Wednesday, October 29, 2008
Sunday, October 19, 2008
What is Math Talk? The National Council for Teachers of Mathematics (NCTM) emphasizes the need for students to discuss their mathematical thinking as a way to increase understanding. It is more than having students take turns telling about their problem solving methods or participate in undirected talk rather than actually analyzing and comparing methods. Teachers should help students move along a learning path toward more effective methods of problem solving.
The components of the Math Talk Learning Community are: questioning, explaining mathematical thinking, source of math ideas, and responsibility for learning.
A. Questioning – There is a shift from the teacher as questioner to the students and teacher as questioners.
B. Explaining math thinking – The students increasingly explain and articulate their math ideas.
C. Source of math ideas – A shift from the teacher as the source of all math ideas to students’ ideas also influencing the direction of the lessons.
D. Responsibility for learning –The students increasingly take responsibility for learning and evaluation of others and of themselves. Math sense becomes the criterion for evaluation.
The question of “Is it language or is it Math?” evolved from how a problem is presented. Teachers should model the math, model math talk, stand to the side, and bite their tongue (let students solve, explain, and question.) This was an interesting session that approached math as a scientific discovery model.
Written by: Maria Mallon
- Some people can accomplish amazing things. (Michael Phelps, Usain Bolt) Talented students need a chance to fly.
- Sometimes a new star is lurking behind the others. (Kerri Strug, Jason Lezak) We need to expand our reach and know who needs to be developed.
- It is easy to miss great things when all you are focused on is results. (Guo Jingjing) We need to look and listen carefully to what students are doing.
- Persistence and perseverance pay off. (Dan O’Brien) We may be teaching students not to persevere (TIMMS Study) We don’t give students as much time to conceptionally develop strategies. “Constructive struggling” is good. We should expect students to think and work hard.
- The right tools make a difference. (Michael Johnson) Write down something you are not good at and work to get better. We have to get past our fear of knowing that students should have xyz memorized before they get to us. We hold kids back trying to fill gaps. Sometimes when you move ahead, they will fill in the gaps themselves by using tools. Tools exist to get us to higher levels.
- Sometimes success comes from where you least expect it. (Jefferson Perez) Raising expectations for every student does not mean to do the same stuff only harder or earlier. It does mean challenging our own habits or beliefs. It does mean setting standards high, believing students can reach them, and doing whatever it takes to help them get there.
- We may not ever know what students are dealing with in their life outside of school. (Oksana Chusovitina) Our students are often preoccupied.
- Sometimes we mess up. (
Mens Gymnastic team) The tyranny of testing the students may never show us what they know best on every test. Testing can be made more important than student learning. We have to use appropriate ongoing assessment to inform our teaching. US
- We can always improve – our capacity to learn is unlimited. We can do better than we have ever done before. Do we know who is in our classroom? Differences/challenges/struggles. Do we know or can we learn what it will take to help each student.
- We have to pass the torch. Influence them to be the best they can be.
Melissa Ross and I started the second day of our FCTM conference with a session called "Reorganizing the Candi Shoppe: A Place Value Problem." The presenter of this session was Joanne LaFramenta. We started the session by creating our own definition of the phrase "place value" from a student's point of view and from a teacher's perspective. From there, Ms. LaFramenta explained how uses the situation of a candy shop to get students thinking about place value. For this session, she made the problems more difficult than what would be used in most elementary classrooms. Here was the question that she gave us: How can a candy shop owner keep track of his candy in a more efficient way? All candies are packaged as 8 pieces in a roll and 8 rolls into a box. One situation was to find all of the ways to organize the quantity 192 candies. After several minutes of work time, participants came up with a variety of ways to organize the candies in rolls, boxes, and pieces or a combination of some of the three. Some solutions that were suggested were 3 boxes or 24 rolls. I liked the idea of teaching place value in this way. It would be easy to create accommodations (extensions and easier variations) using the candy shop model.
Students would create an origami or an accordian style book out of student designed watercolor paper. Students would, then, write on the pages, the elements and principles of design as well as a descriptive poem. Student also made pinwheels for the "Pinwheels for Peace" project incorporating the elements and principles. Some of the books, designed, were more sculptural in their design using intricate cut outs that "popped out" when opened, making for a beautiful art piece.
Other projects that our instructor told us about was having students create "new" inventions that reflected a certain principle of design. They worked in groups to go through elaborate planning and advertising of their new invention from the imagination" stage all the way through to the "advertising" stage. Of course, this would take more time than I have with the students, but it was amazing how many academic disciplines were involved from start to finish. The examples that she showed were really quite creative. Maybe we can do some cooporative work and bring this down to our students creative level
Written by: Jen Snead
Saturday, October 18, 2008
Algebra is becoming mandatory in the eighth grade around the nation. However, if the foundation for number sense is not strong, students will be lost and frustrated with mathematics. The speaker talked about the challenge for intervention. She said it is not about reteaching missed skills. The focus should be on rebuilding the critical foundation – a core set of knowledge – and connective learning streamlined to the most important topics.
Students should have a robust sense of whole numbers. Fluency equals numbers sense. Fluency is an understanding of place value, the ability to compare and decompose numbers, and grasp the meaning behind the operations (recognize addition and subtraction situations). It is so important that students have the knowledge to apply the operations of problem solving and understanding how to represent a problem (graphic organizers.)
A student was asked, “Do you know what 100 – 3 = ? – Yes, that’s 97. Do you now what 100 – 98 = ? No. That’s too hard. Instead of teaching subtraction as “take away” it should be taught as “distance from.” (Which I was glad that that’s how we teach it at CCE).
Big Ideas of Addition
Ten is an organizer of our number system. Numbers and be composed and decomposed. Students need time to practice and time to internalize. The 10-frame and the open number line is are useful and effective tools for this purpose.
The speaker spoke of pre-assessments and post-assessments, streamline lessons, and review in order keep teaching effective.
Written by Maria Mallon
Friday, October 17, 2008
Written by: Jen Snead
A few points were very interesting. She stated that the Grade Level Expectations used to be that a student could grasp a concept in 2-3 days. Now the GLE is 10 to 14 days. This allows teachers to focus and deepen understanding of concept that is being taught. In their county, there used to be and average of 83 standards to teach, now there are 18. Kindergarten has eleven. In addition, worthwhile mathematical tasks were emphasized in order to engage the student intellectually and to help develop math understanding.
It is important to note that reading is critical to Math. Students need to be able to read and interpret word problems and incorporate reading and math in the world around them. Furthermore, problem solving is a life skill. Teaching students how to go about problem-solving is necessary. Questions need to be asked such as:
ð What do I need to find out?
ð What do I need to know?
ð What is my solution?
ð Was my solution correct?
ð What if…?
We worked on a few hands on activities which included: Shifty Shapes (pattern blocks); Suitcase Solutions (tangrams); Shape Searches (decomposing shapes to identify hidden shapes); What is the One? (identifying relationships in fractions); Blocking Out Fractions (solve problems involving whole numbers, unit fractions, and mixed numbers).
“We’ve Got Problems” was a wonderful session that had us engaged in worthwhile mathematical tasks that I can’t wait to share with my students.
Written by: Maria Mallon
Thursday, October 16, 2008
With no time for lunch, Ashley and I grabbed a bagel and rushed to the next presentation, Math Fair in a Box, presented by Carmen Sleeth. The description stated “Boost FCAT scores, increase family involvement and enhance student understanding with a Math Fair in a Box. All components included for a fantastic event!” We were not sure quite what to expect, but we knew it would be good.
We opened with an icebreaker – one of my favorite ones yet, might I add. (I can’t wait to try this one with my kids on Monday.) Everyone at the table holds hands. A balloon is thrown into the center of the table. You cannot let go of the hands beside you. “Balloon in the air, feet on the floor.” As you can imagine, the room erupted with laughter as 40 adults in small groups tried to keep their balloons off the table top.
On to our learning. We were blown away by this product. The Math Fair in a Box is everything you need to host a successful family night centered around math. They are adaptable game stations that work well for large or small groups.
Game station topics include: geometry, visual and verbal communication, time and calendar, addition, subtraction, multiplication, division, values of fractions and equivalent fractions, sorting, graphing, money, and spatial thinking to name a few. For more information on this product, contact Claudine Reece at 727-804-3409 or email at firstname.lastname@example.org.
This session was presented by Angela Phillips and Rick Pinchot. Their session was about using instructional games to create an engaging and powerful forum for the development of students' strategies in addition and subtraction. A few minutes prior to the session beginning Angela and Rick went around the room to get to know the participants and find out where everyone was from and their backgrounds. This helped create an easy going atmosphere in the room. As the session began it was clear that everyone was spell bound by their presentation. The audience happily participated in the discussion and games. I believe the reason for this easy demeanor of the room is because of the dynamics of Angela and Rick. To watch them teach other teachers is a treat.
They began the session with a conversation about Dominoes. They wanted each table to add up the dominoes found in the middle of the table. This seems like an easy task with few differences. However, each table organized and counted their dominoes differently. It lead into a discussion of strategies and organization.
Next the room discussed the plus/delta's of using games in the classroom. Some of the plus': games are interactive, students are motivated, reinforces lessons already taught, multiple strategies are used. The delta's discussed: parents have misconceptions about games, missing pieces, noise level, preparation. Things to remember: recap the game to talk about what they have learned and play each game multiple times.
Rick and Angela also showed videos of students playing games from classrooms at Chets Creek. After watching a clip, the audience had the opportunity to discuss the work they saw and play the same games. It was a powerful session. I am sure all of the participants walked away with a new understanding of the importance of using games in math.
She has written a teacher manual called Math Rescue: Whole Number Computation. The activities are presented in three categories: Concept Manipulative Activities, Practice Activities and Problem Solving Activities.
One concept manipulative activity she shared was Criss-Cross Multipliers. To play the game you would need spaghetti or sticks and overhead projector. You would create the array from the above picture under the overhead. You would ask the students what multiplication problem this array shows. (4 sticks X 3 sticks) Ask, "How can we determine the answer to 4 X 3?" (Count the places where the sticks cross.) You would have the students continue modeling a variety of multiplication problems. Someone thought this might be confusing to students if they tried to count the squares instead of the cross sections. Mrs Bradsby said you would need to make sure the students understood to only count the places where the two noodles crossed.
The first session Ashley and I attended, Putting Place Value in Context, was presented by Wendy Bray, Ph.D. from
We began by looking at the new Sunshine State Standards for first and second grade exploring place value. The standards are getting harder, but our goals are well defined. We looked at models of each state of the learner’s development as well an analyzing several student work samples.
Check out the handouts below. Do your students fall within the base-ten strategies discussed?
Today I had the opportunity to attend the Florida Council of Teachers of Mathematics Conference that is being held in Jacksonville. The first session I attended was The Ants Go Marching. The presenter was Dr. Karol L. Yeatts from Warner Southern College.
Her session talked about using a study on ants to teach math and science. Some of the pre-number concepts she talked about were sorting and classifying, seriation, patterning, comparisons, counting and number relationships. She shared a list of ant facts she likes to teach her students. Did you know that ants can appear in shades of green, red, brown, yellow, blue or purple? Also an ant brain has about 250,000 brain cells. A human brain has 10,000 million so a colony of 40,000 ants has collectively the same size brain as a human.
Dr. Yeatts also shared many games like Hide and Seek with an ant to teach spatial awareness, matching ants to number cards using raisins for one to one correspondence and singing and marching while singing The Ants Go Marching to teach seriation and Counting.
Dr. Yeatts shared a list of her favorite books to use during her ant study. Some of the stories are books that are familiar. Ant Cities by Arthur Dorros, One Hundred Hungry Ants by Elinor Pinczes, and Hey, Little Ant by Phillip Hoose are a few she showed us.