Wednesday, November 29, 2017

Catalyzing Change in High School Math

Math and STEM Ed
It’s been a long time since my last blog, but I didn’t want to miss the opportunity to comment on the new High School initiative that will be available for sale at the Annual NCTM Meeting in Washington next April.

NCTM has a newly drafted, rather optimistic manifesto for high school math teachers titled Catalyzing Change in HS Math which offers an alternative (Option A) path to what I call the Royal Road to Calculus - 4 years of high school math culminating in a year of Calculus (Option B.) Option A includes statistics and other electives in the last year and half of a student’s high school math experience.

Option B is a given for those students that have the mindset to persevere in math. Jo Boaler in Mathematical Mindsets writes that that doesn’t mean these students will necessarily experience the joy, wonder and beauty that math learning can bring to those who learn math intrinsically.  But these eager beaver students will persevere and get the grades they want. But what did they learn and what will they remember? (1) In option A NCTM proposes 2.5 years on the road to Calculus, then a choice: statistics and/or other electives like quantitative literacy, discrete mathematics, financial mathematics, mathematics in the fine arts, and history of mathematics. I was amazed that STEM pursuits were not included. But that’s not surprising after president Matt Larson claimed in his monthly message that "Math Education Is STEM Education" which I disagree with. See my comments following Matt’s message.

CLIME “After Hours” Meeting in Washington, DC
We will be holding a CLIME get together in Washington to celebrate 30 years of CLIME participation as an affiliate group of NCTM.

Date: April 26, 2008
Time: 7:15-8:15 (right after Shadowcon)
Room: Marquis Salon 14 (Marriott Marquis)

(1) For a good review of Boaler’s Mathematical Mindsets, read Mathematical Mindsets and Easy Fixes by Dylan Kane.

Saturday, September 30, 2017

CLIME Updates

Next April, 2018 CLIME will be celebrating its 30th anniversary and I will be stepping down as president and I look forward to have someone step forward to take my place to continue to lobby NCTM to promote powerful uses of technology in math education.

Technology is our best hope to break the cycle of continued failure particularly with our underachieving students. What it will take is something similar to an Apollo-like project that Keith Devlin encourages where motivation via video games play a central role in math learning.

Please let me know ( if you are interested in leading CLIME to next level wherever that goes. I will continue to play a support role (e.g. supporting the CLIME blog).

We will be holding a CLIME get together in Washington to celebrate the 30 years of CLIME participation as an affiliate group of NCTM. More details will follow.

CLIME Connections (Issue No. 217)

Sunday, September 24, 2017

Breaking News: NCTM splits with Math Forum

"At its July meeting, the NCTM Board of Directors decided that effective January 1, 2018, in order to create synergies on staff and among volunteers and reduce expenses, that all full-time NCTM employees would be located in the Reston, Virginia office. The decision to consolidate all NCTM staff in Reston was not purely a financial one, but was made for other business reasons as well, including the potential positive energy The Math Forum staff could have brought to the focused work of the departments at NCTM headquarters in Reston. Math Forum staff elected not to continue their employment with NCTM. The Board of Directors is very disappointed in this outcome, but NCTM is pleased to have been able to extend the Math Forum’s existence after Drexel ended their relationship with The Math Forum. We thank each and every member of the Math Forum for their commitment to mathematics education and hope each of them reconsiders their decision to leave NCTM." (Read entire post written by Matt Larson & Robert Berry.) Also, read this Twitter post.

Saturday, September 23, 2017

Designing Curriculum that Students Would Love

Over the past twenty-five years, we have learned that standards alone—no matter their origins, authorship, or the process by which they are developed—will not realize the goal of high levels of mathematical understanding by all students. More is needed than standards. For that reason, NCTM has developed Principles to Actions: Ensuring Mathematical Success for All, the next in its line of landmark publications guiding mathematics education into the future.
-Principals to Actions (preface)
As I review the NCTM Orlando conference list of sessions (details in my next blog), I’m reminded again that technology plays a "secondary" role in the scheme of all things NCTM. The main thrust is teaching and learning - mostly without technology. Principles to Actions (PTA) devotes 53 pages to T & L with very little mention of technology. Technology and Tools (which include manipulatives) gets 11 pages of cover. But there is very little to offer in the way of examples of how technology plays a role in teaching and learning. As in your typical standards the details of how best to use technology is left to the teacher. I was promised that the new NCTM’s Taking Action series would show how to implement effective math teaching practices. I got a copy of Taking Action: Implementing Effective Mathematics Teaching Practices (Grades 6-8) hoping that there would be good examples of using technology in the classroom. But alas it’s a rehash of  PTA with very few ideas about using technology in the classroom.

What makes this all depressing is that math achievement has not changed much since forever. So what would make a major difference?  If only the curriculum was designed with children’s interests in mind. A few textbooks have made an effort in this direction. Harold Jacobs' books and EDC’s Transition to Algebra come to mind, but they are in the minority. Textbooks should be books that children actually want to read and technology is the best platform to make that happen. Lessons should include games, puzzles, challenges and projects that will excite students. They should be in the mainstream if we ever want to engage students in math in a powerful way. This won’t happen as long as math education remains in the custody of most textbook companies that are unwilling to experiment (take risks) with their products.
Next April CLIME will be celebrating its 30th anniversary and I will be stepping down as president and hope that someone will take my place to continue to lobby NCTM to promote powerful uses of technology in math education. Technology is our best hope to break the cycle of continued failure particularly with our underachieving students. What it will take is something similar to an Apollo-like project that Keith Devlin encourages where motivation via video games play a central role in math learning.

Please let me know if you are interested in leading CLIME to next level wherever that goes. I will continue to play a support role (e.g. supporting the CLIME blog).

We will be holding a CLIME get together in Washington to celebrate the 30 years of CLIME participation as an affiliate group of NCTM. More details will follow.
CLIME Blog #215

Thursday, September 7, 2017

The World's Greatest Collaborative Project: Replicating Eratosthenes' Measurement

Measuring shadows in Passic, NJ (2006)
Back in 2010 John Burk wrote about this measurement in his blog:
"I’ve wanted to do this experiment ever since I was a sophomore in high school, and heard of how Eratosthenes was able to measure the circumference of the earth just by looking down a well in a couple of towns in Egypt 2000 years ago. A few years ago, when I was at a boarding school, I even got up on stage and challenged the students to come with me to measure the earth with a stick, but somehow, I never followed through. This year, I had the equinox marked on my calendar, and contacted my reliable, physics partner in crime, Frank Noschese. [...] We thought it would be great to give skype a shot, and try reproduce the Eratosthenes measurement between our two classrooms." (Read John’s entire blog.)
I too was inspired to recreate the measurement way back in 1972. Here’s what I wrote about it iin my book “The Wannado Curriculum” starting on page 100:
"In 1972, I came across an article in an issue of NCTM’s The Mathematics Teacher that described one teacher’s effort to collaborate with another school in an attempt to duplicate the astonishing experiment in which Eratosthenes successfully measured the circumference of the earth from Alexandria, Egypt, in approximately 200 BCE. I was inspired to try the activity with my second-year algebra class. I attempted to involve two schools—one in Michigan and the other in Florida—but sadly, nothing materialized.
Fast forward to 1995. While creeping along the Internet (surfing was in its infancy), I read that a high school mathematics teacher in Illinois was hosting something that she called the Noon Observation Project. It turned out to be a worldwide collaboration among schools that sought to recreate what Eratosthenes had done so long before. Because the experiment required participants to measure shadows at about the same time (when the sun was at its highest point in the sky), “real-time” communication was extremely important."

Fast Forward to today. You too can recreate the measurement! It's a great way to kick off the school year with your students. The easiest way to do this is to participate in the World Wide Noon Day Observation Project starting this week.

Friday, August 18, 2017

Tech Use in Math Classes Continues to be Minimal

This year's edition of the "Technology Counts" survey from Education Week found 74% of eighth-grade math students "never or hardly ever" use computers in class, and just 1% of students say they use computers in math class daily, according to EdTech: Focus on K-12. (more)

While the percentage of students who use a computer in math class at least once every few weeks has been steadily increasing over the past few years, 74 percent of eighth-grade math students report they never or hardly ever use computers in class. (more)

Every once in a while I come across articles like this that remind me that we still have a long way to go in order to get school districts to get their teachers to use computers in teaching math. When teachers are asked why they don't, they usually come up with at least one of these reasons:
  • Lack of of necessary equipment and/or software
  • Not enough teacher training
  • Preperation for testing doesn't allow for time to "explore" with computers
And thus the beat continues.

I recently got a copy of NCTM's Taking Action: Implementing Effective Mathematics Teaching Practices for Grades 6-8 hoping to see how the guiding principle of "technology as a tool" would be highlighted especially in this grade band where using technology can be so effective. But alas there was almost no mention of technology until the last chapter (which has the same name as the title of the book). There they indicated that technology should be used appropriately. Even in the video vignettes there were no computers involved only graphing calculators mostly sitting on tables and not used by the students. Clearly the focus of Taking Action (6-8) is about effective mathematics teaching practices without computers.

I can see value for using this book with teachers involved in lesson study or at the university level. I don't think very many teachers will use it as a guide for teaching because it's too much like a textbook for teachers learning how to teach math. Anyone agree or disagree with me? Let's have a "conversation" at #climetech.

Monday, August 14, 2017

Remembering Sharon Dugdale & Don Cohen

Sharon Dugdale & Don Cohen
I've been amiss in not sharing earlier the passing of two wonderful educators (here and here) both of whom were influential in my thinking about teaching math (Don) and using technology (Sharon) to empower my students.  In the 1970's both Sharon and Don worked with Plato an early prototype of a computer-assisted instruction system that ran educational software. Don shared an example of software that was a part of the Madison Math curriculum with me at a conference in 1977. Sharon worked earlier on the Plato system to develop a fractions curriculum (including Darts and Green Globs - 2 of my all time favorites) which are still available today. Don went on to work with students (ages 3 to 73) for 38 years teaching them a variety of math topics including Calculus for 4th graders. My condolences to both their families.

Friday, August 4, 2017

Top Education Researchers Jump Ship to Join Digital Promise

Dr. Jeremy Roschelle and Dr. Barbara Means
"Education research is about to pick up its clock speed.

When people talk about the “gold standard” of research, the name SRI International often comes up. Now they will have to add Digital Promise to that list.

Nonprofit Digital Promise said today that two of education’s leading researchers, Dr. Barbara Means and Dr. Jeremy Roschelle, who had co-directed the Center for Technology in Learning at SRI, are joining Digital Promise. Means and Roschelle plan to create a new research center at Digital Promise that will help scientists look for ways to better tie research to practice in the classroom."

So begins the article (title of this post) about two outstanding researchers in the area of technology and education. Jeremy has been a long time friend of CLIME and his research in technology and math have forwarded CLIME's thinking in how technology can be used effectively in the math classroom. Their new plans at Digital Promise sound exciting and we at CLIME look forward to following their progress. Here's the link to the article noted in the title. Also a link to some of their their planned work at Digital Promise.

Tuesday, August 1, 2017

ALC brings Equity & Advocacy to the Forefront

Figure 1.
I attended the ALC (Affiliates Leadership Conference) last week in Baltimore where the theme was “Intent to Impact: Addressing Access, Equity, and Advocacy in your Affiliate” (1).  One of the goals of the conference was for each affiliate to come up with a game plan to forward the action on this theme in their affiliate group. CLIME had already considered what to do about contributing to NCTM's advocacy positions (2) on this topic. CLIME will collect stories about how districts are making sure that ALL their students have access to computer devices and appropriate resources to ensure powerful learning. This will hopefully contribute to inspiring districts to pursue the vision of liberation (see figure 1) in the way they structure their school environments and curriculum.

Our first story is about Kerease Epps "Using Math To Multiply Access For All Students" a blogpost on the LEE (Leadership for Educational Equality) website.

Chicago native Kerease Epps (TFA Detroit ’13) knew growing up that the system she was a part of as a Chicago Public Schools student wasn’t one that gave all students a fair chance. Now as a recruitment manager for an education nonprofit dedicated to closing the achievement gap in mathematics, she’s working to ensure that students get the support they need to succeed.

Explain what led you to care deeply about educational equity. What personal values, experiences or beliefs inform this?
I was born and raised on the Southside of Chicago and attended Chicago Public Schools (CPS) for my entire academic career prior to college. (more)

For more stories about math, technology and minorities see link.


(1) Affiliates are organized by geographic area or a specific topic in mathematics education. The topical groups - 11 in all - are called Affiliates-at-Large. CLIME with their focus on technology is an affiliate-at-large group. (See the directory of all affiliate groups.)

(2) Access, Equity and Empowerment: Advance knowledge about, and infuse in every aspect of mathematics education a culture of equity where each and every person has access to and is empowered by the opportunities mathematics affords.
Advocacy: Engage in public and political advocacy to focus policymakers and decision makers on improving learning and teaching mathematics.
Curriculum, Instruction, and Assessment: Provide guidance and resources for developing and implementing mathematics curriculum, instruction and assessment that are coherent, focused well articulated and consistent with research in the field, and focused on increasing student learning.
Professional development: Provide professional development to all stakeholders to help ensure each and every student receives the highest quality mathematics education.
Research: Ensure that sound research in integrated into all activities of the Council.
Technology: Promote strategic use of technology to advance mathematical reasoning, sense making, problem solving and communication.

(Approved by the NCTM board of Directors, October 20, 2012.)

Friday, July 28, 2017

Let's Retire #MTBoS?

In his latest blog Dan Meyer calls for retiring the hashtag MTBoS and replace it with #iteachmath. Dan writes:
"I’m not asking us to retire the #MTBoS (unabbreviated: the Math Twitterblogosphere) the collection of people, ideas, and relationships that has provided the most satisfying professional development and community of my life. I’m asking us to stop referring to it as “the MTBoS” and to stop using the hashtag “#MTBoS” in online conversations.
That’s because this community is only as good as the people we invite into it. We currently represent only the tiniest fraction of the math teachers in the world, which means we (and I’d like to believe they also) are missing out.
That fraction will stay tiny so long as our name alienates people. And it alienates people. [...] So I’m going to stop referring to my participation in “the MTBoS” and instead talk about how much I love “Math Teacher Twitter.” I’m going to stop tweeting using “#MTBoS” and instead tweet using “#iteachmath.” (more of his blogpost)
 I'm not quite sure what to make of it.

 I'm a little confused. :-) I agree with Dan that MTBoS is a little off-putting and another, better name would improve things. But not #iteachmath which is too general and misses the point of MTBoS which is a group of math educators that tweet and/or blog and those folks need to continue to share their empowerment in using those tools.

Monday, July 17, 2017

Youtube's Take on the Future of Education

I’ve been spending some time looking at Youtube videos about math education and education in general and came up with two  interesting ones with contrasting points of view. First there is “This Will Revolutionize Education” (7:06/1,558,501 views) where the speaker's main conclusion is: "For as transformative as technology seems to be (…) what really matters is what happens inside the learner's head and making a learner think seems best achieved in a social environment with other learners and a caring teacher.” Sounds familiar, doesn’t it? Not terribly earth shattering. Hard to disagree with that one. But a revolution? I don’t think so. We have had great teachers for ever. (You can find out what it takes to be one with a simple google search.)  In other words, the speaker in the video still believes that this low tech approach will spurn a revolution. Unfortunately the great teachers live on the high end of the bell curve and in all of the years of school reform movements the bell curve hasn’t shifted all that much so I have little confidence that just focusing on improving teachers will make the revolution happen any time soon.

On the other hand CGP Grey in "Digital Aristole: Thoughts on the Future of Education” (5:43/1,511,488 views) doesn’t claim that a revolution in high tech tools will alter the teacher performance bell curve, but rather will send the average teacher from their central position at the front of the class to being a guide on the side. And if the curriculum materials are more engaging for students they may actually learn more than the average student in a more traditional setting. What the author suggests is that every student be given a “digital Aristotle” since having a real Aristotle
available for 1-1 tutoring is not humanly possible, too expensive and not as gifted a teacher as Aristotle was. The Internet has opened up the possibility for great learning. But this doesn’t mean teaching the same old curriculum with shiny new things. Also having personal tutors like Salman Khan available doesn’t guarantee effective personalized learning. What Grey does envision is adaptive technology that will personalize learning in a way that will motivate, inspire and empower students to learn things they are interested in. His vision of a digital Aristotle for everyone will tutor students individually and adapt appropriately over time to produce the most effective resources for each individual student to determine scientifically what works best. He uses Khan Academy as an example of where we are now, but in the future the software will result in a more personalized and effective learning modality that is better than what the average teacher can do with students today.

Being the president of a technology oriented organization you might suspect that I would lean towards Grey’s vision and less towards the human revolution promoted by the previous video. But I’m inspired by both visions. The problem is that we pundits take sides and that doesn’t help in creating a future for our students and teachers that is better than what we have now. What we need is a future where students are pursuing learning things that they are interested in in a deep way. And the teachers job is to guide their students to achieve not only their goals, but also their dreams.

Tuesday, July 11, 2017

Math Education Is STEM Education! Really?

Matt Larson, NCTM President

May 17, 2017
What design principles would you include to ensure that an effective STEM (science, technology, engineering, and mathematics) program builds mathematics understanding? 
So begins Matt Larson's piece in the NCTM blog. It's definitely worth a read. (Link) He asserts that a good math education is all that's needed for a good STEM program. I disagreed.
I shared my thoughts in the comments section and got 2 replies from Matt. We found some common ground.
Tracey Knerr - 5/18/2017 7:45:32 AM
Thank you for writing this.  In our district, the science supervisor and I have been trying to leverage the Standards for Mathematical Practice with the NGSS and ELA practices.  We use the NGSS Venn diagramvisual to help inform the work everyone is doing.  Unfortunately, as a district, we are not all on the same page and rather than thinking of STEM or STEAM as a way of thinking and doing business most of our colleagues still see STEM as a separate class.  It would be fabulous if all interested parties could come together and discuss a common vision.

Ihor Charischak - 5/19/2017 3:48:35 PM
Tracey: It will be very challenging to have a common vision. What STEM is really about is the integration of these 4 areas and the APPLICATION of math to the other 3 subjects; for example, building bridges and programming robots. Doing the traditional common core math program does not lend itself well to projects which is the heart and soul of STEM education. I'm disappointed that Mr. Larson does not see it that way.

Matthew Larson - 5/19/2017 4:14:18 PM
Ihor: As I indicated in the message I support curricular connections and the application of mathematics to science and other subjects. My point is that in doing so we must be careful to maintain the integrity of the mathematics learning objectives. In too many cases this is not being done. Matt.

Ihor Charischak - 5/20/2017 10:14:04 AM
Maintaining the integrity is a given for NCTMs view of an ideal math curriculum. Good STEM projects would not do any harm to your vision. But it does make teachers concerned about doing STEM projects "right" so they probably won't even try unless they have to and that's not a good way to do it. Sharon's comment below indicates some of the concerns teachers have. You're going to run into this problem again when your high school reform committee plans alternative paths for students. STEM projects would be a great alternative to Calculus for those students who are planning STEM careers. Colleges need to rethink whether Calculus should be taught in high school instead of a solid STEM course.

Matthew Larson - 5/20/2017 10:19:53 AM
Ihor - Good points that I will pass along to the High School Task Force. Thanks. Matt.

An Email to David Wees re NCTM Affiliate's Conference

Hi David,
I just signed up for this conference in Baltimore that’s taking place in a couple of weeks. I’ll have our New Vision to do list  in hand which will give the other participants a good handle on what CLIME is all about. I’ll be sharing what happens while I'm there and in a blog post when I get back. Anything else I should bring up while I'm there?

On Jul 10, 2017, at 10:34 AM, NCTM Affiliates <> wrote:

Dear Ihor Charischak 

Thank you for registering for the 2017 NCTM Affiliate Leaders Conference, to be held in Baltimore, Maryland, July 22-24, 2017. We are truly looking forward to working with you during our time together! Both you and your Affiliate will benefit as we focus on this year’s theme, “Intent to Impact: Addressing Access, Equity, and Advocacy in your Affiliate.” In addition to building leadership capacity, the conference will include opportunities to exchange ideas and connect with the NCTM President, Matt Larson. You will be able to network with other Affiliate leaders in a variety of activities, develop Affiliate action plans, and learn more about being a partner with NCTM.

NCTM Affiliates across the country are faced with challenging issues related to mathematics education. Come together with other Affiliate leaders to consider the most urgent work in your setting through the lenses of Access, Equity, and Advocacy. Learn about tools and frameworks to support your work, and walk away with a specific, supported action plan to address your Affiliate-specific issues. This summer’s conference will launch a collaborative, ongoing learning model to enact your action plan during the 2017-18 school year.

Additionally, as a conference participant, you will have opportunities to— 
  • Develop strategies to empower your Affiliate and individuals within your Affiliate to take action for a high quality mathematics education for each and every learner;
  • Increase your self-awareness of micro-messaging and its impact on your work;
  • Learn how to minimize micro-inequities and maximize micro-affirmations;
  • Create an action plan to address an Affiliate-specific issue;
  • Mobilize the work of your Affiliate through your spheres of influence;
  • Challenge leaders to be deliberate about Equity, Access, and Advocacy in your Affiliate’s structures, practices, and activities;
  • Explore NCTM resources, including the Advocacy Toolkit;
  • Learn about the NCTM structure, resources, and initiatives, and participate in discussions with NCTM President Matt Larson, NCTM Staff, and Representatives of the Affiliate Relations Committee;
  • Discuss, collaborate, and network with other Affiliate leaders.
Free wireless internet will be available in the meeting room. Participants are encouraged to bring a laptop or tablet.

Gina Kilday
Membership and Affiliate Relations Committee
NCTM Board Liaison and Affiliates-at-Large Representative 

Sunday, June 25, 2017

Math Sessions at ISTE Computer Conference 2017

Tech words @ math sessions
The ISTE (International Society for Technology in Education) conference is starting today. I haven’t attended one in several years. I stopped going because there were not enough math related sessions and the ones I sat in on were not all that good. 

Back in the early days when the ISTE conference was known as NECC (National Education Computer Conference) I attended many of its conferences and presented at them as well. I always hoped that the conference would make more of an effort to highlight a math strand within the conference. The technology hype was a bit overwhelming even within the math sessions. 

NCTM had a problem with promoting technology as late as 1989. In their Standards document that year it mentioned that some math software might be useful as a tool for teaching math. Also, many math teachers became computer teachers in the 1980s and that didn’t sit well in the NCTM community. It would have been useful for more collaboration between ISTE and NCTM to find common ground. 

In their Standards document in 1989 NCTM noted that computers and graphing calculators should be available to students and the teacher should have a computer in their classroom for demonstration purposes. By the 2000 Standards it was important to note that technology (broadened from just computers and graphing calculators) should be used as a tool in the classroom but not the focus of the lessons. That was the job of the technology teachers assuming of course that the tech and math teachers were operating on the same page.

Since I haven’t paid much attention to the ISTE conference in a while I thought I would take a closer look at what was going on this year at its conference in San Antonio. From the almost 1500 sessions listed, I came up with 142 (10%) using math as a keyword in the search. Many of these had a math or STEM/STEAM theme but it also included other subject areas. 

Here’s a list of (34) math related sessions that I found useful.

Interesting. Not one mention of TI calculators. Desmos has three sessions.

Highlight sessions

Sessions I would go to if was there:

How getting rid of desks, replacing them with comfortable furniture and allowing students to work at their own pace changed student engagement and performance in the math classroom. Also included: using OneNote as a platform to allow the classroom to be completely paperless and run in a nontraditional, efficient manner.

Discover how to use technology to redesign tasks by giving students choice in selecting tools to create products that demonstrate understanding and allow them to share their creations in an interactive virtual community. We'll focus on web-based tools that support differentiated mathematics instruction with the Mathematics Practice Standards.

To prepare students for an ever-changing future, we must focus on developing skills that encourage persistence for students to pursue their passions. This panel highlights how leaders can support a vision of transformation extending beyond the classroom to develop a growth mindset, deep connection to and love for mathematics.

Tuesday, June 6, 2017

Mathematical Mindsets

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

A Radical Educational Idea You Can Adopt Today

Image source: @bryanmmathers
The sketch on the left shares a radical idea. Something right out of A. S. Neil’s Summerhill.  Not very likely in our current reality of testing and grading. But someday maybe a boat like this can float in many bodies of water.

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.
These ideas are not new. John Dewey, Jean Piaget and Seymour Papert wrote extensively about how kids learn and what we can do to empower them. So that begs this question: What can we do today in our classrooms to make motivated learning happen?

The Shift from Engaging Students to Empowering Learners

Great video! ****

Tuesday, May 9, 2017

CLIME's New Vision

To dos
           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.
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 ( 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

Will the High School Math Experience for Students Become Better Any Time Soon?

Matt Larson
In his latest message to the NCTM community President Matt Larson writes:

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 
  • Provide narrative descriptions of course exemplars, including their big ideas, that could populate the pathways. 
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. 
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

Post Conference Debrief

Click above to see a more readable version.
This is a wordle of the 108 sessions that had a technology theme at the NCTM conference in San Antonio. If you eliminate the largest words (Students, University, CC [i.e. convention center], School, and Session) from the picture you start to see patterns that tell you something about one of the conference's main themes: Technology. So it's no surprise that it is the most dominate in the wordle.  The words learning, Learning and Learn tell you that the presenters want you to learn while you are in their session. How much did you learn? You can share your learning via a blog! Also you can "join" the MTBoS movement especially if you have never blogged before.

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 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

NCTM San Antonio Conference Technology Preview

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

Curriculum Reform Done Right

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:

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

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.