interest in math has been reignited.”

“Starting this course, I was not very enthusiastic. Math has always been a tough subject for me. I struggled with it through junior high, high school, and into college. I always had to get tutors and extra help to be able to pass the class. I would get frustrated because I would think that I understood the subject and then I would take the test and miss a step and everything would be thrown off. I hated the subject because to me there was one answer and only one perfect path to that answer.

The first day of class we were asked to write down what we thought a mathematics classroom looked like. I wrote down that it would be kind of bland and maybe have one fun activity put up on the wall. I had a not-so-positive attitude about the subject.
The class started and I felt like a whole new world was opened up to me. A
video was shown of kids sitting on a carpet solving math problems and sharing
with the teacher and the class how they solved the problem. Each student

solved the problem differently and was encouraged to look at the problem differently. I felt like a light bulb went off in my head, or maybe a new door had been opened. All I know was that I started to look at math in a different way. It did not have to be one perfect way to finding an answer.”

“When I began this class, I was not looking forward to learning about mathematics. I have never considered myself a math person, in fact it has always been my least favorite subject. The first night of class we were asked to write what we thought a math class looked like, I thought it was an easy question to answer. I wrote that a math class was quiet place, where nervous students work alone and try to compute as fast they can. This was how every math class I had ever been in had always felt but this class has shown me that math class does not have to be a dreadful place. I have learned so much throughout this course and grown as person. My entire perspective of math has changed as well as my outlook on teaching it. I have learned ways to make math exciting and fun for everyone. There are so many resources available to make a math class collaborative and innovative. There are many games and activities that can keep kids involved in the learning process. I used to believe that math was the subject where there is always one right answer and there is always one right way to get there but I now know that this is incorrect; math is not so black and white. Now I know that there are many ways for students to work through problems and that the real learning occurs through the process of them making mistakes. It is important to allow students to work through problems using whatever strategy that they are comfortable with. The teacher’s job is to ask a lot of questions that cause the students to really think about what they are doing and why. Math classes are no longer about just knowing algorithms, they are much more complex.”

“During this five week course I have learned that math is no longer a subject that is to be scared of and there is more than one way to get to the solution to a problem. Math was my most difficult subject in K-12 and my most difficult general ed class in college but after taking this course, I feel much more confident in my own math abilities.

This class has taught me that all students “are math people,” and as an educator it is my job to help students be math people by taking the time to understand their thinking and use strategies to help them understand math.”

“Mathematics has always been a challenging subject for me to grasp. To be honest, I was not particularly excited to take this course but by the end of the first class my biases about math had begun to change. One of the moments in class that I thought was perfect was when Mr. Hall told us that he praised his kindergarteners for being amazing mathematicians and scientists. Just that simple belief in our students can completely change the way a child sees their abilities. Sometimes giving our students confidence is easier than praising ourselves when we do amazing work. Mostly, this class has taught me to be more confident in myself when it comes to math and science and hopefully that confidence will reflect in my students.

I appreciate the dedication and help that Mr. Hall has shared with us and as a result I feel more confident in myself and in teaching elementary math.”

“Not unlike the rest of the world, I came into this class with the attitude that I wasn’t that great at math. In fact, my mantra was that I was great at algebra but struggled with geometry. Imagine my surprise when I found that not only am I good at math, but I love teaching it.

At this point in time, my attitude has completely changed. I’m going to approach math with excitement and joy. In my classroom, we will all be mathematicians.”

“Math used to seem confusing and pointless. On the first day of MALT 603, I wrote, “math was a bunch of numbers that I did not understand.” In high school, I remember my teachers would use the projector to write example problems then provide all students with a sheet of problems to be completed by the end of class. There were no games, no use of the imagination, or variety of ways to arrive at the same answer. Math felt dry and left me feeling mentally drained.

In college, I would cry after my math test believing I was not smart enough to pass. When I received my test back with an 80% written on the front, I would be in shock thinking that there had to be some kind of mistake. I knew I was bad at math so I would find any resource to help me study and I would write as small as I could on a note card that we could use during the test to fit in all the facts I felt I needed. Even when I did pass, I still believed I was not good at math. I would say I got lucky on the test and prayed that I would be able to do it again on the next test.

I never believed I could enjoy math until attending Professor Hall’s class. Now I see math as colorful and fun instead of boring and incomprehensible.”

“On the first day of class we did a jigsaw reading of a chapter from Teaching to Change the World, about how some teaching philosophies hinder the learning of students. The Essentialism philosophy encourages teachers to only exhibit one way of how to solve a problem although all students learn differently and they teach to the test which takes away from teaching critical thinking. These examples are ones that I have witnessed first hand when I was in grade school and I have always been someone to say that math wasn’t my thing. It might have not been my thing because I wasn’t taught in the most efficient way that catered to my learning abilities. The Progressivism philosophy encourages teachers to explore teaching without using a book and to take time when teaching math. Math is a complicated subject to understand and we should give our students enough time and support in order for them to grasp it completely.

All in all this course left me shocked and a bit jealous that I wasn’t taught math like this when I was in grade school. I believe I could have excelled in math if i had a teacher who practiced number sense with us everyday or every other day.”

“Through this course, I had to fully transform my thinking in regards to teaching math, because the methods of instruction have changed so much since I was in elementary school. I do understand the reasons behind the change now, and I

believe the focus on giving students a better understanding of mathematics as a science of problem-solving is important for their cognitive development and futures in a technologically-centered world. Math is no longer a subject of memorization and drills and crying students. Our students are mathematicians, not robots.”

“The word mathematics itself scared me, let alone the thought of teaching it. In the beginning of the course I was nervous, overwhelmed, and excited all at once. Just the thought of the common core state standards made me nauseous. In my journey through college, I dreaded taking mathematics courses because I was sure I would fail. I felt that all math courses were the same, and I would assure myself that the outcome would always be failure and disappointment. However, after taking MALT 603, I can honestly say that I see mathematics through a whole new lens. I learned that math does not have to be difficult, that there is not just one right answer, that math can be fun and exciting, and that the possibilities are endless.

I was a bit confused after the first day of class. For some reason, I thought that we would spend every lecture solving hideous problems in what seemed to me like a foreign language. Instead, I found myself learning new and effective teaching practices that not only made math fun, but also helped promote critical thinking among students of all ages.”

“Coming into this course (MALT 603), I was very nervous. I have always struggled with math. I always received good grades but it took a lot of hard work on my part and I never remember walking out of the classroom feeling as if I had truly understood what I learned. In college, I took only the necessary math I needed to graduate and approached each course with a negative attitude, expecting it to be hard and terrible.
My shift in career paths led me to substitute teaching, which led me to the credential program at University of Redlands. I began my journey toward conquering the dreaded CSET tests, and approached those tests with the exact intimidation and fear that I had always held when taking a math class/ test. I saved CSET 2 (math and science) for last. I have never had so much test anxiety in my life as when I went to take this test. In fact, looking back, I think the reason I missed passing by only a few points was more due to my anxiety than my knowledge. I passed his test the second time around, and I was a nervous wreck the entire day knowing those scores would hit my email. I was convinced I had failed again! Passing that test was a shock to me as I have always went through my life saying “math is not my thing.”

Taking MALT 603 has truly increased my confidence as a future teacher of math. I feel more confident in my ability to create diverse lessons to meet the needs of all different types of learners inside of the classroom. I am so thankful to have taken this course and learned of the many resources we have available to us as teachers. I now realize how much of our own thinking and attitudes can get in our way and how my role as a teacher will truly impact that thinking in my students!”

“In the beginning of this class, when we were asked to describe what a math class would look like to us, I instantly thought of a rigid and cold environment.

This class has changed my ideas and thoughts drastically. I have struggled in math ever since the third grade. It’s funny how I do not remember what I ate for breakfast this morning but I can sure tell you how I felt during math time in third grade. I remember what the class looked like, where I sat, everything. I can still feel the pounding of my heart when the teacher called me up to the chalk board to do a math problem in front of the class. I know now that my negative math experience was unfortunate and could have been prevented. Thankfully, teaching styles and philosophies are changing. The education system is moving away from a rigid essentialist style classroom to a more interactive progressive style classroom. When I was in elementary school the teacher taught and I listened, there wasn’t a lot of interaction. There wasn’t much differentiation in her teaching style and I didn’t get the additional support that I needed. I felt discouraged, lost, and helpless. I started tuning out during math lessons. Taking this class has given me hope, I felt validated knowing that math was hard for a lot of people not just me. It has encouraged me to be conscious and encouraging to myself and to others struggling in math. If I were to describe my teaching philosophy regarding math I would have to say its completely the opposite of what my third-grade math teacher was like. My philosophy is that math should be fun, encouraging, interesting, helpful interactive, and adjustable. I am inspired by what author and Professor of Mathematics Jo Boaler said in a TED Talk video, “that nobody is born with a math brain”. She also said, “when we change our beliefs on what we can do it changes our mindset”. This is so true, if you change your mindset about math then that alone will allow you to open up to the possibility of learning it and enjoying it.”

Thank you MALT 603 for sharing your mathematical revelations and your emotional journeys with me!
Viva la revolution!

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Seeing Students in HD

I had the opportunity to see Dean Andrew Wall of the University of Redlands School of Education speak recently at the #BetheOne Open House on the campus of the U of R. He spoke about viewing education as a river with tributaries in which the tributaries (like NCLB, Common Core, ESSA…) affect the river and can even change the course of the river, as opposed to viewing education as a cliff in which we are in danger of falling over because we are failing.

 

I would like to use a similar structure to look at the state of curriculum and instruction.

 

How many of us have heard of the “pendulum” that swings back and forth? The pendulum that divides two views on education that cycle back and forth. The pendulum that has everyone saying, “We’ve done this before. Here we go again.”

 

I would like for you to not view curriculum and instruction as the pendulum as you read this, but instead think about it as a television set. If you will indulge me, I will try to adjust the antenna and make this picture clearer.

 

I would propose that the reason many people see the pendulum is because they are seeing education from the small TV set with dials, no remote, and a small screen. We have more research about learning than we’ve ever had in the history of education, but because our lens to view it, our picture to see it is a small standard definition screen, we often don’t see the bigger picture. We focus on small bits and pieces because that is all we can see in that small screen. Viewing our HD and even Ultra HD world on a small screen can alter the picture and make you miss important details.

 

Curriculum developers that design “Common Core” curriculum do this when they create curricula that is designed to cover the standards, in a way where you can almost use the standards as a check off sheet as you go through the year. At the California Mathematics Council-South Convention in October of 2015, Cathy Fosnot said that in Dutch there is one word “leren” that means both teaching and learning. The point is you didn’t teach it if the students didn’t learn it. As educators, we can’t teach curriculum, we must teach students. We can’t focus on isolated skills or work through a textbook and expect students to be 21st century learners.

 

A narrow view of the Common Core standards can prevent you from seeing in HD. The Common Core was designed to evaluate, critique, compare, apply, and communicate knowledge. This is the real work of the Common Core.

 

But how do we teach that? The answer is not in a teacher’s guide. It’s not in a curriculum map. To find the answer, we need a different lens to view curriculum and instruction; we need a newer television. We need a 21st century widescreen 4K Ultra HD television set. We need to see the bigger picture in education. We need to more clearly see all of the research (for example: growth mindset work by Carol Dweck, visible learning research by John Hattie) about learning. We need to see the whole picture.

 

Let me give you a preview of a premium channel. In October 2015, I saw Lucy Calkins speak at the California Reading Association conference in Riverside, CA. She spoke about nonfiction reading and writing. She made the point that “organizing is how people learn.” Structure of texts is critical to understanding and creating text. Ruby Payne’s work with understanding the culture of poverty was groundbreaking. She discussed the idea that students from poverty often don’t understand the structure of a story. Story structure in a culture of poverty is often circular, going on and on, but not really progressing through a sequence of events. A couple of weeks ago, I attended a district ELD training. We looked at the shift in the California ELD standards from a focus on isolated skills to an understanding of the structure of language. And currently, I am taking an online course called Number Sense 101. The instructor, Christina Tondevold, shared a strategy for working with story problems with younger students. The idea was to uncover one part of the story at a time. Each time pausing to ask the students, “What do you notice? What do you think will happen next?” As you work toward the end, then you can ask, “What do you think the question will be?” The point is to focus on the structure of the story problem, not look for keywords or other “shortcuts” to find the answer.

A common theme among all of those examples was how important it is for students to see structure, because then they can evaluate, critique, compare, apply, and communicate knowledge.

 

When you view educational research on a bigger screen, you will be able to evaluate, critique, compare, apply, and communicate knowledge.  This is the same type of thinking we want from our students.

 

So I ask you to invest in a new television, not the old TV that only allows you to watch the pendulum swing, but the big new 4K Ultra HD widescreen that allows you to see the bigger picture.  The picturesque view of the research on learning. Only then will we truly see our students in HD!