Curriculum

The Future of Math Education

Lately I have been asking the question, “What is  math education going to look like in the future?” As of right now, I don’t have a clear picture and I’m fairly optimistic that significant changes will not take place in the near future. While I frequently hear from teachers (not all) that math requires students to practice learning the steps to solving problems that will lead them to being able to apply their learning afterwards. It seems to me that they are saying that the traditional lecture, in class practice, and homework practice is the way that it has to be.

“If we taught dancing like we teach math we’d never let people dance until they drew out all steps on paper.” Seymour Papert (From Gary Stager’s TEDxASB talk)

On the other hand I’m hearing from others that math education has to change. Forget the flipped classroom and Khan Academy, they’re talking about substantial changes. What are they?

Dan Meyer’s 2010 TED Talk, “Math class needs a makeover”, certainly got people thinking about this topic back in 2010.

Since then I’ve been on a quest to search for the future of mathematics. I had a small epiphany at the recent ASB Unplugged Conference when I attended Gary Stager’s workshop, Electrifying Children’s Mathematics. Now I’ve seen Gary speak many times but this was the first time that I participated in one of his hands on workshops. By actually being able to work through the exercises in a constructivist way I was able to make just a little bit of sense out of the possibilities in the math classroom.

Gary started the presentation by showing us that,

“The NCTM Standards state that fifty percent of all mathematics has been invented since World War II. (National Council of Teachers of Mathematics, 1989) Few if any of these branches of mathematical inquiry have found their way into the K-12 curriculum. This is most unfortunate since topics such as number theory, chaos, topology, cellular automata and fractal geometry may appeal to students unsuccessful in traditional math classes. These new mathematical topics tend to be more contextual, visual, playful and fascinating than adding columns of numbers or factoring quadratic equations. ” (Stager and Cannings, 1998)

We then watched a video of math instruction in an elementary class where the teacher uses Piaget’s theory to help students construct knowledge on concepts. The videos are the work of Constance Kami, Professor of Early Childhood at The University of Alabama at Birmingham. My take-aways from this video are that…

  • students don’t need to know all of the ways to solve a problem. Whatever works for them is sufficient.
  • the refrains from telling the student whether or not their answer is right or wrong. teacher should let the students talk through their methods and to let them work through the problems together. The less teacher involvement, the better.
  • doing endless numbers of problems that you already understand does not do you any good.

We then moved into the hands on portion of the workshop and in a very short amount of time I realized the value of playing with tools and ideas to learn mathematical concepts.

We played with Turtle Art. We were given a simple exercise to get started and then were left to play on our own. The connections to mathematical thinking were easy to make and the results were definitely visual.

We used MicroWorlds to try to figure out a problem that we later learned was unsolvable. Something that is referred to as the 3N + 1 Conjecture, Collatz Conjecture, Ulam Conjecture, and many others. It was amazing how much math we were having to use to struggle through this problem. It was a good learning experience and it’s probably better that we didn’t know that it was unsolvable.

But, my favorite activity had to do with determining values for iTunes radio users’ actions. The work had us tackle computational thinking. Gary was very clear about his views on teaching computational thinking skills.

Computational thinking is useful when modeling a system or complex problem is possible, but the programming is too difficult.

The activity involved assigning values to the following actions.

Photo from About.com from Sam Costello
We also considered when the person just let the song play.

This was a room full of math teachers and I’m pretty sure that none of them had the programming skills to code the algorithms behind these choices. We did struggle with equating a value while thinking about the users’ thinking and how the numbers would be used behind the scenes. Many of our students have no idea of what is taking place behind the scenes when users click on a button. While very few actually have to know how to do the programming, there is definite value to understanding the computational thinking.

So, after the workshop I asked a couple of math teachers if they felt that they learned skills and/or knowledge that they could take back to their classrooms and, the general consensus was, “most definitely”. These were primarily teachers in international schools.

So, what are your thoughts on the future of mathematics?

OK, LET’S GET PRACTICAL – CHANGE YOUR ASSESSMENT

In the book Curriculum 21: Essential Education for a Changing World by Heidi Hayes-Jacobs she suggests that the first step that educators should take in integrating technology in teaching and learning is to change the assessment so that it includes the use of technology. Not only that it incorporates technology, but that it’s relevant for today’s world.

Start with changing the assessments – Her suggestion is to consider what “21st century social scientists, scientists, mathematicians, artists, writers, language specialists, musicians, and business men and women might produce…”  To put this in place she suggests the following steps.

Step 1 – “Develop a pool of assessment”

Step 2 – “Teachers working with IT members, identify the existing types of software, hardware, and Internet-based capabilities in their school…” Suggestion for teachers to become comfortable with at least one new tool per semester.

Step 3 – “Replace a dated assessment with a modern one.”

Set aside a book report and replace it with a podcast, virtual literary tour, video or magazine book review.

Step 4 – “Share the assessment upgrades formally with colleagues and students.”

Step 5 – “Insert ongoing sessions for skill and assessment upgrades into the school calendar.”

There are some exciting options for assessment with the use of Infographics. This type of assessment can be used in any and all subject matters and the skills and knowledge that students learn are certainly 21st century. The possibilities are endless, but here are a few examples.

To find more examples you can check out this Cool Cool Infograhics blogInformation is Beautiful or the 50 MOST STUNNING EXAMPLES OF DATA VISUALIZATION AND INFOGRAPHICS.

What do you think? Can you find places in your curriculum where this would be effective? What type of professional development will be needed to make this shift?

Great Ideas from Curriculum 21: Part 1

Crossed Posted on 1to1 Schools

This is part 1 of 2.

I slowly worked my way through Heidi Hayes-Jacobs book Curriculum 21: Essential Education for a Changing World for the past couple of months. It’s been slow only because I haven’t had much time for serious reading lately. Once I got my new iPad I was able to breeze through it.  While I was skeptical about the content at first, I have to say that I was pleasantly surprised with what I learned from the book. Hayes-Jacobs with help from Stephen Wilmarth, Vivien Stewart, Tim Tyson, Frank W. Baker, David Niguidula, Jamie P. Cloud, Alan November, Bill Sheskey, Arthur Costa and Bena Kallick present an argument, along with practical steps for “upgrading the curriculum”. This first post will focus on two key points from the first four chapters by Heidi Hayes Jacobs.

What year are you preparing your students for? 1973? 1995? Can you honestly say that your school’s curriculum and the program that you use are preparing your students for 2015 or 2020? Are you even preparing them for today?

Start with changing the assessments – As I visit classrooms I’m constantly asking myself how will the lesson change when everyone has ubiquitous access to the right technological tools (we’re preparing to go 1:1 in 2012). As we talk about this transformation I agree with her in saying that the first practical step to take is to change the assessments to. Her suggestion is to consider what “21st century social scientists, scientists, mathematicians, artists, writers, language specialists, musicians, and business men and women might produce…”  To put this in place she suggests the following steps.

Step 1 – “Develop a pool of assessment”

Step 2 – “Teachers working with IT members, identify the existing types of software, hardware, and Internet-based capabilities in their school…” Suggestion for teachers to become comfortable with at least one new tool per semester.

Step 3 – “Replace a dated assessment with a modern one.”

Set aside a book report and replace it with a podcast, virtual literary tour, video or magazine book review.

Step 4 – “Share the assessment upgrades formally with colleagues and students.”

Step 5 – “Insert ongoing sessions for skill and assessment upgrades into the school calendar.”

Upgrade the Content -While changing the assessment is a good first step, upgrading the content through changes to the curriculum get to the heart of the matter. We, in international schools have the luxury of being able to develop our own curriculum. The suggestions that Heidi Hayes-Jacobs offers are refreshing and exciting. How would students feel about the following units?

  • How does cultural anthropology shedding light on the economy of resource-rich Brazil?
  • Science units focused on ideas that changed the world. Also thinking ahead to future ideas that have the potential to change the world.
  • Physical education students organizing a 5k run for the community to promote healthy lifestyles.
  • A unit on book to film where students study the process and results of making a movie from a book.
  • Using an integrated approach to teaching math/economics where students look at the economics of real life problems. The students create their own Freakonomics scenarios.
  • Students organizing a virtual orchestra concert with musicians from around the world.

I believe that these steps can help us make a transition into a school that is preparing students for 2011. Has anyone tested the ideas out?

If you’re interested in joining the Curriculum 21 Learning Commons you can join the Ning.

Part  2 will be devoted to key learnings from the other authors.

1895 – 2010, Very little seems to have changed

My uncle recently sent me the 1895 8th grade final exam e-mail that has been floating around the internet. While most people try to answer the questions and comment on how dumb they are, I interpreted the test in a different way. I sadly thought about how little the U.S. education system has changed in 115 years. In 1895, the students were taking content based tests to prove their knowledge of the curriculum. Many of the questions look similar to tests today. The focus is on factual knowledge and math skills.  Here in 2010, students are doing the same.

Do we really think that today’s children still need to know all of this stuff? Just doesn’t seem like progress to me.

EXAMINATION GRADUATION QUESTIONS
OF SALINE COUNTY, KANSAS
April 13, 1895
J.W. Armstrong, County Superintendent.

Examinations at Salina, New Cambria, Gypsum City, Assaria, Falun, Bavaria, and District No. 74 (in Glendale Twp.)

Reading and Penmanship. – The Examination will be oral, and the Penmanship of Applicants will be graded from the manuscripts.

************************
GRAMMAR
(Time, one hour)

1. Give nine rules for the use of Capital Letters.
2. Name the Parts of Speech and define those that have no modifications.
3. Define Verse, Stanza and Paragraph.
4. What are the Principal Parts of a verb? Give Principal Parts of do, lie, lay and run.
5. Define Case. Illustrate each case.
6. What is Punctuation? Give rules for principal marks of Punctuation.
7-10 Write a composition of about 150 words and show therein that you understand the practical use of the rules of grammar.

************************
ARITHMETIC
(Time, 1 ¼ hour)

1. Name and define the Fundamental Rules of Arithmetic.
2. A wagon box is 2 ft. deep, 10 feet long, and 3 ft. wide. How many bushels of wheat will it hold?
3. If a load of wheat weights 3942 lbs., what is it worth at 50 cts. Per bu., deducting 1050 lbs for tare?
4. District No. 33 has a valuation of $35,000. What is the necessary levy to carry on a school seven months at $50 per month, and have $104 for incidentals?
5. Find cost of 6720 lbs. coal at $6.00 per ton.
6. Find the interest of $512.60 for 8 months and 18 days at 7 per cent.
7. What is the cost of 40 boards 12 inches wide and 16 ft. long at $20 per m?
8. Find bank discount on $300 for 90 days (no grace) at 10 per cent.
9. What is the cost of a square farm at $15 per acre, the distance around which is 640 rods?
10. Write a Bank Check, a Promissory Note, and a Receipt.

*************************************
U.S. HISTORY
(Time, 45 minutes)

1. Give the epochs into which U.S. History is divided.
2. Give an account of the discovery of America by Columbus.
3. Relate the causes and results of the Revolutionary War.
4. Show the territorial growth of the United States.
5. Tell what you can of the history of Kansas.
6. Describe three of the most prominent battles of the Rebellion.
7. Who were the following: Morse, Whtney, Fulton, Bell, Lincoln, Penn, and Howe?
8. Name events connected with the following dates: 1607, 1620, 1800, 1849, and 1865.

*******************************************
ORTHOGRAPHY
(Time, one hour)

1. What is meant by the following: Alphabet, phonetic orthogaphy, etymology, syllabication?
2. What are elementary sounds? How classified?
3. What are the following, and give examples of each: Trigraph, subvocals, diphthong, cognate letters, linguals?
4. Give four substitutes for caret “u”.
5. Give two rules for spelling words with final “e”. Name two exceptions under each rule.
6. Give two uses of silent letters in spelling. Illustrate each.
7. Define the following prefixes and use in connection with a word: Bi, dis, mis, pre, semi, post, non, inter, mono, super.
8. Mark diacritically and divide into syllables the following, and name the sign that indicates the sound: Card, ball, mercy, sir, odd, cell, rise, blood, fare, last.
9. Use the following correctly in sentences: Cite, site, sight, fane, fain, feign, vane, vain, vein, raze, raise, rays.
10. Write 10 words frequently mispronounced and indicate pronunciation by use of diacritical marks and by syllabication.

*****************************************
GEOGRAPHY
(Time, one hour)

1. What is climate? Upon what does climate depend?
2. How do you account for the extremes of climate in Kansas?
3. Of what use are rivers? Of what use is the ocean?
4. Describe the mountains of N.A.
5. Name and describe the following: Monrovia, Odessa, Denver, Manitoba, Hecla, Yukon, St. Helena, Juan Fernandez, Aspinwall, and Orinoco.
6. Name and locate the principal trade centers of the U.S.
7. Name all the republics of Europe and give capital of each.
8. Why is the Atlantic Coast colder than the Pacific in the same latitude?
9. Describe the process by which the water of the ocean returns to the sources of rivers.
10. Describe the movements of the earth. Give inclination of the earth.

1. Where are the saliva, gastric juice, and bile secreted? What is the use of each in digestion?
2. How does nutrition reach the circulation?
3. What is the function of the liver? Of the kidneys?
4. How would you stop the flow of blood from an artery in the case of laceration?
5. Give some general directions that you think would be beneficial to preserve the human body in a state of health.

Prezi

The Type of Collaborative Experiences that Our Students Require

Over the past few weeks I have been working with David Sinclair from Taipei American School on a presentation that we will be giving at the EARCOS Administrator’s Conference in Manila. The presentation it titled, Leadership for 1:1 Laptop Initiatives. Google DocsDuring this time we have been using Google Docs to share information, ideas, links to sites and blogs, and photos. On several occasions we have skype_logoskyped to talk through ideas and we are using PreziPrezi as our presentation tool. All of these provide us with access to real time changes 24/7.

OK, so none of this sounds that earth shattering these days, but there was a moment the other night when I realized that this is so COOL. I was out sitting on my deck working on the presentation with my mini laptop, listening to the sounds of crickets chirping and the waves rolling onto the sand. In the middle of my work David skypes me to discuss the presentation. We are both reviewing our notes and the presentation online and making changes as we go. Meanwhile, my wife, who is helping us with the presentation design, is in another room on another mini editing the presentation. All three of us were collaborating and we weren’t even in the same room. David was even thousands of miles away. When we were talking he said, “what’s that noise?” so I told him about the crickets and the waves. Not a bad location to get some work done.

In today’s world there is no reason why our students should not have these experiences frequently. Our job as educators is to create the opportunities for them to collaborate with students and/or experts from around the world. Aside from the cost for the machines and access to the internet, the rest of the tools are free.

Equation for Success

 Equation for Success

I’m a big fan of ISTE’s National Educational Technology Standards for Administrators (NETS-A), Teachers (NETS-T) and Students (NETS-S). They provide schools with performance indicators for all three groups. 

Some schools choose to focus  solely on developing curriculum around the NETS-S.

Other schools choose to focus on the NETS-S and the NETS-T. 

The third type of school focuses on all three. This is where the administrators, teachers and students are all focused on their respective performance indicators.

 

Imagine a school where:

The school administrators are working to…

1. inspire excellence through transformational leadership;

2.establish a robust digital age learning culture;

3.advance excellence in digital age professional practice;

4.ensure systemic transformation of the educational enterprise;

5.model and advance digital citizenship

The teachers are working to …

1.facilitate and inspire student learning and creativity;

2.design and develop digital-age learning experiences and assessments;

3.model digital-age work and learning;

4.promote and model digital citizenship and responsibility;

5.engage in professional growth and leadership

It may even be possible for a school to begin with the NETS-A and NETS-T and then eventually transition to the NETS-S. I even wonder if the first two will naturally lead the the third. 

I believe that the students will gain so much more than the knowledge and ability to use technology, as defined by the NETS-S. They will be able to explore learning in a multitude of areas and the possibilities are endless. The schools that are truly transforming teaching and learning are incorporating all three NETS into their school culture. If yours isn’t, maybe it’s time to start.