Wednesday, April 23, 2014

Maria Droujkova - Make Math your Own

This morning I listened to a recording of Maria Droujkova giving a keynote address at the Learning Revolution Conference Online. The title of her talk was "From adventurous learning to disruptive innovations: brave design in mathematics education." Here's her description of the talk:
Robert Lang is building a space telescope as long as the island of Manhattan. His out-of-the-box origami play helped to figure out how to fold the telescope into a rocket’s tiny storage box. Vi Hart is a mathemusician. Her whimsical sculptures, videos, and workshops are deeply therapeutic for hundreds of thousands of people suffering from math anxiety. Hans Rosling is a doctor, a statistician, and a data superhero who influences the decision-making of millions with interactive infographics. The issues our society faces require innovative, brave solutions. We already have a lot of creative dreamers and doers: our kids! At Natural Math, we design education that recognizes and supports students as creators of their own math. We grow local and global communities of math learners. We advance the view of the mathematical education as an adventurous journey. We develop tasks that are rich and complex, yet easy. And we introduce advanced math concepts to young children, including calculus for five-year-olds.
Maria really captures what young people should be doing: to make math your own, you need to make your own math. Listen to her presentation and be inspired. I was. Here is the link to her slide presentation.

Wednesday, April 16, 2014

Teachers Leveraging Technology in the Classroom Panel Discussion

Do you think this conversation is happening in Finland,  that the Finnish Council of Teachers of Math is having sessions about leveraging technology in the classroom?
-Karim Ani

At the NCTM conference last week I attended a panel discussion and was struck by Karim's comment. He continued with "sometimes I'm a bit of Luddite because often times we use technology as a thing to pursue in lieu of the thing that we actually want to pursue." [That thing being children learning math.] It reminded me of what Seymour Papert wrote back in 1990.
"Well, how many more [conferences on computers in education] should we have? Isn’t it time for us to grow up? And as we grow up, we should stop seeing ourselves as specialists of computers in education, because that casts us in the role of a kind of service profession. Accepting the role allows that other people are the ones to decide the big goals of education, what the curriculum is, how learning happens, what’s a school. And at our conferences we talk about how their decisions can be served by the computers. Well, fine, up to a point. This certainly allows revolutionary actions as long as we are at the stage of crafting Trojan horses to throw into the system. But at some point we have a responsibility to break out of that marginal role and take on our true vocation, which is not one of service but one of leadership. At some point it will be as ridiculous to have a world conference in computers and education as to have a world conference on pencils and education.Perestroika and Epistemological Politics, Seymour, Papert - Sydney, Australia – July 1990
Has Finland turned the corner and "grown up" focusing on learning and teaching? Just like Karim I'm not sure. But it's clear that we as a nation have not achieved that kind fluency with technology that these young panelists exemplify.

Technology can be a distraction. Because unlike a pencil which can be mastered in minutes, technology takes a bit longer and it's easy to get lost in its intracacies and one can lose sight of the prize we are after. But all the panelists on Leveraging Technology in the Classroom embraced technology as a strategy for winning the hearts and minds of children and teachers in our classrooms.

I think at this session there was an attempt to focus on the prize (students learning math). There weren’t any debates about which software was better (e.g. Sketchpad vs. Geogebra.) Though there was consensus that the Desmos calculator was a productive tool in helping children interact with mathematics in a genuine way.

Each panelist contributed something essential in this endeavor to transcend leveraging technology from a “thing” to a support system for the pedagogical idea that teachers value.

Ashli Black reminded us that teachers interacting face to face is still the ideal mode of the learning process. This NCTM conference provided that for educators. So do regional and local conferences. Maybe we need more conferences she suggested.

Conferences are great, but they are expensive said Karim. He’s right. Unlike 1990 when Papert wrote his article pre-Web 2.0 the online platform for collaboration was not available especially via blogs. It’s still not common mode for communication for most teachers, but it is growing steadily.

What’s NCTM’s role in this? Jon Wray said NCTM's mission simply put is to promote successful teaching and learning of math. One concern is that the average age of an NCTM member is 57.5 years. This has to change. I spoke up at the session and encouraged younger participation in NCTM. But NCTM also has to encourage younger teachers to get involved. The NCTM journals need to become more Web-based and interactive to appeal to a younger audience. Also to encourage math blogging and highlight math bloggers in their e-blast publications which tend to focus on what the President is saying rather than what the young teachers are doing. (Their Illuminations effort is more aligned with this, but needs to be better promoted.)

Blogging clearly needs to be promoted. Kate Nowak shared three components of blogging: (1) it has to be sustained over time (2) directy linked to classroom activity and (3) interaction with colleagues is crucial. Don’t do it alone.

The panel was asked what tools they found useful. The response was the technologies that promote communication, discussions and debates.

Raymond Johnson offered that building simulations that helped textbook problems come to life is important. He mentioned Simcalc and the Freudenthal institute as two groups that are making this kind of software available at a minimal cost.

Technology is not yet seamless in schools, but this panel made me more optimistic that blogging will be a powerful tool in encouraging more powerful conversations for students and teachers. That bodes well for the future.

Panelists and their blogs:
Chris Hunter -
Ashli BlackIllustrative math
Karim Ani –
Dan Meyer –
Kate Nowak –
Raymond Johnson –
Jon Wray - panel moderator

Saturday, March 29, 2014

Noon Day Adventure at Panther Academy

Nestled in a nondescript area of Paterson, NJ surrounded by aging warehouses and auto repair garages lies Panther Academy a high school I visited last Thursday and was fortunate enough to watch a small group of high school students - budding future scientists and engineers -  recreate an experiment that Eratosthenes did 2200 years. Mr. Salama helped his  students use the shadow angles and some trig functions to come up with the central angle of the earth. The class partnered with a school in Kuantan, Malaysia to get their sun angle. By subtracting Paterson's sun angle  from Kuantan's they determined the angular separation at the center of the earth known as the central angle was 37.2 degrees. They also knew that the Malaysian school was 4130 km away by comparing latitudes.  So they were able to figure out that there were 360 / 37.2 = 9.68 "Kuantan to Paterson distances" that circumnavigated the globe. Making that calculation 9.68 * 4130 = 39,937.1 km the students discovered that their measurement was very close to NASA's listing of the circumference as 40,030.2 km.
Mr. Salama helps steady the meter stick as the students
determine the shadow length.
Shafi Ahsanul gave the summary report.


In May, the class will go on the field trip and use Al-Biruni's method for determining the circumference of the earth. I'm looking forward it.
Diagram illustrating a method proposed and used by Al-Biruni
to estimate the radius and circumference of the Earth

Friday, March 28, 2014

Access and Equity in Mathematics Education - Where's the Technology?

This week I received the following email. I want to share it with the CLIME community. Please read and comment. Mine is the first one.
Ihor Charischak

NCTM At-Large Affiliate Presidents:
Over the past two years, NCTM has been working to revise its position statement on equity.  As part of this process, it was suggested that each of you be invited to review and comment on the statement from the perspective of your organization.  The attached statement reflects the work of NCTM Board members and some discussions among the Board.  You are invited to submit your comments for the consideration of the authors and the NCTM Board.  We would appreciate your comments by April 3.

Kind regards,
Ken Krehbiel
Associate Executive Director for Communications
National Council of Teachers of Mathematics

Access and Equity in Mathematics Education
A Position of the National Council of Teachers of Mathematics
(Note: Work in Progress - not final version - for review only)

What does creating, supporting and sustaining a culture of access and equity in the teaching and learning of mathematics require?

NCTM Position
Creating, supporting, and sustaining a culture of access and equity requires being responsive to students’ backgrounds, experiences and knowledge when designing, implementing, and assessing the effectiveness of a mathematics program. Acknowledging and addressing factors that contribute to differential outcomes among groups of students is critical to ensuring that all students routinely have opportunities to experience high-quality mathematics instruction, learn challenging mathematics content, and receive the support necessary to be successful. Addressing equity and access includes both ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement.

The practices of access and equity include, but are not limited to, high expectations, access to high-quality mathematics curriculum and instruction, adequate time for students to learn, appropriate emphasis on differentiated processes that broaden students’ productive engagement with mathematics, and the strategic use of human and material resources. When access and equity have been addressed well, student outcomes—including achievement on a range of mathematics assessments, disposition toward mathematics, and persistence in the mathematics pipeline—cannot be predicted by students’ racial, ethnic, linguistic, gender, and socioeconomic backgrounds.

Achieving equity with respect to student learning outcomes by closing existing learning gaps and increasing opportunities to learn requires that educators at all levels operate with belief that all students can learn, focus on ensuring that all students have access to high-quality instruction, challenging curriculum, exciting extracurricular opportunities and the differentiated supports and enrichment opportunities necessary to support student success at continually increasing levels.

To provide access and equity requires all stakeholders to monitor the extent to which all students have access to challenging mathematics curriculum taught by skilled and effective teachers who differentiate instruction as needed, monitor student progress and make needed accommodations, and offer remediation or additional challenges when appropriate.  To do this effectively, teachers must work collaboratively with others educators, including special education, gifted education, and ELL teachers, to ensure that all students have the support needed to maximize their success in the mathematics classroom. In addition, teachers need to collaborate with colleagues to implement the effective teaching practices to promote a growth mindset in their classrooms and school.

Districts and schools must review policies to ensure that systemic practices are not disadvantaging a particular group of students based on assumed stereotypes. This should include a review of the use and impact of tracking, protocols for student placement in mathematics, regular opportunities for both remediation and enrichment, and student outcomes, including persistence within the PreK-12 mathematics pipeline over time. 

Friday, March 7, 2014

Two Activites to Help You Spring Forward

This is Spring?
Yesterday while returning from a Vet appointment, I passed a church that had a sign out front saying “Pray for spring.” I was reminded of that this morning as I looked out on my backyard (see pic) and noticed that the prayer wasn’t answered yet. Despite that, there are a few hopeful signs. I spotted a robin this morning forging for food with the rest of the hardy year rounders that are always taking advantage of my generosity with bird seed. The other sign is that today is March 7th and the spring equinox is only two weeks away. That means that students will be going out soon to measure shadow angles for the Noon Day Project. This year is special because my local math group AMTNJ is celebrating their 100th anniversary and the Eratosthenes measurement of the earth project is their highlighted activity. If you haven’t ever participated in the project do yourself a favor and watch Carl Sagan tell the story of how Eratosthenes measured the circumference of the earth to high accuracy using only sticks, shadows, a measuring device and brains!

The other event that reminds me that Spring is around the corner is March 14 better known as Pi Day.  See my post from last year entitled “A Pi Day Mystery”. Another possible treat for you is that I discovered the website put together by Luke Anderson. He’s the author of the Pi Rap that you will find there. His story is well worth a read!

And then of course there is Vi Hart now with Khan Academy. Check out her controversial(?) video pi is (still) wrong!

You might also have some fun with this headline Mathematicians stunned when Computer reaches last digit of Pi and Dan Cohen's TED talk entitled The Last Digit of Pi
Happy Spring Equinox and Pi Day. Can't wait.

Sunday, January 26, 2014

Flipped Classroom: A minor tinkering or a paradigm shifter?

Borrowed from Eric Sheninger's blogpost
I was pleasantly surprised that there were eight sessions devoted to the idea of the flipped classroom on the program for NCTM’s Conference in New Orleans. Usually the flipped approach is to assign a video for homework to the set the stage for the classroom lesson to follow the next day. Of course, there is no guarantee that the “teaching” will be any different using this novel approach. There are plenty of canned videos that may or may not be “better” than what would occur in a the classroom. I like the idea because technology is used in a potentially effective way. But will  it change the paradigm from teacher-centered classrooms to student-centered ones? These sessions should help you answer that question.

I've listed the 8 sessions below that I'm flipped about. If you attend (or are giving) any of these sessions, please let me know how it was (or will be) either with a comment below or email me at

66- Flip It Good! Creating an Interactive Flipped Math Experience
In this session, learn how teachers can use educational web pages and interactive iPad apps to turn the traditional flipped classroom model into an interactive social community engaged in process-based, collaborative math instruction.
Thursday, April 10, 2014: 9:30 AM-10:30 AM
223 (Convention Center)

95- Flipping Out about Math
This presentation will introduce or expand your knowledge of the trending instructional strategy called “flipping the classroom.” Participants will see how a flipped math classroom is conducted, become familiar with the technology and tools needed to effectively implement this strategy, and discuss results and challenges that may occur.
Thursday, April 10, 2014: 9:45 AM-11:00 AM
Grand Ballroom B (Hilton)

121- Ratio and Proportion: A Common Core Progression for Grades 6–7
This session presents a two-year, flipped sixth- and seventh-grade ratio and proportion unit using instructional videos viewed at home and Common Core lessons in the classroom. Participants will be shown how to effectively use ratio tables and bar models to develop their students' proportional thinking.
Thursday, 9:45-11:00
Grand Salon 19-22 (Hilton)

229 - Transforming Geometry for Tomorrow’s Classroom
We did it all! We flipped our geometry class using iPads. We spent class time doing small-group activities, ones that demanded critical thinking and collaboration to solve problems. We used formative assessments to differentiate instruction, and we implemented the Common Core. Our instruction is still meaningful, still rigorous, but now reaches all students. Find out what worked and what didn't.
Thursday, 2:00-3:00
R05 (Convention Center)

262 - Building "Mathematical Talk" in an Early Childhood Flipped Classroom
Attendees will consider early childhood teachers' experiences as they learned to "flip" their mathematics classroom to enhance mathematical discussions in a project-based learning environment. Learn about the challenges and successes the teachers faced throughout the process and discover strategies to effectively manage the transition.
Thursday, April 10, 2014: 3:30 PM-4:30 PM
235/236 (Convention Center)

307 - Flipping with a Twist: Promoting Inquiry while Flipping the Classroom
This presentation encourages people to amend the usual method for a lecture/homework flipped classroom. I have added inquiry-based activities both before and after video lectures. Many of these activities can be done in other classes to promote understanding of Common Core concepts. We will simulate a typical two-day cycle of this form of instruction.
Friday, April 11, 2014: 8:00 AM-9:00 AM
R07 (Convention Center)

359 - Flipping the Classroom: Lectures and Homework Trade Places
Have you ever wondered what would happen if students listened to lectures outside the classroom and class time was devoted to problem solving? This session will explain the pedagogical implications of flipped classrooms. We will also discuss practical considerations and see how to teach the Pythagorean theorem in a flipped classroom.
Friday, April 11, 2014: 9:30 AM-10:30 AM
242 (Convention Center)

440 - Flipped Mastery Learning: Mathematics without Boundaries
Join the Algebros for a presentation of their flipped mastery model which allows students to progress at their own level by demonstrating mastery of all mathematical standards. We will explain why flipped mastery is changing how students learn and provide in depth information for flipping your class. Check out and bring questions.
Friday, April 11, 2014: 12:30 PM-1:30 PM
245 (Convention Center)

458 - The Flipped Math Class: Why We Love It!
Learn how to flip your class and become more thoughtful in your practice. Our students watch our notes online for homework and spend class time developing mathematical habits of mind. We will share how we use the iPad, Camtasia, and other tools to improve student engagement and how we make the most of our class time with students.
Friday, April 11, 2014: 12:30 PM-1:30 PM
Great Hall B/C (Convention Center)

See previous blog about the NCTM Annual Conference in New Orleans.

Monday, January 20, 2014

New Orleans Annual meeting Technology Preview

Top 10 Key Words @ NCTM 2014 (to see count of all
key words, click on image above.)
Welcome to my annual technology preview of the NCTM conference in New Orleans next April. There are 653 sessions of all shapes, sizes and themes. I read them all and again as in previous years I highlight a subset of sessions that have the technology principle (TP) in mind. Supporting that principle has been CLIME’s goal since TP's introduction in "Principles and Standards for School Mathematics" in 2000. More recently a new bolder theme has emerged to be CLIME’s focus something that I refer to as Math 2.0. I realize that it is not something easily defined though I keep on trying to capture its essence. My working definition of Math 2.0 is:
The New Orleans conference program committee designated several strands but only one had a technology theme: “Teachers leveraging Technology.”

At first glance I was surprised there were only 5 sessions, but what a treat these sessions appear to be! I plan to attend 4 of them skipping only Karim’s because that happens at the same time as my session. They all take place on Friday. Here’s a rundown of the sessions.

Math Teachers and Social Media: Professional Collaboration or Support Group?
Raymond Johnson
Jasperwood (Hilton)
8:00 AM-9:00 AM

Video Games and Making Math More like Things Student Like
Dan Meyer
Great Hall A/D (Convention Center)
9:30 AM-10:30 AM

Keeping It Real: Teaching Math through Real-World Topics
Karim K. Ani
Great Hall B/C (Convention Center)
11:00 AM-12:00 PM

The Mathtwitterblogosphere: Creating Your Own Online Professional Learning Communities
Ashli J. Black and Chris Hunter
225/226/227 (Convention Center)
12:30 PM-1:30 PM

One of Us: Every Teacher a Blogging Teacher
Kate Nowak
Grade Band Audience: General Interest/All Audiences
2:00 PM-3:00 PM

I’m not exactly sure why mine was left off the list since I think leveraging (using something to maximum advantage) technology is a big part of what Math 2.0 is all about.

Each of the 5 sessions focuses on themes that are significant in a Math 2.0 classroom environment: Social media, video games, real world applications and blogging as a significant new form of professional development.

Of the 653 descriptions of sessions that I read (with this vision of Math 2.0 on my mind) 161 sessions have a technology theme.  That’s almost 21% which is down from a high of 38% at the Philly Annual Meeting in 2012 and 28% in Denver in 2013.

I’ve highlighted 16 that are on my "plan to attend" list. (This list includes my session #398 on Math 2.0 at the Hilton at 11am.)

If you would like to have your session highlighted let me know. I can also add a photo and additional links to your listing.

It’s been a long time since you submitted your proposal and you might want me to add some updates to your session listing on the CLIME conference technology site. Send me an email with the updates (your photo, links, etc.) and I will immediately post them to the website.