FOR-PD Chat Transcript
Date: October 9, 2007
Time: 7:00-8:00PM EST
Topic: Comprehending Math in a K-12 Setting
Guest: Arthur Hyde, National–Louis University
Our guest for the October 2007 content chat was Arthur Hyde, a professor of mathematics education at National–Louis University. While a high school mathematics teacher in Philadelphia, he obtained a doctorate in curriculum and instruction from the University of Pennsylvania. He has conducted extensive professional development programs in Chicago and surrounding school districts.
Please visit the following sample chapter from Professor Hyde's book, Comprehending Math, Adapting Reading Strategies to Teach Mathematics.
FOR-PD Project >> Hello everyone. Welcome to tonight's Content Chat.
FOR-PD Project >> At tonight's chat, you will have the opportunity to ask questions and receive answers about the content used in the course.
FOR-PD Project >> The chat will be an hour long and conclude at 8:00PM.
FOR-PD Project >> I would like to introduce members of the FORPD staff that are present in tonight's chat.
FOR-PD Project >> Lourdes Smith is our Reading Specialist.
FOR-PD Project >> Dr. Art Hyde will be our featured speaker tonight.
FOR-PD Project >> I would like to go over the chat protocol for tonight's chat. Please make sure you follow the protocol as this makes the chat flow more smoothly.
FOR-PD Project >> The Exclamation Point - !
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FOR-PD Project >> The Ellipse - . . .
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FOR-PD Project >> To type in the chat window you must type in the white box below ENTER YOUR MESSAGE HERE and then hit the enter button. What you have typed will show up in the chat window.
FOR-PD Project >> If there aren't any questions about the chat protocol - I will turn the chat over to Lourdes.
Lourdes >> Hello and Welcome to our October 2007 Content Chat!
Lourdes >> Our guest tonight is Arthur Hyde, author of the book, Comprehending Math, Adapting Reading Strategies to Teach Mathematics.
Lourdes Smith (lourdessmith)>> For the first half-hour I will chat with Dr. Hyde about literacy and math development. Then for the second half-hour we will open the floor for questions.
Lourdes >> Art, it's a pleasure to have you here tonight!
Lourdes >> Would you like to share with us some of your background and biography?
Art >> Thank you for inviting me.
Art >> I am a former high school math teacher from Philadelphia. I didn't start teaching right after college. I went to graduate school in psychology and got a master's degree. When I began teaching and had to take education courses. I found the math ed folks were 20 years behind the cognitive psychologists. I incorporated a lot of cog psych into my teaching. I was fortunate to get to know some excellent English and reading teachers along the way from whom I learned a lot about reading comprehension strategies.
Lourdes >> wow, you've done quite a bit....
Art >> Sorry. I am still getting used to this !
Lourdes >> not a problem, Dr. Hyde
Lourdes >> math and literacy are both very hot topics
Art >> I found that to make math real to kids I had to link language and thinking and math
Lourdes >> Why are making connections to literacy development important in content areas? Why math?
Art >> Humans think with language. The Third International Math and Science Study (TIMSS) included not only achievement test data but also follow-up videotapes of eighth grade teachers of mathematics. Six-hundred thirty eight mathematics lessons were video-taped from randomly selected, teachers from the United States and six other countries whose average student achievement on the test was higher than that of U.S. students. A team of researchers (Hiebert, J., et al, 2003) analyzed videotapes about 100 from each country, examining dozens of factors related to teaching (e.g., calculator use, time spent on problem, type of problem). They could not discern any factors that would generally predict high achievement by students across the countries. They did perceive a culture of teaching mathematics in each country.
Lourdes >> Language is indeed the cornerstone of literacy.
Art >> The researchers found that the culture of teaching mathematics in those higher achieving countries did have something in common ---- “the way in which teachers and students worked on problems as the lesson unfolds.” (Stigler and Hiebert, 2004, p. 15). In these countries, when their students had problems intended to build conceptual understanding by making connections among concepts, the teachers through various means of questioning and dialogue actively helped students make connections. In stark contrast, none of the United States math teachers implemented the making-connections problems with questions or conceptual dialogue about the mathematical connections. Instead, they transformed all of these problems, rich in mathematical concepts, into procedural exercises (e.g., by the teacher giving the students a formula and telling them to plug in the numbers). One-third of the time, the teachers simply gave the students the answers! The researchers stated, “even when the curriculum routines to transform the problems and reduce their instructional potential."
Art >> How can we encourage teachers of mathematics in the United States to move beyond ineffective, culturally-conditioned teaching routines such as transforming a conceptually rich, mathematical feast into procedurally plain, non-fat yogurt? Teaching by telling, taking the pencil out of the student’s hand to show him how to do the problem and then doing it for him, or drilling on procedures to get the right answer quickly are embedded in the culture of math teaching in the United States. How can we help them to build a conception of math teaching that includes questioning and stimulating dialogue to enable students to make connections? For their students to understand mathematical concepts, the teachers need to realize the importance of infusing their math teaching with cognition and language. They must know what to do and be able to do it. I have used the metaphor of braiding because when three things are braided, the result is stronger, more durable, and more powerful than any single strand. When mathematics, language, and cognition are braided, the likelihood of conceptual understanding is increased exponentially.
Lourdes >> Yes, making connections is a vital part of teaching almost any subject. Have you run across many teachers that feel that math and literacy do not relate with each other?
Art >> Yes but once I start explaining, they realize that there are connections that they can make, that they didn't think of and that would help children.
Lourdes >> In your book, you note many wonderful strategies that stretch across content areas...
Lourdes >> making connections, asking questions, visualization are just a few that I recall
Art >> It's something they have not thought about but once they get the idea, they start making connections they hadn't seen before on their own.
Lourdes >> I liked in your text how you made the relationship between the strategy and math seem so relevant and "doable"...
Lourdes >> Visualization is an excellent strategy and one you write about in your book...
Lourdes >> Why is visualization a strategy that can work with both math and literacy development?
Art >> zen teachers and I systematically adapted them for math.
Art >> Visualization was one of the 7 strategies we looked at carefully and analyzed how to adapt it for math. Kids are not used to visualizing problems, they are used to just finding numbers to calculate...
Art >> 3 types of visualization in math. 2 of them are directly related to reading. The 3rd is more unique to math. In reading kids have to create mental images as they read and of course we want to help them do that when they are working on story problems. They have to imagine the situation...
Art >> Many teachers have found that their students don't want to read the story problem thoroughly, they've been taught to just look for key words. This is a mistake! In problem solving we must use every device in our arsenal to encourage them to actually read the problem, and imagine the situation... The key word strategy basically says don't read the story...don't read the problem.
Art >> The 2nd kind of visualization that is like reading is when kids create representations of their own mental images ...
Art >> Kids have to create their own representations in order to solve math problems. By creating their own representations, they are expressing their understanding and knowledge that must then be translated into mathematics.
Lourdes >> You make good points here, Dr. Hyde. I think often students lack visualization skills and teachers often do not feel they have the time. But, teaching this specific strategy can benefit students in many ways.
Lourdes >> At this time, let's open the floor to our participants of this chat. Remember to use the ! if you have question or comment for Dr. Hyde and wait to be called on.
Margaret >> !
Lourdes >> Yes, Margaret, go ahead
Carol Gentry >> !
Margaret >> Hi Dr. Hyde, thanks for being here. It is a timely subject tonight as my students were asking what math and reading have to do with each other...
Margaret >> I was wondering if you could please explain a little more about metacognitive monitoring?
Art >> both areas
Art >> Both math and reading are based in cognition...
Art >> The cognitive processes are quite similar...
Art >> In metacognition, we want kids to be aware of what they are doing, how they are doing it, and are they getting closer to what they want to accomplish...
Art >> The more practice they get with specific cognitive strategies, the more readily aware they are of how well they are doing. With younger kids, it is much more difficult for them to be aware of their thinking when teachers model it and kids practice it.#
Lourdes >> Thank you, Dr. Hyde. Carol, you're next.
Carol >> Yes
Carol >> Dr. Hyde, you said "3 types of visualization in math." with one of those...
Carol >> being math rather than reading...to paraphrase
Carol >> what is the math strategy?
Carol >> #
Art >> This is an extremely complex area that goes by several different names and research in the US, Europe, and Asia on this area over the past 50 years, has been conflicting...
Art >> I refer to it as spatial visualization or spatial thinking and it comes up most directly in the math curriculum in geometry. US geometry does not give our kids anywhere near enough experiences working with 2 or 3 dimensional objects in order to explore relationships, attributes, and patterns...
Art >> We tend to push our kids into analytical thinking (in fact narrow analytical thinking) and give them paper and pencil geometry way too soon...
Art >> My work with teachers and students has convinced me that the time we have teachers and kids spend working on very specific geometric problems with objects and discussing them through good teacher questioning, lays a foundation that we can use in analytical thinking in later grades.#
Carol>> You mention time...
Carol >> how do you feel about our assessments being timed
Carol >> #
Suzanne >> !
Lourdes >> Suzanne, you'll be next.
Art >> Go ahead#
Lourdes >> Suzanne
Suzanne >> Math Teachers can find it challenging for students to understand what the...
Suzanne >> problem is asking. What is "The Question"...
Suzanne >> do you think the visualization skills you discussed will help?#
Art >> Timed tests for factual recall is valid. They should be games and without stress.#
Karen >> !
Art >> Visualization really helps everything...
Art >> I am much more in favor of extended questions for assessment because they allow kids to think and give them time to think.#
Lourdes >> Karen, your turn
Karen >> I'm concerned about the legislatureturning toward standardized tests like the NY Regents
Karen >> ...
Karen >> Do you think this trend is away from skills based assessment and back toward content knowledge-based?
Karen >> #
Beth >> !
Art >> I don't see a "trend" in either direction. I noted that Florida has changed their curriculum to be more like the NCTM Focal Points. That's a good sign because it will help teachers focus on key concepts at each grade level.#
Lourdes >> Beth, go ahead with your question/comment.
Beth >> What are some good visualization exercises we could use in our classrooms?#
Aston >> !
Art >>
Lourdes >> Aston, you'll be our last question for the evening...
Lourdes >> let's give Dr. Hyde a moment to answer Beth
Art >> I lost my comment! Please wait until I get the response finished#
Aston >> Do you believe that Thinking Maps are Effective#
Art >> Visualization is practiced best by having kids use manipulatives that they compare and contrast and describe with language...
Art >> Pattern blocks can be compared and contrasted then order them by 2 dimensional size...
Art >> tangrams can be used to study similarity, fractions, ratios, and angular measure and even irrational number because the hypotenuse is the square root of 2 times the side length of a right isosceles triangle#
Lourdes >> Our last question from Aston was on if you think thinking maps (graphic type organizers) are effective#
Art >> Yes! I have many graphic organizers for different purposes but there is no orthodoxy here. It's whatever helps kids get their ideas on paper. The question is how much structure do they need to do that. #
Lourdes >> At this time we are at the end of our chat. Wow, time really did fly.
Lourdes >> Thank you all for coming to our content chat.
Lourdes >> A VERY special thank you to Arthur Hyde for sharing his expertise with us.
Lourdes >> A transcript of this chat will be available on our site later this week.
Carol >> Thank you Dr. Hyde!
Lourdes >> I want to ANNOUNCE that our next content chat will be on November 8 @ 7pm E.S.T
Lourdes >> Our topic will be Developing Discussion in Your Classroom.
Art >> Thank you for allowing me to be here!
Erin >> thank you
Lourdes >> Our guest chatters will be authors/educators Mary Adler and Eija Rougle.
Lourdes >> We look forward to seeing you there.
Lourdes >> Dr. Hyde, we greatly appreciate you taking your time to be with us.
Beth >> thank you
Lourdes >> Your books are wonderful and I highly recommend them to all teachers interested in making those reading/writing connections in all content areas.
Jean >> Thank you
Sue >> Thank you
Deborah >> Thank you
Lourdes >> Thank you all for coming!
