Wednesday, December 12, 2018

A Few Things That Annoy Me

Andy Rooney (1919-2011)
As I notice and wonder about blogs that I read, I'm finding two themes (memes?) that are very annoying. They are (1) instructional and (2) notice & wonder routines. Now that I’m retired and become more like Andy Rooney of 60 Minutes fame, I find my personal routines becoming more and more distasteful. After my morning coffee (which I look forward to) I do the following: (1) Clean the litter and litter area (we have 5 cats) (2) Make the bed assuming of course that my wife is up by then (3) brush my teeth with a fancy battery powered toothbrush (Quip) that takes 2 agonizing minutes to complete and (4) take my mouthful of vitamins which takes a while to sort out and swallow. Then I finally make my second cup of coffee and go to my desk to think creative thoughts (like the ones I’m writing now) and time begins to fly by. So needless to say I’m not fond of chore routines. Unfortunately, they are mostly necessary evils.

My concern about using instructional routines in math classrooms is that they can take over and become boring to students. Speaking of boring there are the notice and wonder routines. The ones I notice and wonder about are happenings in classrooms of bright, bushy tailed students that will notice and wonder excitedly about anything including spilled milk. But I wonder about the students who are less enthusiastic noticing, but only wondering and joking about why the teacher is asking such a boring question.

Now don’t get me wrong. If notice and wonder routines work for you, then by all means continue.

I found out from working at an adolescent kid’s camp in Maine back in the 70s that anti-routines where the best anecdote for boredom. At the end of each day the counselors would gather and plan the events for the next day. They were different each day. I know that camps are supposed to be about fun, but they are also educational. The lessons I learned at that camp (when I was in my 20s) served me well. I included an element of surprise in my math classes every day especially for those students who suffered from routines paralysis.

Friday, December 7, 2018

Another Rags to Riches Story

New Version of Fraction Tracks (NCTM)
In a previous blog I lamented over the demise of the Broken Calculator. Well there is another program - Fraction Tracks (FT) - that appears to have disappeared as well for the same reason (unsupported plugins). Why does FT need resuscitation? If this simulated board game is used with care it can be a part of the solution to the number one challenge in elementary math education: learning fractions.  Before we discuss this NCTM FT "miracle" app, a little background may be useful.

If you search for a fraction app on the Web you will be amazed at how many there are. FT was/is a golden needle in that haystack. It encourages students to explore equivalent fractions in order to continue with their moves and win the game. From a teacher perspective it can improve their knowledge base and perspective on teaching fractions.* But, alas, the NCTM version which was developed with funding help from the now defunct Marcopolo project suffers from the "unsupported plugin" plague.

(Put the plague story on hold for a minute or so.) An effective way to introduce the game to students is to use a different modality: a board game version of FT that doesn’t require a computer. Here’s a description of one version of the game.
The Fraction Tracks Game, used in fifth-grade classes at Tollgate Elementary School of Expeditionary Learning in Colorado, provides opportunities for students to use equivalent fractions, break fractions apart into unit fractions, and mentally add and subtract fractions with denominators 2, 3, 4, 5, 6, 8, or 10 as they try to move their game pieces from 0 to 1 along tracks labeled in various fractional divisions. Included here are the game boards, rules for a basic game play, and “extension” rules that provide more advanced practice. 
Another way to introduce the game (and eventually the app) is to play it cooperatively. 
Start the game by placing one chip on each track, at the beginning (0) of each track.
A student then chooses a card from a deck of fractions. The fraction on the card is the total move a player must make using one or more chips.
The first fraction chosen in this game (see figure on left) was 8/10. On the board the bottom chip is moved to 8/10.
 The play can move on one track or on several tracks, but the total must equal the fraction on the card. What if the next card is 4/10? The student may be stumped as to what to do unless he realizes that 4/10 is equivalent to 2/5. Thusly, the fifth's chip can be moved to 2/5 or the student can realize that 2/5 = 2/10 + 1/5 and thus score a point on the 10th's line as well as move the 5th's chip to 1/5. (See figure below.) The ultimate object is to get all 7 chips to wind up on the 1. (Here's more on strategies for making moves.)

If a play cannot be made, the game is over. The team score is the number of chips that made it to 1.
Highlight: Watch this video** of one teacher’s way of teaching FT to her students. 
The app version has been resurrected (written in Flash) and is now available here. It is a two player game and has a timer. Have fun!
** The video is 16+ minutes but well worth it! Watch it soon because it too might disappear. (A different kind of plague: lack of support.)

Wednesday, November 28, 2018

Technology in Seattle - a Showcase of How to Use it Effectively(?)

The Seattle regional conference opens today.
According to my search results there are 262 sessions of which there are 22 presenters that indicated that their session has a technology focus. That’s 8%. A really low number based on my years of counting sessions at previous meetings. I hope the regional meeting’s low number does not portend what will happen at the annual next April. I don’t think there is causation here since the committee for San Diego is different and well on their way to planning what’s happening there.

So why am I so fixated on tech at conferences? A conference could be great without tech sessions, right? Well there has been a lot of progress at conferences on the peripheral side - more Wifi availability - speakers have Wifi access as well and it's less dangerous for a speaker to use now than it was in the wild early days of the Internet. However the way speakers use technology for the most part is just a replacement for transparency slides that were ubiquitous when I first started in the 1960s. That's a shame since sessions should be promoting how to use technology in creative, cooperative ways. Let see if that applies in Seattle.

This link will get you a list of all 262 sessions. If you choose this category type: technology and tools (22) you will see a listing of the 22 sessions - including 2 that have been cancelled.

Here are the descriptors of some of these sessions:
Learn to leverage adaptive, game-based challenges and gamification principles to provide joyful, "just in time" activities that personalize learning for all students. Teachers, coaches, and administrators will experience practical strategies for 1:1, computer lab, and BYOD device settings to move K-12 students to deeper levels of understanding.
A great task engages students with an interesting problem involving essential content. It builds deeper understanding, supports discourse, and provides the opportunity to persevere. Technology alone does not solve it--nor does technology replace thinking. Learning is enhanced when we leverage classroom technology to guide students to deeper math.
See how handheld technology promotes algebraic thinking and a deeper understanding of sequences, functions, and limits to help students move from algebra to calculus.
With access to technology, K-5 teachers now have opportunities to promote exploration and inquiry, all while encouraging collaboration. Keep the devices out and help students really engage with the content.
Come learn with a Desmos Fellow! I will be sharing activities and teacher moves that have created deeper learning, more relevant and thoughtful discussions, and a greater level of engagement in my classroom through Desmos' Activity Builder. These free activities can be used immediately in your classroom.
Graphs programmed with adaptive "Cold, Warmer, HOT" hints allow students to play hide-and-seek in precalculus and calculus. These dynamic interactive graphs, created with Desmos, purposefully guide students as they explore concepts, make conjectures, and build intuition. Many graphs will be shared. Stop in to check it out--you're getting warmer!
Fractions are complex mathematical concepts that children struggle with. We will present findings from two types of innovative instruction to fourth graders highlighting the use of number lines, scaffolding, and gesturing to enhance children's knowledge of fractions. One intervention used paper-and-pencil and the other used gaming technology.
Desmos and GeoGebra offer free access to all with top-of-the-line, highly reviewed websites. Integrating them into the classroom makes math more relevant, engaging, visual, conceptual, and fun for today's digital native students. This interactive session will cover the basics of each website and include strategies for learning.
Technology can amplify student thinking and creativity, helping students create and understand like they haven't before. It can also think and create FOR students, dazzling them without inspiring or educating them. We'll look at technology (including handheld calculators, Sketchpad, and Desmos) that thinks WITH you and your students, not FOR them. - Eli Luberoff, Desmos 
Augment your calculus teaching by using Desmos to animate its greatest hits! We will share ready-made examples, plus lift the hood to show how to dynamically visualize such classics as secants approaching tangents, derivative sketching, related rates, Riemann sums, the fundamental theorem of calculus, Taylor polynomials, and polar curves.
Learn to integrate benchmark percents with Desmos tables and graphs to develop a percent backstory for a given situation. The number lines, tables, graphs, and equations discussed highlight the proportionality of percents and present students with a mathematical backstory to guide their decision making when solving percent problems.
Sounds like if you go to these sessions you will be inspired. Hopefully so.

Tuesday, November 27, 2018

What to do with a Broken Calculator that's Broken...

Duncan Keith's app
What to do with a broken calculator that is really broken? Back in 1989, Judah Schwarz developed a software package named "What to do with a Broken Calculator?" It was a simple, but brilliant idea. Take a simulation of a calculator that allows the teacher to break (disable) some of the keys and challenge the student to produce an answer, of say, 50 with most of the number keys disabled. This can be a challenge and an important learning experience for young students.

Unfortunately, because of the vagaries of Java-based applications all of the really good versions including Cut-the-Knot, Seeing Math and Mathcats don’t work any more because of “unsupported plug-ins.”  Alexander Bogomolny who developed writes: “While a good deal of the site has lost its interactivity (Java failure), most pages remain interesting and informative, whereas many others that do not use Java, are still interactive. The situation is unfortunate for which I am deeply sorry. Alex had a working version of Broken Calculator which we may never see again. But then who knows. Stay tuned. If there’s a way and time to do it, Alex will figure it out. (Unfortunately, Alex passed away on July 7th, 2018.)

In the excellent, but ill-fated On-Math NCTM publication, Broken Calculator was one the issue’s themes. Here’s a quote from the article:
Broken Calculator is, in effect, an inexpensive, versatile number laboratory. Using Broken Calculator to solve problems forces students to explore operations on numbers and representations much more deeply than does rote application of algorithms. Most important, working with Broken Calculator shifts the responsibility of finding and expressing the answer to the student. Solving problems means inventing a wide variety of strategies to work around the limits set by the disabled keys or functions. Students deepen their number sense, problem-solving capacity, and understanding of the number system— and have fun at the same time! 
So is the idea of Broken Calculator lost forever? Or is it alive somewhere? Alas, there is a working remnant(?) of Broken Calculator alive and well on Duncan Keith's site. I say remnant because it's not the open ended one that was developed by the staff at Concord Consortium and others, but rather by an independent software developer Duncan Keith who somehow manages to keep this site going despite the unpredictability of Java updates. If you go here you will meet Eric (below).

The program has a built-in library of challenges (levels). The one drawback is that it has a timer that may be intimidating for some students. Also it's designed to be used by students independently so it would be difficult to use with a whole group of students to analyze strategies. (Read this.) Also, the calculator does not do order of operations.

So until we hear from one of our Broken Calculator champions of the past (or future) Eric smashing his calculator is our best hope for now.

Unless, you prefer...

There is a low tech version provided by Dan Finkel developer of Here's a New York Times article about his Broken Calculator approach.

Thursday, November 8, 2018

High School Math is Not Working

Here we go again. We've seen similar charts like this before. What are we the math education community doing that's contributing to this trend? Our new NCTM president Robert Q. Berry recently posted a message to the community in response to articles such as this: MATH SCORES DROP TO A 14-YEAR LOW AS ACT SHOWS MANY HIGH SCHOOLERS UNPREPARED FOR COLLEGE.

He writes:
"The decline in recent years in the mathematics score on the ACT exam has many educators and policymakers concerned. There is apprehension about whether these scores suggest a negative impact on science, technology, engineering, and mathematics (STEM) readiness and the potential impact on America's economic, social, and political security. While I understand why these are causes for concern for many, I see the discourse about the ACT mathematics scores as an opportunity to broaden the discussion to include issues of equity, curriculum, and assessment. [...]  
Critical conversations are necessary for knowing and understanding not only the indicators for mathematics and STEM readiness but also the inequities that contribute to the factors that offer advantages to some learners while disadvantaging others."
The inequities problem continues as does the call to do something about it. Holding conversations does help, but the majority of educators feel helpless to do something that would make a significant difference to what is mostly a complex political problem. 

In my opinion the complicated problem we can solve that keeps things at status quo is the continued use of flawed textbooks that not only do not adhere to the Common Core but also do not offer help in effective pedagogy. Many teachers who have the freedom to use substitute lessons that they find on the Internet or develop collaborately with their colleagues at school or on the Internet (ala #MTBoS) help improve student's learning. For example, some creative schools like SLA (Science Leadership Academy) in Philadelphia use projects to motivate the learning of conventional topics from algebra I and II and geometry. The teachers also create their own lessons which are cooperatively developed. Unfortunately too many teachers just follow the textbooks lessons which turn too many students off to math. There are of course exceptions of textbooks that are well designed and conceptually well grasped by students. An example is EDC's Transition to Algebra (T2A) which is designed to make the student's experience of learning Algebra more understandable and interesting. Also, using the Heinemann book, Making Sense of Algebra: Developing Students' Mathematical Habits of Mind help teachers to dive more deeply into the goals of T2A so they can provide an optimal learning experience for their students.

A more radical (creative) approach* to writing textbooks is to make lessons more like stories which are intrinsically interesting to kids. There are videos that tell stories that could be used as part of a lesson: the 3-act kind that Dan Meyer likes. My 3-part lesson is: 1. Set the Stage 2. Do the Activity 3. Debrief.

Three examples are: The Weird Number, Murdered for Math - Making sense of Irrational Numbers, and 13 x7 = 28

Also, STEM should be a math credited course in High School. We moved Algebra 1 to the 8th grade in my lifetime, why should seniors have to wait till college to experience STEM? It doesn't make any sense not to do that. See my previous post on this topic.

*More on "radically" creative lessons in future bog entries.

Monday, September 24, 2018

Regional Meeting in Hartford, CT

The first of three regional conferences is almost here. You can register here. As far as technology is concerned NCTM has highlighted Technology as a Tool sessions in its preview as an essential topic. Here's the description.

Technology and Tools

Discover ways in which tools and technology enhavce meaningful instructional experiences with presentations that highlight opportunities to support students' increased discourse, strategic thinking, and engagelment with importan mathematical ideas.

The opening session sounds good for an overview of issues concerning teachers today.

OPENING SESSION | Thursday, October 4, 5:30 p.m.–7:00 p.m. AMY LUCENTA
Making Equitable Practices Routine
Students face a constantly changing, data drenched world filled with fake news and powerful technologies. Learning concepts and skills will not suffice, and leaving students behind is not an option. Each and every student needs to develop mathematical thinking and reasoning. This can only happen when students
are talking together to make sense of important mathematics and each and every student is contributing to the conversation. So, how do we ensure that all students develop as mathematical thinkers and communicators? Leverage the predictable nature and uniform design of instructional routines to support students and teachers alike.

You will find a list of all the sessions here.

To see all 25 of the Technology and Tools sessions click on the Search Sessions image above. Then choose Technology and Tools from the Category field.

You should see the following list for Friday:

And for Saturday:

There are a total of 195 session so 25 Tech sessions are about 13% of the total.

I was surprised to see that almost all the tech sessions were geared toward high school teaching. Desmos, Geogebra and graphing calculators were the application most used in the sessions. Since my personal interest is middle school, here's the ones I would attend (in no particular order).

Session 27: Geometry Explorations: From Drawings to Constructions, Discovery at Your Fingertips
Workshop leader: Karen Greenhaus
Experience the power of exploring geometry concepts hands-on, starting from simple drawings of geometric objects and going right into manipulating their attributes, testing conjectures, and developing geometric properties. Participants will participate in a hands-on workshop working with technology and geometric problem-solving activities.
Session 103: D^3: Discourse, Differentiation & Desmos: A Deeper Look at Technology through an Equity Lens
Workshop leader: Allison R Krasnow
This workshop will explore how to integrate Desmos with your curriculum to deepen discourse, differentiation, and formative assessment. You'll experience several strategies for more robust mathematical engagement with Desmos including using word banks, sentence frames, and supporting students to do error analysis on common misconceptions.
Session 142: Ideas for Math Class on Twitter: Sharing, Exchanging, or Lurking
Burst Speaker: Robin Schwartz
Twitter is a great place for math educators to find tasks, routines, and camaraderie. In this workshop, we will visit the #mtbos (Math Twitter BlogOSphere), #elemmathchat, #observeme, #iteachmath, and other Twitter hashtags and people for inspiration and motivation for both teachers and students! 
If you attend any of the above sessions (or any others for that matter) please let me know how it went.

Friday, August 3, 2018

Will Blended Learning be a Game Changer?

Here’s a picture (circa 1968) of me pretending to teach while my students were pretending to learn. But how could I say that given that this was my best Algebra class and most of the kids got As and Bs? Well, what I discovered many years later was that the students were just doing what I asked them to do to please me and no one was very inspired to explore algebra beyond what I fed them. But that was good enough then. My model was the textbook: Mary Dolciani’s Algebra 1. For those of you that remember the Dolciani method you probably recall that it was a hard-nosed, traditional approach. For the kids it was a series of hoops that they struggled to jump through. But to what end? Algebra II of course! I didn’t question this approach at the time, though I did think about alternative ways of teaching math in my university days. My school’s culture was traditional, so I didn’t dare to deviate.

According to an Edutopia article by Beth Holland the peril of such an approach handicaps students. They remain “consumers of teacher-directed content instead of becoming creators of knowledge within a context that they can control.” Will Richardson (during an interview with Beth)* said that he went through a standard school experience and he turned out OK. So what was so bad about that? Beth responded that that model was OK for then, but not for today. We need a new model. This new approach shouldn’t make the old model “wrong” but through a gradual process move teachers to a new way of teaching and learning given all the new resources that are now available. Teacher buy in to new models is crucial. One reason that the introduction of technological devices into the classroom is a good way to start is because most teachers understand that technology tools are important in the lives of students so integrating them into the classroom is an accepted norm by most teachers.

In the aforementioned article in Edutopia Beth writes:
“A few months ago, I noticed an increased amount of discussion around the notion of blended learning. Many of these conversations started on a similar note: “We’re blended—all of our teachers use Google Classroom” (or Edmodo, Schoology, Canvas, Moodle, etc.). However, in probing further, I often discovered that these tools had merely digitized existing content and classroom procedures. […] While blended learning [e.g.] brings with it the promise of innovation, there is the peril that it will perpetuate and replicate existing practices with newer, more expensive tools.” 
“True blended learning affords students not only the opportunity to gain both content and instruction via online as well as traditional classroom means, but also an element of authority over this process. […] blended learning could fundamentally change the system and structure of school, and provide students with a more personalized, active learning experience.”
Previously, Beth interviewed 3 instructional coaches from Bellevue, Nebraska about their 1-1 iPad initiative and move to blended learning.
“These coaches saw blended learning as providing students with control over how they learn, the pace of the learning experience, and where they might choose to learn within the classroom.”
Supporting student agency is one of the main tenets of the blended model (that is described in detail in Michael Horn’s book “Blended”) that districts like the one in Bellevue, Nebraska have adopted. But unfortunately blended learning can become just a buzzword when teachers and administrators don’t understand it very well.

Horn writes on page 34 “Some element of student control is critical; otherwise, blended learning is no different from a teacher beaming online curriculum to a classroom of student through an electronic whiteboard.”

*iTunes podcast “Modern Learners, Podcast #47”

Thursday, July 19, 2018

On Making the Ordinary Extraordinary in Learning Math with Technology

"Based on my own research and experience, and the research of many colleagues in the learning sciences and related fields, I firmly believe that technology can transform teaching and learning environments and help students achieve beyond what is possible without the support of technology.  [...].  It is a tremendous challenge to translate knowledge about teaching with technology from schools that are currently doing extraordinary things—both on their own and in the context of focused research projects—into knowledge that is broadly usable by the majority of schools.  Nonetheless, it is a key challenge that must be met in order to employ technology effectively in school improvement efforts."
So wrote Barry Fishman in his article, "It’s Not About the Technology" (Teacher's College Record) back in July 6, 2006. I don't think he would have anticipated that 12 years later we wouldn't have made more significant progress toward extraordinary than we have so far.

In a recent post I wrote about the SAMR model - a framework for tech integration developed by Dr. Ruben Puentedura.

According to Kathy Schrock, the SAMR (substitution, augmentation, modification, and redefinition) is a model designed to help educators infuse technology into teaching and learning. The  model supports and enables teachers to design, develop, and infuse digital learning experiences into their curriculums. The goal is to transform the student's learning experiences so they result in higher levels of achievement.

SAMR Model
Substitution - Tech acts as a direct substitute, with no functional change
Augmentation - adds some functional improvement
Modification - change the learning task; becomes collaborative
Redefinition - performing a task inconceivable without the tech (i.e. Sketchpad or Desmos)

During my years at CIESE* (1990-2007), we developed a similar model using descriptors that were more user-friendly. Here are the stages of "professional growth."

Year 1
Stage 0: Awareness. Announcement of a technology integration project. Participating teachers attend an overview of the project.
Stage 1: Learn. Teachers learn about the technology they will be using which includes a teacher computer station, digital whiteboard, laptops, tablets, handhelds and software.
Stage 2: Adopt a lesson strategy.** (1) Set the stage (2) Do the activity (3) Debrief.
Stage 3: Experiment. Teachers use a one computer station and a digital whiteboard to do a model lesson using appropriate software. Math coach and/or supervisor helps with the lesson. Eventually, the teacher goes "solo" with the lesson. Practicing the STS-DTA-Debrief model lesson/activity is crucial to moving to the Redefinition (SAMR) phase. Administrative support throughout.

Research has shown that combining many thinking skills improves learning outcomes. Creating, applying, remembering, analyzing, understanding, and evaluating can all be used together in rich, well-designed learning activities and projects to improve the effectiveness and longevity of learning results.***

Year 2
Implementation stage. Experimented lessons become a more permanent part of the curriculum. New models introduced that support collaboration. Teachers write new lessons/activities. Teachers mentoring new teachers in the project. Administrative support continues.

Year 3
Institutionalization stage. Original cohort of teachers continues to share their work with colleagues. This teacher to teacher sharing with the help of the math coach becomes the cornerstone of school life.

That was our model at CIESE. And it worked extremely well at the middle school level in Passaic, NJ by 2007. The teachers learned a lot, but what about their students? Unfortunately, they were still bound by textbooks which from my observations kept learning to a minimum. (As of 2015, test scores remain low in Passaic.)

Textbooks continue to be barriers to extraordinary learning. We need dynamic curriculums that not only engage students but develop in them a passion to learn.
*Center for Innovation in Engineering & Science Education at Stevens Institute of Technology in Hoboken, NJ

**The heart of effective problem-based teaching is this: the teacher sets the stage with a problem, puzzle, or game containing an interesting context, where school math isn’t the focus; the students then engage in the activity, followed by the teacher debriefing the activity with the students and the math learned is revealed. When all is said and done, the students will learn some powerful mathematics. (Examples forthcoming.)

***21st Century Skills: Learning for Life in Our Times, Trilling, B. & Fadel, C. (Jossey-Bass, 2012), P. 51

Wednesday, June 27, 2018

It's the Pedagogy, Stupid

In my early days of giving talks at conferences, I occasionally used the word pedagogy in the title of my talk. I didn't get many takers. In fact, on one occasion no one showed up. So I stopped using the word in the title of my talks. And presto, attendance improved. So you're probably wondering about why I'm using the word in the title of this blog. Some background should help to answer the question.

 Recently, I read Larry Cuban's latest book "The Flight of a Butterfly or the Path of a Bullet?" in which he
[...] looks at the uses and effects of digital technologies in K–12 classrooms, exploring if and how technology has transformed teaching and learning. In particular, he examines forty-one classrooms across six districts in Silicon Valley that have devoted special attention and resources to integrating digital technologies into their educational practices. Ultimately, Cuban asks if the use of digital technologies has resulted in transformed teaching and learning in these classrooms. (Source)* 
Cuban found that about 2/3 of the teachers became regular users of technology and were happy that it made for a smoother delivery of instruction to the students. But did it produce better results? In other words, were the students learning better? Cuban doesn't answer the question because he didn't focus on results. He leaves that to future researchers. He did discover that teachers in Silicon Valley do use technology and found that it makes them more efficient with getting resources out to kids. But the question: did they learn better? doesn't get answered. I would characterize what the students were experiencing was Blended Learning. But were they learning better than before? Since Cuban doesn't help me with that I looked for some research on Blended Learning to help me.

In reviewing a conference presentation by Rebecca Griffiths ("What Works in Blended Learning") the author, Doug Lederman had this takeaway:
[...] The use of technology itself appears not to be primarily responsible for [...] improved outcomes. Rather, the accumulated studies they shared found that the biggest effects came when the instructors changed what material they taught and how they taught it. "If you just use a new digital learning technology without changing anything else, chances are you're not going to have a significant impact" on learning, Griffiths said. 
So it appears that the bottom line is what Cathy Davidson wrote in her book (The New Education):
"The real lesson for the New Education is that we need more active, creative ways of teaching that put some of that computer power to good pedagogical use." 
So we've come full circle. What do we/you mean by good pedagogical use? In other words, how do we get kids to really want to learn what you want them to learn? That's the holy grail.

In my thinking about pedagogy, I went exploring and discovered the Cult of Pedagogy. The title is meant as a joke (there's no cult here) but the website is really good for folks who want to improve their personal pedagogy especially in using technology. The author, Jennifer Gonzalez, does make a living from this site so it will cost you some, but it's reasonable.

*This source includes a 30-minute podcast interview with the author, Larry Cuban.

Sunday, June 10, 2018

Logo Summer Institutes 2018

These workshops are intensive immersions in creative computing for K12 teachers, parents, and technology integrators. Our project-based approach supports computational thinking and STEAM learning and teaching.

Learn to code as you explore and create projects using Scratch, Makey Makey, Hummingbird, micro:bit, Arduino, and a variety of other hardware and software platforms.

We’re in the midst of some big changes in the technologies available for creative computing, which we will be incorporating into the Logo Summer Institutes:

Scratch 3.0 is rolling out this summer, promising a wide range of extensions for physical computing, including LEGO, Arduino, micro:bit, and more. Scratch 3.0 also runs on iPads and Android tablets.

The versatile and inexpensive micro:bit is becoming a popular platform for physical computing and robotics. And, it is now integrated with the Hummingbird.

Register Now

Registration remains open for two Logo Summer Institutes:
- June 18-21 in Sugar Land, Texas
- July 9-12 in New York City

For more information visit or contact us by email:

Tuesday, May 22, 2018

Focusing on the M in STEM in the High School Math Curriculum

In 2014, CNN reported that only 16% of high school seniors end up pursuing careers in STEM, despite the fact that industry-related jobs are growing at a rate 1.7% faster compared to non-STEM-related professions. Furthermore, many of those who have related degrees end up pursuing careers outside of what they were trained in.

It seems that it would be useful to offer a STEM Math course in high school that would prepare students to study STEM in college so that they will be ready for a STEM career. This doesn’t have to violate what NCTM has outlined in Catalyzing Change in High School Mathematics where the authors say that in the first 2.5 years of high school students should continue to work on and be able to use the essential math concepts that all students should know. This includes statistics which should be included in the algebra 1, algebra 2 sequence. Students who want to do AP Calculus would continue along a path that includes a pre-calculus course. Course selection after the common pathway should be based on students’ needs, goals, and interests. This is where a course in STEM would serve a useful purpose. I would call it steM where the focus is on mathematics within the context of science, technology, and engineering. Matt Larson has written that STEM in its present implementation is not strong in its math component. I agree. And that’s why we need to develop a STEM course that focuses on the math component and makes it come alive for students. One example that came to mind was the example in Dan Meyer’s blog: The Teaching Muscle I want to Strengthen in 2018.  In it, he mentioned a Desmos activity called Complete the Arch that could become a part of the lesson of building an arch-style bridge. I searched for an arch bridge building lesson which I didn’t find (most of the bridge activities were for elementary students) but I did find some neat videos that would be perfect to show in the contents of a high school lesson.

So in summary what I’m calling for is for NCTM to organize a committee that would focus on developing an excellent steM curriculum that could be an option for students who are not on the calculus path.

Let me know what you think.

Thursday, May 10, 2018

More from the CLIME Meeting

Neil speaking at an Ignite session
Neil Cooperman, long time CLIME member and supporter, offered these comments at our recent CLIME get-together in Washington, DC. The question on the floor was:

What are effective ways to use technology?

Neil says:
"A lot of people using technology are using it as a subsititute for what they did before. They are not using the SAMR model. They are not using technology to really change how learning and teaching happen."
According to Kathy Schrock the SAMR (substitution, augmentation, modification, and redefinition) is a model designed to help educators infuse technology into teaching and learning. Popularized by Dr. Ruben Puentedura, the  model supports and enables teachers to design, develop, and infuse digital learning experiences into their curriculums. The goal is to transform student's learning experiences so they result in higher levels of achievement.

The key word of course is transform. How do we know if students learning has been transformed? What usually comes to mind is test scores. But there are other more informal and powerful ways. These include:

  • Jo Boaler's Mathematical Mindsets describes how students perception of mathematics can be changed by providing students with practical strategies and activities. This can help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math.

But both of those are not technology specific. This next one is.

The program Green Globs available from David Kibby absolutely transforms students attitude and skill level with functions. (Neil would definitely concur with me on this choice.)

More technology specific activities in my next blog entry.

Tuesday, May 8, 2018

Shall CLIME meet a Demise or a Renaissance?

That was the question I pondered as I stood at the entrance to Marquis Salon 14 in the Marriott Marquis Hotel in Washington DC where the annual CLIME meeting was to happen. My meeting was to start at 7:15pm and it was now 7:30pm. I knew I had steep competition. Who could resist free food, adult beverages, and a T-shirt at the Casio reception next door? I watched as people passed me by to go there. It looked like the ghost of demise was the answer to my question. Well not exactly. I did meet Patricia Dickenson, Associate Professor of Teacher Education at National University, San Diego, CA the day before and she was interested in a leadership role in CLIME that she was just beginning to learn about. She cheered me up and I was encouraged. Eventually, a group of friends (that's what I call members and members-to-be of CLIME) showed up and a lively session ensued. Before the session ended one of the participants John Stevens an instructional math and technology coach at Chaffey Joint Union High School District in Ontario, CA said he was interested in working with us to lead CLIME into that Renaissance I was dreaming about. So the initial goal is to have and plan for a CLIME event at the San Diego meeting in 2019. Are you also interested in helping out? Here are some ways you can do that:

1. Send in a proposal to speak at the NCTM annual meeting on a technology theme in San Diego next April. Link. The deadline is May 15th. If you succeed let CLIME know ( so we can promote your session.

2. If you are speaking at one of the regional conferences this year, let me know so I can promote your presentation as well.

3. CLIME's mission is to is to empower math communities to transform the teaching and learning of math through the use of dynamic tools in our Web 2.0 world. If you believe strongly that CLIME should exist to continue to lobby NCTM to promote the effective use of technology in math education, then membership is for you! Membership in CLIME is free. Just send me an email that you support our effort.

Previous Posts

NCTM Annual Meeting & Technology (A Closer Look - Part 1)
NCTM Annual Meeting & Technology (A Closer Look - Part 2)
NCTM Annual Meeting & Technology (A Closer Look - Part 3)
CLIME Renaissance 2018?

Tuesday, April 17, 2018

CLIME “After Hours” No Frills Meeting in Washington, DC

We will be holding a CLIME (Council for Technology in Math Education) get together in Washington to celebrate 30 years of CLIME participation as an affiliate group of NCTM.

Date: Thursday, April 26, 2018
Time: 7:15-8:15 (right after Shadowcon)
Room: Marquis Salon 14 (Marriott Marquis)

I apologize for multiple copies of this announcement, but I want to make sure that our CLIME friends are aware of this important meeting.

After 30 years of participation in CLIME I’ve decided to step down and offer an opportunity for another individual to take the helm of an organization that has played a significant role over the years in keeping technology on the front burner of NCTM’s vision for quality mathematics education. 

If you are interested in playing a role in CLIME's future please let me know ( If you are attending the Washington Conference, please stop by our meeting and let me know of your interest.

NCTM Annual Meeting & Technology (A Closer Look - Part 1)
NCTM Annual Meeting & Technology (A Closer Look - Part 2)
NCTM Annual Meeting & Technology (A Closer Look - Part 3)
CLIME Renaissance 2018?

Friday, April 6, 2018

Math, Technology & STEM at the CLIME NCTM Meeting: a Closer Look (Part 3)

Figure 1
NCTM is introducing a new book at the conference: Catalyzing Change in High School Mathematics. There are 2 paths proposed: (1) a 4-year course that ends with Calculus and (2) an alternative that devotes the final year and a half to math electives such as statistics, probability, modeling, and precalculus. Electives sound promising for good students who would love to get away from the 4-year "Royal Road to Calculus" path and do something more meaningful in the time they have left in high school. STEM programs which would be excellent alternatives are left out of the discussion. With all due respect, Mr. Larson, Math Education alone is NOT STEM education! For a senior that would do a STEM project that illuminates the mathematics that he has been learning could be a game changer for that student. He may actually see the value of math for the first time since elementary school.

So despite my recent disappointments with the turn of events and my leaving as president of CLIME I'm an optimist at heart and believe strongly that we still need an organization that will not be afraid to step out of the box and challenges unproductive directions that NCTM likes to follow.  I hope one of you who agrees with me and will step forward and take the mantle of CLIME to the next level whatever that turns out to be. (Maybe Council for STEM in math education?) I will continue to be a friend of CLIME (our designation for member). If you are so inclined to lead CLIME into the future, please let me know ( Also, let me know if you are planning to attend the 30th annual CLIME meeting.

CLIME “After Hours” No Frills 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: Thursday, April 26, 2008
Time: 7:15-8:15 (right after Shadowcon)
Room: Marquis Salon 14 (Marriott Marquis)

I apologize for multiple copies of this announcement, but I want to make sure that CLIME members are aware of the challenges that lie ahead. STEM is NOT about separate courses for math, science, engineering, and math but an overlap of these topics. (See figure 1.)

This is more than just an advocacy position but a plan for a transparent curriculum designed for students to learn about STEM intrinsically. It's new and it needs lots of work to make it real in the lives of students. I hope you join us in this effort. If you're going to Washington later this month, please stop by our meeting time and share your vision of STEM in math education. Our leaders are not doing it!

NCTM Annual Meeting & Technology (A Closer Look - Part 1)
NCTM Annual Meeting & Technology (A Closer Look - Part 2)
CLIME Renaissance 2018?

Thursday, April 5, 2018

NCTM Annual Meeting & Technology (Part 2 - STEM)

Review of Tech & STEM sessions

Keynote - When Content Meets Context: Toward a Revolution in STEM Education
In this address, Professor Christopher Emdin, Columbia University explores the historical and contemporary landscape of urban education and provides a new lens for viewing how and why teachers must focus on deep excavations of culture in order to gain new approaches to improving STEM pedagogy. In particular, he merges cutting-edge research with real-life examples to provide ways that educators may re-imagine their roles in STEM teaching and learning and meet the needs of their most marginalized students.
I'm curious. Does this talk contradict Matt Larson’s blog post: Math Education Is STEM Education!?

Here's some highlights from the post:
STEM is frequently a program strand at the NCTM Annual Meeting or Regional Conferences. The “STEM ground” would seem to have been well covered by NCTM. (9 sessions in Washington.)
Despite all these efforts, the questions concerning STEM and the requests to speak and address STEM education just keep coming. It is clear that resolution on how STEM education fits with our goals for mathematics education still lacks clarity in the minds of many. 
Let me make one thing abundantly clear: I support STEM education—including science, technology, and engineering. But I support STEM education, as Michael Shaughnessy (see endnotes) wrote, from the perspective of “political advocacy.” As mathematics educators, it is incumbent on us to be advocates for STEM education because advocacy for STEM education is advocacy for mathematics education.
Could K–12 math classrooms fail to have students engaged and learning the mathematics content and practices necessary to advance in the curriculum, but have integrated some technology, engineering, coding activities, or connections to science and be called a “STEM Program”? If students are not equipped to pursue a post-secondary STEM major and career, is it really an effective K–12 STEM program? My answer is no. No number of fun activities or shiny technology will overcome this fatal shortcoming. 
What Larson doesn’t mention is the impact that motivation plays in a student's successful learning of math. Just because he or she hasn’t found a high school program that teaches appropriate high school math within a STEM framework doesn’t mean one couldn’t exist. I found in my teaching that calculus without a soul is meaningless to high schoolers. The modeling is contrived (ala Dan Meyer’s pseudo context) taken from a 20th-century framework that doesn’t integrate what's needed for our students today. STEM should be in the high school curriculum as a math application. We’ve had hundreds of authors of high school math textbooks who have come and gone and not much has changed since the new math was introduced in the 1960s. Most students find it irrelevant and boring. Yet they persevere because they know its good for you (like spinach) to include the advanced course in their college application. What a lousy reason for students to pursue a topic! Isn’t a teacher/writer out there that could make that connection that motivates students to actually want to learn math intrinsically? STEM could be a topic that lights a fire under a student to learn science, technology, engineering and of course math in an engaging, integrated way.

High School Seniors Aren't College-Ready
Only 37 percent of students are prepared for college-level math and reading, according to newly released data.

Dan Meyer Ted Talk 2010
“I sell a product (math) to a market that doesn’t want it but is forced by law to buy it. It’s just a losing proposition.”

Michael Shaughnessy
Those who are implementing any STEM program should be able to identify the specific mathematical foci of the program. With all due respect to our colleagues in the other disciplines, we assert that the letters in STEM are not all of equal importance in the pre-K–12 education of our students. Mathematics is paramount, mathematics is primal, mathematics is the most important STEM discipline. The other three disciplines are fundamentally dependent on the strong mathematical preparation of our students. As president of NCTM, I find myself in the position of speaking as a strong advocate for “steM.” In our rush to secure much needed funding for our states and schools, let us keep in mind that STEM is an advocacy position, and not a content area in and of itself. As we develop plans for STEM education initiatives, we must maintain a clear vision for the role and importance of mathematics in the education of our students. It is critical that we preserve the mathematical meat when faced with the salad bowl of STEM, lest we make a MEST of it all!
CLIME's 30th anniversary after hours "get together" in Washington DC

NCTM Annual Meeting & Technology (A Closer Look - Part 1)

Wednesday, March 28, 2018

NCTM & Technology: A Closer Look (Part 1)

The annual NCTM meeting is less than a month away and as usual CLIME takes a closer look at the technology related sessions. Technology and tools is one of the 8 general topics mentioned as themes for this conference. If you search for sessions with the tech theme you will find 74 sessions listed. I read all 722 session descriptions and found an additional 25 which are listed hereTo preview all the other technology related sessions what you can do is:

1. Go to and click on the online planner.
2. Sign in.
3. Click on the Add New button and you will see this screen.

4. Click on -ALL- next to Category and select Tools and technology. You should see the 74 sessions listed. 

You now have access to the 99 sessions that have noted the use of technology as an important part of their presentation. That is approximately 14% of the total number of sessions.

In my next blog I will go into more detail about these sessions and other important matters related to CLIME.

Add to your NCTM Conference calendar:

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

Previous CLIME Connections blogs:

Tuesday, March 6, 2018

Comments on Matt Larson's post: Why Teach Mathematics?

Why teach mathematics? There are many reasons to study mathematics, but in most schools it can all be boiled down to this: math is good for you. This reminds me of a time when my mother would serve me boiled spinach at dinner time and I of course refused to eat it; but my mother insisted because it was good for me. Of course, the answer didn’t help me since I disliked the taste; but like a good boy I ate it since dessert would not be available otherwise. Unfortunately, for too many kids that is the experience of doing arithmetic and then math starting in Algebra 1. Though for the most part students dislike and don’t appreciate math, we like good boys and girls “eat” it. We want the grade to please our parents. As a math teacher I wanted more than that. But I had difficulty in coming up with ways of teaching that actually make the math taste good. (My mother would add butter to the spinach which made the spinach taste better for me.) Games make math “taste better” for most kids. We have so many math resources that purport to make math fun, so why do we fail to get kids to appreciate and like math for its own sake? Because of the way it is presented to kids. Pick up most textbooks and you will see why. Like spinach they are distasteful. Kids like to read books that are interesting, fun and engaging i.e. story-like. For example, textbooks like “Mathematics: A Human Endeavor” by Harold Jacobs are story-like and not surprisingly students actually want to read them. What a difference it would make if our math curriculums were written with student's interest in mind. (See next blog.)

At the high school level students should have more of a choice as to what to study. STEM is a productive venue for students who dislike spinach math. But if they engaged in well designed STEM projects that illuminate math ideas, spinach math would be something they actually would enjoy. Pass the butter,  please.

Note 1: In Washington NCTM will be introducing a new book Catalyzing Change in High School Mathematics which offers 2 tracks for students. (see Dan Meyer’s blogpost about that.) Learning math is not a zero sum game as Matt Larson implies. He says that math education is the key to students becoming great critical problem solvers in all walks of life. That’s absurd. There are many successful paths to achieve critical thinking skills. Look at those articulate students who survived the school shooting in Parkland who are passionately engaged in pushing for gun control. How much did their math education contribute to this? The answer is unclear, but I doubt if it did much for those students who are currently surviving spinach math. (They see no purpose in studying Calculus in high school, other than it looks good on their college application.)

Note 2: No mere vegetable ever gained the fame that spinach did in the 1960s through the cartoon character Popeye. Often in vain, parents encouraged their children to eat their spinach so they would grow up to be big and strong. Why did Popeye eat so much spinach? The Surprising Answer.

Monday, March 5, 2018

The Calculus Story: A Mathematical Adventure

Link to Amazon
This is a book that every high school student thinking of studying a formal course in calculus should read. That's because a calculus textbook does not include what's in this book and what could make the subject more interesting for students. (Thank you, David Acheson.) From the book's dust jacket:

What is calculus?
And why is it the key to so much maths and science?

David Acheson believes that the main ideas can be understood by anyone, using only basic school mathematics. He presents calculus as a story, in which Newton, Leibniz, and others gradually build the subject, often by battling with infinity.

Whether you are new to calculus, returning to the subject, or just enjoy a mathematical adventure, David Acheson provides an exceptionally crisp and engaging account of this beautiful and immensely powerful part of mathematics.

Sunday, January 14, 2018

CLIME Renaissance in 2018?

Figure 1 - NCTM Conference, 1995
Demise of Coalition of Essential Schools (CES)
In a recent blog, Larry Cuban writes about the demise of Ted Sizer’s Coalition of Essential Schools. In it he asks this question:
Is this a story of a reform birthed in one educational crisis dying during a later one? Or is it a story of a reform centered on one person who, over time, built an organization that lost ideas and energy while failing to generate sufficient funds after the founder left? Or is it a time-tested story of a reform that succeeded by spreading its progressive gospel far and wide appearing in many other policies, programs, and places?
Demise of CLIME?
After 30 years of participation in CLIME (Council for Technology in Math Education - an affiliate of NCTM) I’ve decided to step down and offer an opportunity for another individual to take the helm of an organization that has played a significant role over the years in keeping technology on the front burner of NCTM’s vision for quality mathematics education.

Like CES but on a smaller stage CLIME had some significant high points:

1. In the beginning there was Logo.
Seymour Papert was an inspiration for many math educators who believed that his Logo program and philosophy could make a huge difference in math education. An “after hours” meeting at the 1986 Washington NCTM conference resulted in the formation of a committee (of which I was a member) that eventually became that affiliate of NCTM in 1988.

2. The membership grew over the years.
In 1995 at CLIME’s annual “after hours” session (similar but on smaller scale to Dan Meyer’s Shadowcon) CLIME invited Seymour Papert to speak. Over a hundred educators attended the event anticipating Seymour’s talk. Unfortunately at the last minute Seymour was not able to attend, but the rest of the agenda (figure 1) went on as scheduled. An interesting side note is that as far as I know Seymour was never invited to speak at a NCTM function. What alarmed NCTM board directors was that he was critical of NCTM’s approach to reform. Judge for yourself. Here’s what he had to say in 2000.
I think they [the Standards] are going in the right direction but they are incredibly conservative, from my point of view. But again, I’d make reservation that if one has to work within the framework for schools as they are and curriculum as it is, maybe there isn’t very much room for making radical change. One of the ways in which the council is conservative is that it does not make full use of a computer-based construction of learning. I think the would have done much better if they had originally integrated Logo* in their proposals. But there is no question that an imaginative Logo-using teacher wants to follow these Standards can do it better with Logo.” - Seymour Papert**
3. In 1996 The CLIME newsletter went electronic and was named CLIME Connections. 
A Website was considered at Clime's 10th-anniversary Meeting in San Diego. The remarkable story of Daryl Stermon's Internet trailer intervention at the annual NCTM meeting that year is definitely worth a read. (I was there. I’m sorry I didn’t take pictures.)

4. In 2012 we made a significant difference with NCTM.
See the late Mark Workman’s letter to CLIME which acknowledged our contributions. For more details see my blog which acknowledges our resolution for improving how technology can be more effectively showcased at NCTM conferences.

5. In 2015 was there a paradigm shift?
A comparison of CLIME's after-hours sessions and Shadowcon. link

At that time (2015) I was hopeful that more meaningful changes were coming to NCTM. However, I was dismayed by two recent actions promoted by the current president of NCTM. First, there was the president’s post "Mathematics IS STEM Education." This was an indication to me that things at NCTM would be “business as usual” in a situation where the majority of students who are bored with math will continue to have to suffer that condition at least until a president shows up who doesn’t just toe the conventional wisdom, but also encourages creative and, yes, radical approaches to math curriculum reform in the spirit of Seymour Papert.

The second event is the highly anticipated roll out of the book "Catalyzing Change in High School Mathematics: Initiating Critical Conversations." Originally NCTM published a draft of this book for public review. Dan Meyer blogged his comments about it here. Here's a quote from Dan's blog:
NCTM proposes that all students take four years of math in high school. 2.5 of those years will comprise “essential concepts,” taken by every student regardless of career or college aspiration. Students may then take one of two paths through their remaining 1.5 years, one towards calculus, the other towards statistics and other electives.
Electives sound promising for good students who would love to get away from the 4 year "Royal Road to Calculus" path and do something more meaningful in the time they have left in high school. STEM programs which would be excellent alternatives are left out of the discussion. With all due respect, Mr. Larson, Math Education alone is NOT STEM education! For a senior that would do a STEM project that illuminates the mathematics that he has been learning could be a game changer for that student. He may actually see the value of math for the first time since elementary school.

So despite my recent disappointments with the turn of events, I'm an optimist at heart and believe strongly that we still need an organization that will not be afraid to step out of the box and challenge unproductive directions that NCTM likes to follow.  I hope one of you who agrees with me and will step forward and take the mantle of CLIME to the next level whatever that turns out to be. I will continue to be a friend of CLIME (our designation for member). If you are so inclined to lead CLIME into the future, please let me know ( Also, let me know if you are planning to attend the 30th annual CLIME meeting.

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

Technology sessions in Washington Part1 Part2 Part3

Recommendation: The Panel recommends that computer programming be considered as an effective tool, especially for elementary school students, for developing specific mathematics concepts and applications, and mathematical problem-solving abilities. Effects are larger if the computer programming language is designed for learning (e.g., Logo) and if students’ programming is carefully guided by teachers so as to explicitly teach students to achieve specific mathematical goals.
** Here’s an 18-minute clip of Papert talking about middle school math as it was implemented in 2000. Have things changed all that much since? (I think not.)

For a more detailed look at CLIME's story (1986-present) see the link.