Mathematical Mindsets is all the rage these days primarily due first to the work of Carol Dweck who introduced the idea in Mindset: The New Psychology for Success and now Jo Boaler who turned it into its current name. I considered myself good at math initially back in the 2nd grade because my mom praised me for doing well in arithmetic (getting an A on my report card). But I didn’t believe I was a math genius because of my habit of making too many “silly” mistakes in regurgitating what the teacher was teaching us. Other students got higher scores than I did, but I managed to hold my own with a B+ average. Then one day in the 4th grade my teacher challenged us with a question referring to baseball. “How do you determine a pitcher’s earned run average (ERA) in baseball?” she asked. No hands went up except mine. Being an avid baseball fan and having collected and analyzed all the players bubblegum cards, I had memorized the formula for finding that statistic. The teacher was very impressed. But then she asked me “How did you figure out that formula? “I didn’t,” I said. “I saw it in a book about baseball.” She was disappointed, but so was I. So I went to the library, found the book and this time I read the explanation. It took me a while to understand it, but I managed and then excitedly shared what I learned with my teacher. "That’s great," she said, "but next time don’t just memorize the formula, understand it." Given my passion for baseball that was not a problem for me anymore. I never forgot that advice for the rest of my life. It’s no good knowing anything of interest without understanding it deeply. From then on I was a “math person*” which in Jo Boaler’s terminology meant I had a mathematical mindset.
As a math teacher I tried to get many students who were set in their ways about disliking math to want to appreciate the power of math. They did while they were in my class. But once they left and went back to doing math the old way, they stumbled back into their “fixed” mindsets about math. So why did a significant event in my life change my mindset in a positive way, while my students who clearly enjoyed my class did not have the same transformation? One thing that helped was that I had good feedback about my math “ability” as early as the 2nd grade. So good experiences are needed right from the beginning of learning math. I have a 5 year old grand nephew who can count (proudly so) to a hundred. His father is a born again math person who struggled most of his life with an aversion to math. He became math savvy while he was employed as a car salesman. I look forward to my grand nephew having a mathematical mindset throughout his school career.
The activities that Jo Boaler shares in her book are all good ways to develop a mindset that will hopefully continue to grow throughout a student’s school years.
*To me a "math person" is someone who has a mathematical mindset, works in a field that requires math in problem solving and is proud of it.
Tuesday, May 30, 2017
|Image source: @bryanmmathers|
I’ve been listening to David Bodanis’s book Einstein’s Greatest Mistake and was pleasantly surprised that Bodanis told the story of Flatland where 2 dimensional figures such as circles, squares and lines are the inhabitants that could never imagine a 3 dimensional world. Einstein’s genius was recognizing a new dimension that goes beyond the 3 dimensional world we inhabit. He was after a unified theory of the universe when he realized along the way that the universe’s structure could be curved. This realization eventually led to his ground breaking general theory of relativity. It made me think about a statement made about the latest iteration of the NCTM standards Principles to Actions (PTA) which followed the 2000 Principles and Standards and the 1989 Curriculum and Evaluation Standards for School Mathematics. PTA was almost as good as you can get claims the current president of NCTM and will survive the test of time. Each iteration of the standards has taken a new dimensional look at mathematics education and suggested what teaching and learning math should be. But is there a "dimension" that’s missing? I challenge the following statement in thinking about a new paradigm: "Good teaching is a prerequisite for good learning in schools."
Teaching and learning are going through an identity crisis. There was a time when it was easy to distinguish the teacher from the learner. But times and roles are changing in today’s schools. The main function of teachers is to facilitate learning. The assumption of course is that the students are doing all the learning. That’s not true any more because in the modern classroom teachers and students can switch roles. We’ve known for a long time that a great way to learn something is to teach it. As a result teachers have honed their craft well, but the same can’t be said for students. Especially the ones sitting in the back of the room looking out the window. But those kids can’t look out the window so easily any more since they are busy collaborating with their peers preparing to present to the whole class what they have learned. Teachers in the meantime are coaching, facilitating, and observing students making sure they are on track for their upcoming presentations. Occasionally the teacher will jump on stage and share something very cool that is of interest to everyone. This scene is an example of personalized learning at its best. A win-win for teacher and students. So if PTA is describing a third dimension of “teaching and learning” I’d like to suggest a 4th dimension paradigm shift which turns the 3rd dimension on its head calling it “learning and teaching” or good learning leads to good teaching. It’s a subtle distinction but an important one. It begs the question “when (and how) do students learn?” In schools that's usually the teachers job and the good ones make the students learn. (Not always. See Alan Schoenfeld’s When Good Teaching Leads to Bad Results: The Disasters of “Well-Taught” Mathematics Courses.)
The bottom line is that students learn well when they are interested. (The chief enemy of learning is boredom which is way too prevalent in schools particularly in math classes.) The challenge to good teachers is to adjust their teaching and support a vision where all students are interested. Our curriculums need radical reform for this to happen. (More about this in future blogs.)
When motivated, students try their hardest, reach out for help, and receive supportive help from teachers. This happens best in student-centered learning environments.
Here’s my list of criteria for student-centered, personalized learning environments.
- Math is learned best in a community of learners where students are engaged in authentic activities that illuminate important powerful ideas (intellectual tools) in math.
- The environment can be, for example a school, which is a hub for personalized learning.
- The curriculum is a project based design for a creative, student driven learning path.
- The community is constantly evolving with teachers, students, administrators and parents acting as change agents.
- Choice and voice for student agency are prized.
- Learning styles are respected.
- Commitment to ongoing professional development for teachers so they can be the best coaches/guides for their students.
- School time is flexible designed for anytime/everywhere learning.
- Students learn best when they are interested in the topic being investigated.
- Technology is a tool that is a platform for personal learning.
Great video! ****
Tuesday, May 9, 2017
Blog about new perspectives of technology in mathematics education e.g. Technology as a platform for learning and teaching. Technology is more than something integrated into an old style curriculum. But rather it is integral* to a modern learning curriculum that is designed for 21st century learning. What this actually looks like will be shared by the CLIME community as we investigate how to improve math learning and how technology supports that.
Make CLIME a learning, social media hub for discussing modern math learning issues with a focus on learning with math educators interested in technology as a platform for math. Further details to be determined.
Encourage young teachers (e.g. MTBoS folks) to participate in the CLIME hub and thus become a part of the NCTM network.
Emphasize that technology helps bridge the divide between the haves and have nots. CLIME will collect stories how districts are making sure that ALL their students have access to computer devices.
Emphasize that technology helps bridge the divide between the haves and have nots. CLIME will collect stories how districts are making sure that ALL their students have access to computer devices.
Research and share promising curriculum initiatives (e.g. Interactive Mathematics Project – IMP – now distributed by It's About Time) and new resources like Desmos’ new Geometry tool.
Share modern learning classroom models. Example: David Thornburg's From the Campfire to the Holodeck: Creating Engaging and Powerful 21st Century Learning Environments.
Suggest alternative curriculum paths for learning and teaching. The MET schools (Bigpicture.org) is an example. Here’s a sample of a student’s experience enrolled in a BP school.
Stay in touch with Matt Larson and follow NCTM president’s messages suggesting alternatives to current math education trends.
Share CLIME’s motto: Good Learning drives Good Teaching via a technological platform which means…. Using tech tools is a great movitator for learning. Teachers respond by supporting the learning through coaching and just being “a guide on the side.” Teachers provide the context as they custom tailor four areas of student engagement: curriculum, resources, environment, and assessment through the integral use of technology.
*Integrate means to combine (one thing) with another so that they become a whole; Integral makes that whole complete.
Friday, May 5, 2017
For perhaps the first time in our history there is clear and growing consensus concerning what constitutes effective mathematics instruction, kindergarten through college.
He emphasizes “through college” because based on the latest reports he confidently says:
And the next time someone says to you that some practice “isn’t what students will do in college,” make sure you share with them the evidence that postsecondary mathematics instruction is beginning to change in ways that are consistent with long-standing recommendations at the K–12 level. As K–12 teachers of mathematics, we certainly don’t want to prepare our students for a past that is in the process of changing and will increasingly no longer exist.Good news also on the high school front. In another post Larson writes:
It is with great excitement that NCTM announces it is embarking on the development of Pathways through High School Mathematics: Building Focus and Coherence (working title). This new publication will
- Address the purpose of high school mathematics and include guiding principles such as access, equity, and empowerment;
- Define math curricular pathways leading to college pathways and career readiness, as well as active participation in our democratic society; and
The goal of high school mathematics education must always be to expand options for students in ways that appropriately accommodate the post-secondary goals of different students.
- Provide narrative descriptions of course exemplars, including their big ideas, that could populate the pathways.
The NCTM Board of Directors has appointed a nine-member task force representing the constituencies that make up the larger mathematics education community at both the K–12 and post-secondary levels. The task force’s charge is to develop and present these high school pathways with the same level of focus and coherence that currently exists in the NCTM Curriculum Focal Points and the K–8 Common Core State Standards.This is promising news because CLIME has usually found that the worst part of the high school experience for students is boredom. Also, I hope to see more attention paid to student interests and differentiated paths. The high school experience can be an exciting time for students.
Hopefully, the work of the task force will help to achieve a more positive experience for students.
Friday, April 14, 2017
|Click above to see a more readable version.|
My “short” trip to NCTM
My plan this year regarding the NCTM annual meeting in San Antonio was not to go. I did my annual routine with the technology sessions making note of them via a CLIME blog. So I decided that would be enough since I started a very ambitious 8 week “course” entitled change.school led by Will Richardson and Bruce Dixon. But I changed my mind because David Wees was going to attend the NCTM affiliate events (At-large Caucus and Delegate Assembly) for the first time representing CLIME and I didn’t want him to go alone. So I made arrangements to stay only through Thursday morning and fly back home on Thursday afternoon. That was the plan until Delta stepped in and cancelled my flight. The good news was that I was now able to attend the conference on Friday.
The highlights for me were:
Ed Burger (#580) - Very slick presentation (4 out of 5 stars). Mostly promoting his book “The Five Elements of Effective Thinking” One of the reviewers summarized it’s proposed strategy as Think…fail…question…understand…change…learn: the path to the genius of learning.
Patrick Vennebush (#294) - who works for Discovery Learning - (5 stars). He presented interesting and engaging problems that use crowdsourcing.
Eli Luberoff (#458) - CEO of Desmos (5 stars) shared a new project with the audience: A Sketchpad-like Geometry component which got oohs and aahs from the audience.
Cathy Yenca (#529) (5 stars). Did a nice job of mixing a variety of online tools and activities to weave a nice presentation.
Dan Meyer & Robert Kaplinsky (#119) - How to Apply and Present at NCTM Conferences (on video) which I watched after I got home. Very valuable information for perspective speakers. Being able to watch videos like this after the event is very valuable. It extends the conference experience for those who missed the sessions in real time. I found myself rewinding the tape and making notes (which I wouldn’t have done in real time).
I went to a few more sessions with titles that included key word(s) such as crowdsourcing, productive struggle and “tools to transform learning” but wasn’t impressed. I guess that will always be true at conferences. Though the titles/descriptions are attractive, they don’t live up to the hype that the title/description convey. For example:
Intro to Coding: Scratch session (#537). Unfortunately the “light” Wifi provided for the conference wouldn’t allow me to open my Scratch files. So I sat there frustrated. Left early.
If you have a great idea for a presentation don’t hesitate to submit a proposal for the next annual conference (Washington, DC April 25-28, 2018). Please submit your proposal by May 1 here.
On the CLIME scene, David Wees and I will be reviewing/updating some of the initiatives for the upcoming year that David highlighted in his CLIME blog last year.
Wednesday, March 29, 2017
Last May (2016) I wrote a blog entitled Encouraging Effective Use of Technology in sessions at the NCTM Conferences. Some highlights follow.
Comments from that blog post:
David Barnes: I think that while some sessions need to put technology out there in front, what we should be working towards is sessions where it is seamlessly integrated as well. […] So the question for you and your crew [CLIME readership] is what makes a quality technology session? What does it need to do. […] And what are some things that it should not do? What types of tech session would you be okay with saying that doesn’t really fit within the program?
Dan Meyer: I don’t consider myself a technologist, though I do work for a technology company. But I love technology to the extent it energizes pedagogies that I love. […] I never feel cheated by a tech session if the tech session focuses on larger themes that transcend tech brand or even technology itself. If it's a technology session I want to know what the big pedagogical ideas /before/ you show me how a particular tool can realize them.
So that brings me to the eve of of the annual NCTM meeting in St. Antonio. Do the tech sessions reflect our latest thinking on seamless integration that realizes big pedagogical ideas? After sorting out the technology sessions and reading them, I come to the conclusion that the answer to the question is: YES. First some data.
Total sessions: 772 (this number includes 64 exhibitor sessions)
Total tech sessions: 106 (includes 29 sessions not highlighted as a TECH session)
This is almost 14% of the total which is average for annual meetings. (The most ever was 38% in Philadelphia, 2012 the last time technology was a theme at an annual meeting.)
NCTM Conference app can be downloaded here. The app keeps improving all the time. You can see all tech sessions using the tech and tools filter.
Twitter handles instead of emails in session descriptions. What does this mean? Have we turned a page on communication? Aren’t emails more likely to be answered than tweets? Interesting question. I’ll try a little experiment by contacting the 50 technology speakers who listed their twitter handles and see how many responses I get. (If you get this link from my twitter feed please let me know. (@climeguy).)
BYOD. There are 12 sessions where the speaker(s) encourages you to bring your own device. This allows for audience participation which is a definite plus.
Key tech words/expressions. Desmos was by far the most mentioned tech application. Others included Geogebra, Scratch and Sketchpad. See a list of all the technology key words in the descriptions of the technology sessions here. (If any of the key words intrigue you can download either the PDF or Word document of all the tech sessions and search for it.)
Crash course in tech math ed. Imagine if you could take in all of the 106 sessions? You should be able to get college credit for that. Almost every possible topic in using technology in math classroom is there.
Here’s an example:
366 TECH Reimagining Curriculum-Based Mathematics Tasks with Technology. But where do you find tasks to fit your mathematical goals, or the time to add them to your lesson? Start with existing activities. BYOD. Sounds like my effort with CIESEmath back in 2007.
Not enough of ones like this:
59 PROF The Crafting and Use of Technology for Professional Learning A variety of digital formats for professional learning such as MOOCS, blogs, forums, and online courses with both synchronous and asynchronous designs have been tried in the past with varied success. This session will present research results and potential new possibilities for the future that allow teachers more control over their own learning.
Maarten Dolk and Cathy Fosnot
So I believe we have turned a corner in having sessions that encourage a seamless “integration” of technology in the classroom. What’s still on the back burner is discussing the future of technology in math classrooms where the focus is more on student motivation and collaboration. That’s what Maarten Dolk and Cathy Fosnot will be focusing on in their session on Thursday.
David Wees and I will be attending the Affiliates at-large caucus and the Delegate assembly on Thursday morning. More about that later.
Saturday, February 4, 2017
I recently reread Rick Hess’s book The Same Thing Over and Over: How School Reformers Get Stuck in Yesterday’s Ideas. In it Hess argues that “most of today’s reforms thought to be cutting-edge – merit pay, charter schools, extended school days and years, Teach For America – aren’t really cutting-edge at all. And in the long haul, most aren’t likely to result in significant change.” Also he says that “…most of our current strategies to get better teachers into classrooms, including alternative certification, are essentially just “throwing thimbles of water into a river” – which is a slightly more polite way of saying they’re totally inconsequential.”
Why? Because, Hess says, we aren’t willing to start from scratch in our thinking about what it means to be a teacher in the twenty-first century.
Of course in “starting from scratch in our thinking” is something that is tried frequently but always fails because the obstacles to real change (or common sense change in contrast to status quo change as Hess puts it) are so difficult, if not impossible. On my wish list of difficult/impossible, but transformative reforms is something that at its core makes sense to everyone involved that's interested in math education reform.
My version of common sense reform is much “simpler” than what Rick writes about. It’s about dramatically improving curriculum materials for students. Isn’t it possible to create programs of study that students would actually enjoy reading? My current list of math books that I’m enjoying reading (and some re-reading) are:
- The Calculus Wars: Newton, Leibnitz, and The Greatest Mathematical Clash of all Time by Jason Bardi
- Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander
- The Irrationals: A Story of the Numbers You Can’t Count On by Julian Havil
- The Librarian who Measured the Earth by Kathryn Lasky
Why do I reread them? Because like cinema and theater I love math when it is couched in a fascinating context. In other words because it is intrinsically interesting, engaging and challenging.
Why can’t student materials be written in this spirit? Hess says because status quo reformers just want to tinker around the edges of current textbooks which doesn’t stop alienating most students in their study of math. A colleague of mine Gary Stager (who is definitely a true common sense reformer) calls “curriculum” a dangerous idea. That’s because math curriculum in the form of textbooks are such an abysmal read for most students. And even the students that do well and like math usually are mostly influenced by good teaching that makes the drab material come to life. I’m really tired of the fact that Dan Myer has to make “fun” of actual activities in math books in his blog. (See http://blog.mrmeyer.com/2017/pseudocontext-saturdays-tornado/)
We have the talent to do better, but unfortunately not the will.
If you agree let me know and maybe we can start a movement protesting text book companies for their poor approach to writing textbooks. Instead of resigning to choose the best text out of all the bad choices offered, we force them (are you listening Pearson & McGraw Hill?) to start from scratch and come up with well written books/media that would inspire both teacher and student to read.
Is this possible or am I just dreaming? I’d like to hear from you.
Hess, Frederick M. The Same Thing Over and Over: How School Reformers Get Stuck in Yesterday’s Ideas. Harvard University Press, November 2010.