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.