Salt Lake City Blog

Well, the conference has been a great experience--just never enough time to get to everything that I want! Today (the last day) I attended an interesting session on developing ideas about the unit circle The session was hands-on, and the "cutting and pasting" we did directly linked to the model and the concepts around the development of the unit circle.  The presenters even had a GSP script to demonstrate and support as well, and the materials needed are readily available. Using concepts from the presentation, students (and teachers!) will be able to see connections to the Pythagorean Theorem, special triangles, circles, degrees, radians, congruency, translations, and the list goes on...

Part of the presentation was developed using a Mathematics Teacher article from a couple years back--I must locate it!

I plan to take these ideas back and work with some teachers who I think will really like using it with the wide range of students they work with. It will help all levels, languages, and interests.

Hope you had a good conference experience--I did and am ready to return and spread the excitement of doing mathematics!

Posted by Trena Wilkerson, 4.12.08

It is always a treat to attend NCTM. The learning, the networking, and the running into friends everywhere. This year has made me think often of last year's conference.

I am very impressed with the facilities, particularly the proximity of all events and sessions. The conference center is excellent. Last year in Atlanta, you really had to plan your day carefully because of the unusually long distances between things, particularly getting to the exhibit hall. Not so in '08!

Yesterday I was able to move easily from one session to another without worrying about being on time. I even was able to stop and chat with friends.

I know that to keep the conference moving from region to region, that the best facilities cannot be had every year, but I am glad we have them this year.

Thanks!

Posted by Mary, 4.11.08

Quite often, we show students great mathematical representations. Less often, we allow students to create their own mathematical representations.

Stuart J. Murphy has made a career of creating illustrated math books for young children. But in his "Visualizing Math" talk on Thursday morning, he suggested that it's important for students to create their own products containing the same elements that his books contain—images, words, and mathematical ideas. Children can develop their own books that contain charts and graphs, pictures, and text or mathematical expressions to explain it.

Allowing students to create their own books helps to develop visual literacy, the ability to understand, use, think or learn in terms of images. The Center for Math and Science Education at Queensland University described visual literacy as "basic and fundamental to the educational process." Murphy argued that one of the ways to develop motivation for visual literacy is to use data relevant to students' lives—allow them to create a bar graph using the ages of their family members, or use a chart to show how many students in their class have various types of pets. (Interestingly, the talk occurring in the next room was titled, "Let's Teach Data Analysis Using Class Assessment Data." No doubt that the presenter of that session, Jim Bohan, also believes that data relevant to students' lives can be motivating.)

As a footnote, Murphy told an anecdote that made me think about motivating the toughest students. In fourth grade, Murphy had a reputation for always talking in class. The teacher could have repeatedly told him to be quiet, but instead she said to him, "Stuart, you tell such great stories. Why don't you write some of them down?" The rest, of course, is history, and it made me think that all of us can encourage kids to accomplish great things if we focus on the positive traits that are often wrapped in less desireable actions.

Posted by Patrick Vennebush, 4.11.08

Today in the inaugural Iris Carl Equity Address, Dr. Carol Malloy challenged educators to make mathematics classrooms equitable for all students. In her talk, she used NCTM's "Every Child" statement to express what she meant by every child. This is a statement that she felt was very important to Iris Carl.

Dr. Malloy stated that we are still struggling with equity. She said that we need to be mindful of beliefs we may hold that keep us from interacting in productive ways with particular students.  She stated that we must work through those beliefs so that we can help all students reach their full mathematics potential. She asserted that it is not enough to just be concerned about the important mathematics. We must learn who our individual students are and show them that we value them and that we want them to succeed.  It is not enough to acknowledge that differences between us and our students exist, we must understand those differences and use them in positive ways to move our students forward. 

Moreover, she stated that like Iris Carl, we must believe that we can convince people to do things they do not believe are possible. We must convince teachers that they can help all students to learn and understand mathematics well, and we must convince all students that they can learn mathematics well.

She also challenged the mathematics education community to take steps toward eradicating the inequities that exist. She used the words of Dr. Martin Luther King, Jr. to conclude that this will not just happen by itself.

I was inspired and challenged by her address. 

Posted by Dr. Marilyn Strutchens, 4.11.08

Being in the middle of an interesting political season provided a relevant backdrop to John Allen Paulos' contention that numbers can mean different things to different folks. We are familiar with the exit polls that were way out of whack in predicting the winner in the early days of this presidential race. Why was that? Because pollsters were counting the people who answered their questions, but were missing the "who." The "who" ended up being the significant part of the equation, and without that their predictions were wrong. 

The pollsters used numbers that they then turned into predictions, but they didn't have context. Numbers by themselves are not always reliable. And the human mind has trouble wrapping around what's significant.

Let's say someone asked you if you wanted to live one million seconds, one billion seconds, or one trillion seconds. How long would you choose to live? A kid might say one billion because it sounds cool, but no adult would want to last that long. That would keep you here for 32,000 years. So not only do you have to know a number, but you need to have number sense.

As a former reporter, the session title lured me in—"A Mathematician Reads the Newspaper." It also hit home because unfortunately, too many reporters just don't understand the math. Emotions can also get in the way. We all see this on the talking-head show where dueling numbers are thrown around like pitchers warming up before a game. Without context, numbers have no value.

The example Paulos gave that I liked the most had to do with a teacher who gave a daily quiz. He told his students that they could get 10 extra points if they checked the box at the end of the test. Then he added, if more than half of you check the box, I'll deduct 10 points from your score. So not only did the students start doing the math, but emotions were added into the mix. As the semester progressed the number of students who checked the box hovered around 40 percent. But here's the interesting part—it wasn't the same students.

We may think that we control numbers; but often, without our conscious knowledge, numbers can manipulate us.

Posted by Gay Dillin, 4.11.08

I have been blown away by the participants in today’s New Teacher Strand!

I’m energized by their profound interest in students and in becoming better math teachers—from understanding ratios, to thinking about the themes that can be used to teach math, to motivating and managing classrooms through engagement and empathy.

They bring smiles, energy, and commitment that will take us far. Thanks for being math teachers.  

Now how do we do more to tap into all they bring to the classroom?

Posted by Dave Barnes, 4.11.08

I went to a session related to the work of the Rational Number Program (RNP). It was a very good session on models and representations that will help students develop key understandings of operations of fractions.

I am currently doing research on how students develop understandings of foundational concepts of fractions related to discrete and continous models. Early RNP work related to some of those areas, and now in this round of the RNP, are looking at operations, particularly multiplication and division.

The sample problems we explored, along with the videos of students sharing their thinking, were powerful tools teachers can use to plan and sequence lessons that will help students develop an understanding of operations, especially partitioning.

I can't wait to go back and share some of these insights with my students!

By the way, if you are interested in the previous lessons on fractions, Google "Rational Number Project." The new lessons are still under experimentation and revision—but perhaps soon they will be available as well.

Enjoy the conference!

Posted by Trena Wilkerson, 4.11.08