Thursday, May 23, 2019

About transformation in math education

Note to CLIME Community
As I mentioned in my previous blog, CLIME is retiring from service to NCTM as of June 1, 2019. But that doesn’t mean I’m retiring from working towards my vision of math education. This final entry of CLIME Connections informs that vision. Our new blog will be http://dmcpress.org.

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In a recent blog Larry Cuban writes about the hype of “transforming” teaching and learning.
Three years ago, I published a post. I didn't expect anything much to happen with the over-use of the word "transform" and nothing did. The word continues to be used both seriously and casually without much scrutiny.
I agree with Larry that defining transformation in relation to education is difficult. But though I can’t define it with precision, I know transformation when I see it in the classroom.

In his article “Integrating Technology in the Classroom using the SAMR Model: Substitution, Augmentation, Modification, and Redefinition” Parker Duwelius describes the latter two as transformational.

He writes:
“The first and easiest piece is substitution. This is the most basic form of technology integration in the SAMR model, and consists of merely replacing a traditional lesson item with a technological equivalent.” 
The substitution method was a very popular intervention during the early days of the  CIESEmath project (2000-2007) that I managed. A lesson example would be to pose a problem using a projection device controlled by a computer instead of writing out the problem on a black or white board. Then the teacher would distribute handouts of the problem that was projected on the board. (See, for example, the Road Sign problem and Bus problem.)

On the surface the Bus and Road Sign problem appear to be only examples of standard substitution. But both problems take one step closer to be transformational in that they inform students to reflect metacognitively on what they did wrong and come to a new understanding of the problem. (Read the teacher notes for clarity.)
Duwelius continues: “This next form of technology integration is augmentation, which is very similar to substitution except that it provides a clear enhancement to the student in the activity through the use of technology.”
The Exterior Angle of a Triangle activity demonstrates how dynamic geometry software (like Geometer’s Sketchpad) augments a lesson that would otherwise be a static experience (e.g. using a compass to measure angles).
Duwelius: “Both of these (substitution & augmentation) are considered to be ‘enhancements’ because they still convey the material in the same way, but can often bring benefits with them that expand the learning taking place for the students.”
Now we’re going to find out a little bit more about the “transformation” pieces.
Duwelius:Modification is taking a traditional learning task and significantly changing it with technology.”
See the Factor Game as an example of modification. The activity begins as a whole group game using 3 x 5 cards pasted to the white board. Once the rules are mastered through playing the group game the students play the factor game on the computer. Thy can play individually against the computer or with a partner using the 2 player option. The game is challenging and encourages productive struggle on the part of the students.
Duwelius: “Then, finally, there is redefinition which takes a traditional learning task and completely transforms it in a way that would be impossible without technology. By using technology to transform the learning task, the teacher is integrating technology in his or her classroom at the highest possible level.
In the Noon Day project the students use a geometry theorem that is usually taught separate from any particular context to help them understand how Eratosthenes in 250 BC came up with a method to measure the circumference of the earth. (Geometer’s Sketchpad is used here.)
Duwelius: “These two pieces of the framework (Modification and Redefinition) are rightfully called “transformative” because they change the way the lesson runs, and the way the students interact with the content.”
Over the years of the CIESEmath project (which ended in 2007 with my retirement) our team developed many transformative activities and projects which I am currently revising and making them available here. This is an ongoing project so check in often to watch the progress.

Closing thought:
Math education does not need reform as it equates to rearranging chairs on a sinking Titanic. We need to build a new ship.

Friday, May 3, 2019

CLIME Closes its Shop

Dear colleague,

It’s official. CLIME will be disbanding as of 6/1/2019. I've given it much thought and felt it was time to close up shop. I sent an email to Mary Ferris (NCTM Affiliate Relations Manager) indicating CLIME’s decision.

Here are some closing thoughts.

First of all, I want to apologize to those folks who came to the CLIME meeting in San Diego and didn’t find me there. There was some confusion about the rooms. I was in room 310B which I thought was 310. The actual room was 310A which I wasn’t aware existed.

Second of all, due to difficulties that currently exist, CLIME as we have known it for the past 31 years will as of June 1st no longer exist. It will be replaced with a new web presence that will not be affiliated with NCTM. (More about that in a future post.)

Thirdly, if anyone (or group) wishes to “rescue” CLIME as a affiliate entity, they must be responsible for the following:

Annual dues: $100.00 (Due: June 1st) 
President and NCTM representative must be members of NCTM.
Attendance by NCTM rep and/or president at the at-large caucus held on the Wednesday before the annual conference starts.
Attendance at the Delegate Assembly held on Thursday (7:30am-9:00am) during the annual conference.

For more information about CLIME go to this link.

I still believe an organization like CLIME can serve a purpose within the NCTM community, but it needs new leadership and energy to perform successfully within the conservative framework that NCTM offers. If anyone strongly agrees and would like to lead and/or play a role in a renewed CLIME initiative, please let me know.

Sincerely,
Ihor

Ihor Charischak
CLIME president (till June 1, 2019)
Council for Technology in Math Education
Venice, FL
ihor@clime.org
http://www.clime.org


Wednesday, April 17, 2019

A Letter to the CLIME Community

Dear colleague,

First of all I want to apologize to those folks who came to the CLIME meeting in San Diego and didn’t find me there. There was some confusion about the rooms. I was in room 310B which I thought was 310. The actual room was 310A which I wasn’t aware existed. Patricia Dickenson - our intended keynote speaker - told me about my confusion later that evening.

Second of all, due to difficulties that currently exist, CLIME as we have known it for the past 31 years will as of May 1st no longer exist. It will be replaced with a new web presence that will not be affiliated with NCTM. (More about that in a future post.)

Thirdly, if anyone (or group) wishes to “rescue” CLIME as a affiliate entity, they must be responsible for the following:

  • Annual dues: $100.00 (Due: May 1st) 
  • President and NCTM representative must be members of NCTM.
  • Attendance by NCTM rep and/or president at the at-large caucus held on the Wednesday before the annual conference starts.
  • Attendance at the Delegate Assembly held on Thursday (7:30am-9:00am) during the annual conference.

For more information about CLIME see http://clime.org

I still believe an organization like CLIME can serve a purpose within the NCTM structure, but it needs new leadership and energy to perform successfully within the conservative framework that NCTM offers. If anyone strongly agrees and would like to lead and/or play a role in a renewed CLIME initiative, please let me know.

Sincerely,
Ihor

Ihor Charischak
CLIME president (till May 1, 2019)
Council for Technology in Math Education
Venice, FL
ihor@clime.org
http://www.clime.org

A Post by Scott Steketee*

Hi Seanna,

A few years ago I had the opportunity to work on the NSF-funded "Dynamic Number" project led by Daniel Scher. Our objective was to bring the interactivity and fun of dynamic geometry to the realm of numbers and pre--algebra, and we produced about 70 activities, many of which can be very helpful in developing students' number sense, both by providing memorable dynamic visualization of numbers and operations, and by giving students the power to change the numbers and manipulate the operations.

Each activity has a link to teacher notes, a student worksheet (if appropriate), and a Sketchpad document. Though the activities were originally developed for The Geometer's Sketchpad, Daniel has already moved more than 40 of the activities to Web Sketchpad, making them freely available even if you don't have Sketchpad itself. The list of converted activities is here: www.sineofthetimes.org/...

(One of our best examples is Bunny Times, with a progression of levels in which a bunny, and at higher levels a team of bunnies, learn to multiply by eating all the carrots in a field. It's designed to encourage students to develop multiplication strategies that include skip-counting and flexibly composing and decomposing numbers.)

--Scott

*Taken from https://my.nctm.org/home

Saturday, March 16, 2019

Council for Technology in Math Education Annual Meeting Agenda

31st Anniversary Meeting
Thursday, April 4th, 2019
San Diego, CA
Hilton San Diego Bayfront
Room: Aqua 310
7:30pm-8:30pm

Agenda

Introductions
Ihor Charischak

Presentations
Teaching Outside the Box: 
Integrating Technology into your Math Practice
Dr. Patricia Dickenson
Teachers' pedagogical decisions impact the function of technology and the role of technology to support, enhance and supplement student learning. This presentation will focus on the following questions: What planning decisions do teachers make to implement technology in the classroom? How is technology used by the teachers and students in the learning of mathematics? What routines and procedures are needed  to support in developing technological skill before students can integrate technology with subject matter. Teachers' technological content knowledge is paramount to the successful integration of technology. This discussion will explore pedagogical decisions that were made to infuse technology in a math class. We will discuss how technology can be purposefully used in connection with Blooms taxonomy to support learners in acquiring math content knowledge and create products of learning with web-based tools.

Short Math Stories with a Surprise Twist
Ihor Charischak

Making mathematics engaging for children is essential for math education to flourish. In this presentation you will learn about some fascinating ways to deepen students understanding to what math is all about (with the help of technology, of course)!

Discussion and closure
Ihor Charischak & Patricia Dickenson

Blog # 246

Thursday, March 14, 2019

Thursday, March 7, 2019

Technology & NCTM’s Annual Meeting: A Closer Look - Part 2

Figure 1
As mentioned in my previous blog post, there are 94 sessions which emphasize technology’s role in math ed in their sessions. I did an analysis of the grade levels of the talks. In figure 1 note that the most frequent grade level for tech sessions at the NCTM annual this year is in the high school range. If you include the 8-10 range as partially high school you have a total of 56 sessions appropriate for a high school audience.That’s almost 60% of the total. I suspect the conference program committee missed this fact.

See previous 2 blog posts which discuss the upcoming conference (here and here.)

The Moon Challenge Revisited

John Kennedy, Sept. 12, 1962
There is no question that going to the moon in 1969 was hard, but what's even harder today is making math learning extraordinary. Imagine if we could make the common student statement "I'm not good at math" disappear. It sounds impossible, but it really isn't; it's just plain hard. John Kennedy put a deadline (end of the decade-1960s) on when man would descend on the moon. We as teachers should do the same so we have a target when we'll solve the math problem. The educational gurus have tried to do this before (e.g. No Child Left Behind) and have failed because the goals set forth were not realistic. So what is a realistic goal for math education?

Larry Cuban makes a distinction between complex and complicated problems. See link. Complex hard is different from complicated hard in dealing with problems to solve. The latter can be done through systematic planning and human control. A complex system is more like getting a student to succeed in school.

In math education (ME) we tackle this complex system and don't do very well. (See this.) We could make ME complicated if we stood the current ME on its head and opted for a more student friendly curriculum. For example, what would happen if we created "textbooks" that kids actually wanted to read instead of our current textbooks which focus on what teachers think students ought to endure because like spinach it's good for them? It's possible, but not very likely because solving ME's dilemmas are thoroughly complex.

Here's some ideas worth thinking about when you sit down to write a lesson plan.
"We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too." John Kennedy
"Across the educational landscape, a broad variety of extraordinary teachers and exceptional schools employ technology to transform student experiences, facilitating deep engagement and meaningful learning.  But take a moment to re-read that last sentence.  Note the words “extraordinary” and “exceptional.”  These are words one commonly hears associated with teachers and schools where technology is used in ways that truly enhance learning.  My goal is to be able to someday re-write that sentence so that we can report that technology is helping ordinary teachers and schools to do extraordinary things." Barry Fishman (1)

1. Fishman, B. "It's not about the Technology" Teachers College Record, Date Published: July 06, 2006. http://www.tcrecord.org ID Number: 12584


Tuesday, March 5, 2019

Technology & NCTM's Meeting in San Diego: A Closer Look

In CLIME’s 30+ years as a technology affiliate of NCTM a lot of changes have occurred in the world of technology. From the early programming days of using BASIC and Logo to today’s coding challenges we’ve come full circle. The biggest change is the development of social media (conveyance) tools that expands student’s and teacher’s opportunity to collaborate and communicate via Web 2.0 tools. There is also a plethora of dynamic math (action) software & technologies.

So in the spirit of looking for examples of the above I took a deep dive into the haystack containing 759 sessions and came up with 94 that mention technology terms.

Dynamic Math software and apps

Leading the pack with 16 sessions is Desmos and its applications. STEM and STEAM have 15 sessions. Coming in third (which was a surprise to me) with 10 sessions is coding. Graphing calculators are highlighted in 5 sessions while Geogebra has only 5. Other assorted references to technology appear in 14 sessions.

Here’s a list of all the technology related terms and the number of sessions in which they were found.

It’s interesting how a program like Desmos has caught fire. It is a good graphing program which can be used as an activity builder. But what makes it inspiring is the support and leadership provided by the Desmos staff.

Web 2.0 & Collaboration

There is only one session (#683) devoted to teachers collaborating with teachers online. That’s not to say there are not others devoted to students going online to collaborate with other students. I didn’t come up with any.

Twitter also has one session late on Saturday. Here's the description:
Have you heard Twitter is a great way to connect to other teachers? You've created an account, but aren't sure how to leverage its use for collaboration? Chats are often a nice way to join a conversation. Join us for a burst session focused on making you comfortable with types of chats you may find and some tips on joining the conversation. 
Go here for more details.

The highlighted sessions are the ones I hope to attend.

CLIME Meeting

If you are planning to be in San Diego next month please note the date, time and place for our meeting. More details to follow in future blogs.


The topic for the meeting will be the same as the title of this post: Technology and NCTM's Meeting in San Diego: A Closer Look.

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Sunday, February 24, 2019

Technology Sessions in San Diego?

The rollout of the descriptions of the sessions at the annual NCTM Conference are out now (link)  and as usual CLIME is busy analyzing the technology content of the sessions.

This year is interesting in that there isn’t a tool & technology strand. My thought was that there would be a much lower number of tech oriented sessions since all speakers would pick one of the proposed trends & topics for their talks. Fortunately, many of the speakers managed to include a tech session within the context of the proposed themes which were broad enough to include technology.

Ideally we shouldn’t need a tech & tool strand because most of the presenters (by this time) should be tech savvy enough to demonstrate how they use tech within the context of their theme-based talk/workshop/burst. But based on the number of presentations (12%) mentioning some form of technology I don’t think we’re at a point in time where we can ignore what the revised technology principle envisions.

Technology sessions: Out of 760 sessions there were 93 that were tech related. See list here.

In my next blog post I’ll go into more detail about some of them.

A reminder: Our annual CLIME meeting will be held on Thursday. Here are more details.

CLIME's Annual Meeting
Thursday, April 4, 2019
7:30pm - 8:30pm
Hilton San Diego Bayfront Hotel
Room: Aqua 310

If you are planning to attend please let me know. Link.

More information will follow in our next blog post.

If you wish to be removed from my mailing list, please let me know. Writing Unsubscribe will do the trick.

Wednesday, February 6, 2019

Rolling Dice Microworld and Learning Fractions

Common Core, no more? The new governor of Florida has decided to eliminate their version of the common core standards and replace it with something else. But he doesn’t know what that will be. All he knows at the moment is that he is committed to teaching the basics (reading, writing and mathematics). 

Meanwhile a teacher posting on My NCTM’s community forum suggests that teachers should not use a particular textbook because it isn’t aligned with the standards. 

Another 4th grade teacher who was falling behind her common core pacing chart decided to skip a chapter on probability to try to catch up. My reaction was what a missed opportunity. I’m sure she wanted her students to learn their fractions but skipping the probability chapter is not the best way to do that since fractions can be taught using probability as a motivator. 

She may have known that, but her concern that a poor performance by her students on standardized tests would reflect badly on her teaching forced her hand. 

Probability would enhance student interest in learning fractions, but this teacher needed to save time and go directly to the fraction skills chapter. So how can an elementary teacher get the best of both worlds?

The answer is to blend the learning of fractions in the context of probability using technology in the same lesson unit or chapter. It’s too bad textbook companies don’t do a good job with that. 

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Here’s my attempt to help with solving this problem. I’m working on a mini probability project that includes three dynamic microworlds written in Scratch

These three links will get you an initial peek at these three draft activities.






Friday, January 11, 2019

CLIME - Technology in Math Ed - A Year in Review


Dear friend of CLIME,

Here are some of the blogs CLIME posted in 2018.

Another Rags to Riches Story
What to do with a Broken Calculator that's Broken...
Technology in Seattle - a Showcase of How to Use it Effectively(?)
High School Math is Not Working
Will Blended Learning be a Game Changer?
On Making the Ordinary Extraordinary in Learning Math with Technology
It's the Pedagogy, Stupid
Focusing on the M in STEM in the High School Math Curriculum

Your feedback on any or all of the above posts will be most appreciated.

It's a new year and a time of transition for CLIME. We will be discussing that issue and others related to math & technology at our annual CLIME meeting this year in San Diego.

If you are planning to be in San Diego next April please note the date, time and place for our meeting. More details to follow in future blogs.

CLIME's Annual Meeting
Thursday, April 4, 2019
7:30pm - 8:30pm
Hilton San Diego Bayfront Hotel
Room: Aqua 310