As adult education instructors, we know that our students bring all kinds of preconceived ideas about math into the classroom. Many see math as boring—a subject governed by processes, rules, and formulas that has little connection to their world. Furthermore, because they may have struggled with math in the past, they think that they will never be good at math. “I’m just not a math person.” We’ve all heard that from our students.
Dr. Jo Boaler, a professor of mathematics education at Stanford University and cofounder of Youcubed, has heard this as well. She believes that there needs to be a real shift in the way students think about mathematics in the United States, and she points to widespread math failure and declining interest in math as major problems, especially as the workforce continues to place increasing value on quantitative literacy. With Youcubed, Dr. Boaler and cofounder Cathy Williams want to help teachers change the way their students think about math. Through a series of videos and classroom tasks, Youcubed seeks to “inspire, educate, and empower teachers of mathematics, transforming the latest research on math learning into accessible and practical forms.”
I really admire the way that Dr. Boaler talks about math. In her discussion of Multidimensional Mathematics, she refers to math as a “beautiful, open, creative, and multidimensional subject.” She is a firm believer in growth mindset, and she offers seven positive norms for the math classroom:
- Everyone can learn math to the highest levels.
- Mistakes are valuable.
- Questions are really important.
- Math is about creativity and making sense.
- Math is about connections and communicating.
- Math class is about learning, not performing.
- Depth is more important than speed.
As both a math teacher and a lifelong math student, I love these messages. They so clearly articulate the values that I think we all hope to foster in our classrooms. Dr. Boaler goes on to outline the characteristics of students with a growth mindset rather than a fixed mindset. Growth mindset students, Dr. Boaler points out, try harder and longer. They are okay with making mistakes and even see mistakes as a learning opportunity. They persist in their work and they don’t give up. Encouraging these practices has become a major part of my math instruction, and I really appreciate the way that Youcubed backs up these ideas about good mathematics instruction and growth mindset with the most current research in the field. If you’re interested in hearing more of Dr. Boaler’s philosophy of math instruction, check out any of the videos and articles contained under the Teaching Ideas tab. Even though they make reference to K-12 instruction, the ideas about growth mindset and positive classroom norms certainly apply to adult learners and to our own classes. I would also recommend reading through the full text of “Fluency Without Fear” a short article by Dr. Boaler and her colleagues that serves as an overarching mission statement for the Youcubed project.
While the articles and videos on Youcubed reinforce our values as teachers in the Common Core era, the most immediately useful items on the website are the Tasks, a collection of 42 problem-solving activities for students at all levels. The tasks are easily searchable by concept, grade level, mathematical practice standard, and topic, which is a good thing because there’s lot to sift through here. Some of these activities—like the Four 4s, Ice Cream Scoop, and Squares to Stairs—are low-entry problems that are easy to print out and use in your classroom. Other activities are much larger in scope and would require more classroom time for investigation and discussion. Take, for example, Simpsons Sunblocker. This activity requires a good deal of prep time on the part of the instructor, and it uses a fun scenario—Mr. Burns trying to block out the sun over Springfield using a circular disc—to investigate topics like effective data collection, properties of circles, and proportionality. Another task, titled “Unit: Patterns and Functions” is actually a PDF collection of fifteen very detailed, carefully scaffolded lessons. For teachers looking for a good way of introducing functions, this is a great place to start!
My only issue with the tasks is that they seem a little inconsistent in terms of how much support they provide for teachers looking to use these activities in class. While Simpsons Sunbocker, the unit connecting visual patterns to functions, and a few other assorted activities contain a wealth of guidance for teachers, others provide very little. The Squares to Stairs activity, for example, has only a list of possible questions that teachers could ask of their students. It doesn’t offer much in the way of talking about common student mistakes, ways to scaffold the activity, or where teachers could steer the discussion after completing the activity. Same with the Ice Cream Scoop activity. So, at this point, the tasks section of Youcubed feels a little like a work in progress. The activities are great, but the site would be a better resource for teachers if it provided some more support materials. For a sense of the kinds of support materials I’m talking about, see the Mathematics Assessment Project or my review of the site.
There’s a lot more here, of course. If you really want to dig into Dr. Boaler’s teaching methods and beliefs about learning, you can sign up for her online course, “How to Learn Math,” offered free of charge through Stanford University’s online course portal. You can also find links to Dr. Boaler’s books and contemporary scholarly articles on mathematics education under the Knowledge Center tab. In short, the site is definitely worth checking out. The philosophy behind Youcubed is definitely something that will appeal to math teachers at the ABE and HSE level, and I really like a lot of the activities. If you find something you like, just plan to spend some time doing the activity on your own and thinking about the supports that your students will need.
Have you tried any of the problem-solving activities on this site? Let me know how they went in the comments!
So, I’ve been in Boston at the NCTM meeting (http://www.theatlantic.com/education/archive/2013/11/the-stereotypes-that-distort-how-americans-teach-and-learn-math/281303/) this week and had the pleasure of listening to Jo Boaler speak last night. Her ideas are compelling. She cites recent research that shows the incredible plasticity and adaptiveness of the brain. Her message includes the following: “It just isn’t true that there are some people who are math people and some who are not. We all have the capability to learn the highest levels of math. There is no wall that defines what we can and cannot learn.” This isn’t wishful thinking. It’s based on brain research and many hours spent researching students in math classrooms.
Here’s a great video of Boaler talking to a group of teachers in Ireland about her research and the need for “multi-dimensional” teaching. She talks about how she has found in her research that students who studied less content but really understood did better on tests, even when they hadn’t been taught the content. The students she studied worked on projects that took weeks in some cases to complete, but involved students taking responsibility and developing the math necessary to be complete the projects. When it came to being tested, they understood that math was about figuring out problems, so they did. She gave an example of students who did well on problems involving systems of equations, even though they hadn’t studied them yet. Another class that Boaler compared had studied simultaneous equations, but didn’t do well. The difference was that the second group of students were in a class with a lot of covered material, with instruction focused on procedure. The teacher explained and the students practiced. There is abundant research that this way of teaching doesn’t work and that students only learn in superficial ways. They have to be challenged to figure things out on their own. (Now, this doesn’t mean that they are just left to their own devices. See Deborah Ball for discussion of explicit instruction in support of inquiry-based instruction.)
http://www.ncca.ie/en/Curriculum_and_Assessment/Post-Primary_Education/Project_Maths/Teachers/Teachers-helping-teachers/Stories-from-Research/
i plan to start How To Learn Math in the next few weeks. There is a teacher/parents version and a newer Students version. The first module is Knocking Down the Myths About Math. I can imagine these videos being really useful for starting a conversation with students that can help them reimagine themselves as math students, reconsider what math is and prepare themselves for productive struggle. I hope to use many of these ideas when I start teaching in a few weeks.
You might also like this article that Boaler wrote in The Atlantic a few years ago: http://www.theatlantic.com/education/archive/2013/11/the-stereotypes-that-distort-how-americans-teach-and-learn-math/281303/
I also really recommend the Fluency Without Fear article (link in the article above). It changed my mind about times tables and memorizing under time constraints.
I had recently read What’s Math Got to Do with It, and I fell in love with Dr. Boaler. In the book, she tells about the many issues plaguing math education, but I think her focus was not criticizing the way we teach math, but celebrating and making readers aware of the vary many creative and imaginative ways to teach math so that students are more engaged.
Just recently, I had been in a professional development class in which we talked about brain growth and how to help students get out of the mindset that they are not “good at math”. There is a similar article in Youcubed that talks about how mistakes grow the brain. I think I would use this article in class as part of an introductory lesson to encourage students to think about their “math struggles” from a different perspective. In other words, I would love to convince my students that mistakes are food for your brain.
Here’s the direct link to the article: https://www.youcubed.org/think-it-up/mistakes-grow-brain/
Jo Boaler is at it again. There is a new campaign called With Math I Can – https://www.amazon.com/gp/withmathican. It is sponsored by Jo Boaler (along with NCTM, the Teaching Channel, Edutopia, Amazon and others) and focused on developing growth mindset in students especially around mathematics. I’m just starting to go through the materials, but there is a lot worth checking out. The resources section is broken up into things to use in your class, things to use across your distinct (in terms of professional development and working with teachers around teaching growth mindset) and finally things to explore at home with your family.