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Mary Beth Dittrich
It’s an exciting time to be a high school science or math teacher. The classroom that we knew growing up is slowing fading into the shadows. Taking notes on a boring lecture is being replaced with video lessons, interactive projects, and group inquiry and investigation. As I reflect on my 15 years of teaching math, I have never been so encouraged by the future.
I teach at Carondelet High School—an all-girls, Catholic high school about 40 miles east of San Francisco. In our over-50 year history we have seen a dramatic change in the role of women in society and the work place. Employers who once sought out women for primarily support roles are now actively hiring them for top positions. Carondelet is addressing these changes in our world with new courses and new ways to teach them.
Here are some of the innovative changes we have adopted in the past four years.
Four years ago we instituted a “physics first” program for our ninth graders. Using the Active Physics text, we introduced our girls to a hands-on, investigative physics curriculum. It is an algebra-based program in which they study units on motion, electricity, waves, and light. Each unit begins with a discussion of “what do you see” and “what do you wonder” about a presented situation. These discussions are followed up with more classical physics experiments that combine continued observation and questioning with data collection and hypotheses. Only after completing these activities are they presented with the physical laws that govern what they have discovered.
In the beginning this approach was challenging. Our students were used to be spoon-fed the content. They had little experience in observing, questioning, wondering, and drawing their own conclusions. Many were frustrated with the experiments. They didn’t know where they were going or how they were going to get there. “Just tell me the answer,” was a common plea. Our teachers did not relent and as the year continued students grew accustomed to the process and learned the observation and reasoning skills that they would need in other courses.
Freshman physics is followed by chemistry in the sophomore year and biology junior year. Our life science teachers particularly favor this sequence of courses as it allows more time for the development of students’ reasoning skills before studying biological systems.
One of the reasons we adopted this program was to have our students study science earlier in their high school careers and to encourage them to study more science. As a result 68% of our seniors have chosen to take a fourth science course (this is beyond the three-year graduation requirement). Several have even chosen to double up in their junior or senior year and will graduate with five years of science. Their course choices include AP-level Physics, Chemistry, Biology, Environmental Science, and Computer Principles, as well as Anatomy and Physiology, Marine Biology, Biotechnology, and Forensic Science.
The same year the science department instituted its changes, the math department decided to “flip” all of our Algebra 1 classes. The flipped classroom model takes what was traditionally done in class (lecture and direct instruction) and moves it to the home. Then what was traditionally considered homework (typically practice problems from the textbook) is now completed in the classroom. For their homework students watch and take notes on a teacher-produced video posted on YouTube. Students are then encouraged to communicate to their teacher their understanding of and any questions about the lesson. Currently we are using the EDpuzzle app to facilitate this conversation. When students arrive in class the next day, they are ready to engage with the material and to begin work on the traditional practice problems. The classroom environment becomes student-centered. The focus in class is on students practicing and producing work, not the teacher teaching the concepts in front of the class while the students listen. This model allows the teacher to monitor students more closely and to provide additional support to struggling students.
We strongly encourage our students to work in groups—to talk about the problems and their approaches to solving them. Our math classrooms are ringed with whiteboards. Students enjoy tackling challenging problems collaboratively at the board. It gets them up out of their desks working together. This also provides them the opportunity to see and comment on each other’s work.
Our parents have wholeheartedly endorsed our approach. They are happy that they are no longer burdened by late night homework help and tears over confusing concepts. They appreciate the fact that their daughters are more responsible for and in control of their own math learning.
While this model has worked effectively for the past few years, it has had its limitations. All students still progress through the material at the same teacher-led pace. Some are anxious to move faster bored by a repeat of their eighth grade math course. While others needing a slower pace get left behind never completely mastering the concepts. As well, we felt the need to incorporate more practical application (word) problems that are the reason behind why we do math in the first place. This has led us to a total rethinking of our Algebra 1 program and eventually Geometry and Algebra 2.
In the 2018-2019 school year we will be rolling out a completely redesigned Algebra 1 curriculum. We will remove remedial and honors distinctions from our existing courses and enroll all ninth grade students not taking Geometry into a self-paced, personalized mastery Algebra 1 program. Students will be working collaboratively in fluid groups as they self-pace through the curriculum. They will have the ability to spend more time on topics if needed or can advance at a faster pace potentially completing the Algebra curriculum in less than one year and continuing on to Geometry. Students will also be able to self-select and honors distinction.
The number of rote, out-of-context exercises will be limited. Students will complete just enough of these to show mastery. They will then move on to practical, cross-curricular application problems solved collaboratively in a group. The unit will culminate in a topic challenge (a multi-faceted application) and an assessment (test).
We have purposely removed the traditional textbook and language such as “chapters,” “sections,” and “problems.” Currently very few students see a relationship between what they just did in the current chapter to what they will be doing in the next. Too often they learn the material for the test without seeing its connection to the whole of mathematics or to life outside of school. We want to provide them with challenging, deep and inter-connected math tasks that allow them to struggle, persevere, discover and grow.
As I said earlier, we will begin this program next school year. As such, we are still in the planning process. It is a daunting, yet exciting, task to completely reshape a mathematics program. A colleague in the English department recently asked me, “What if it doesn’t work?”—to which I replied, “It will. We will make it work.” That’s exactly the attitude we want our students to have.
Underlying our curriculum changes, particularly in the math department, is the desire to create and nurture in our students a growth mindset. The concept of a growth mindset was put forth by Carol Dweck in her book Mindset: The New Psychology of Success, 2006 and applied to mathematics education by Jo Boaler in her book Mathematical Mindsets, 2016. A person with a growth mindset believes she can learn anything with enough hard work and perseverance. Her potential is limitless. She embraces challenge. She sees failure as an opportunity to grow and feedback as constructive.
Contrast this with a fixed mindset which says that we were born with certain talents and abilities. Our abilities are unchanging and our potential for growth is limited. Unfortunately this is the fixed mindset math education that most of our students received in their first eight years of schooling with its focus on rote memorization, speed, and problems solved in a vacuum. This system clearly defined who was good at math and who wasn’t. Ability groups pigeon-holed students further reinforcing a fixed mindset which told them you will always struggle with math. Because of this, too many of our students, and unfortunately their parents as well, believe that they don’t have a “math brain” and therefore will never be “good” at math. This is why our math department has embraced the growth mindset and share these insights with our students on a daily basis.
My colleagues in the math department and I love both mathematics and teaching. We want to convey this passion for math to our students. We want them to realize that anyone can master mathematics. We want them to see the importance of determination and grit. We want them to know that their brains can grow. We want them to take their time and think deeply about a problem. We want them to struggle to understand how and why something works the way it does—how it applies to different situations. We want our students to see that math is beautiful, creative, and surrounding them. It is patterns and shapes and colors. It is so much more than equations and solutions—so much more than they ever saw in school.
I recently saw a sweatshirt that said, “Innovate or Die.” While it momentarily took me off guard, I do believe it. The world has changed dramatically in the last 50 years—and it isn’t going to stop changing. Neither should the way we teach our young people. A continual review and updating of our teaching practices is imperative. Our students need to be ready for a world and a job market that doesn’t yet exist. They will need skills we can’t even imagine. To be ready for this future our students need teachers today that are forward-thinking—teachers who embrace and welcome the changes ahead. They need teachers who are willing to try new methods, to take chances, to be passionate and bold. As I said above, it is an exciting time to be a high school science or math teacher.
Mary Beth Dittrich has been teaching math at her alma mater Carondelet High School in Concord, CA for the past 15 years. Previous to that she taught Religious Studies and served as the school's Dean of Students and Academic Advisor. She and her husband Tom, a physicist at Lawrence Livermore National Lab, live in Danville, CA.
These contributions have not been peer-refereed. They represent solely the view(s) of the author(s) and not necessarily the view of APS.