Wednesday, December 26, 2007

Integrating Reading and Thinking Strategies with Math

I recently read an article from Educational Leadership. I was impacted by the interwoven use of Reading and Thinking Strategies to enhance Mathematical Conceptual Understanding. We have talked at numerous professional development sessions dealing with the importance of integrating reading strategies across content areas. We have frequently commented on the fact that far too often teachers must literally give students permission to use Reading Strategies when solving math problems or dealing with Social Studies or Science content.

The article referenced to a study that was conducted by by Hiebert and colleagues' in 2003. They analyzed videotapes of 8th grade lessons that were collected from the Third International Math and Science Study. The study concluded that math classrooms in countries that score high on international comparisons of mathematics achievement have commonalities. Those commonalities consist of cultures of teaching and learning that are designed to assist students make connections and build conceptual understanding. The study also found that teachers in these countries assign students challenging math problems and use active questioning and dialogue to assist students and help them see and understand connections. This sparked my attention because conceptional understanding is at the heart of Math Investigations.

In contrast, U.S. teachers that were videotaped did not use questions or conceptual dialogue to help students explore math connections. The teachers viewed the problems as procedural exercises and proceeded to give students formulas and/or tell them where to plug in the numbers. Basically, the teachers told the students the answers. (Stigler & Hiebert, 2004).

Alimacani is a Standards Based school and has utilized the Readers, Writers, and Math Workshop Model with great success. All of the Workshop Models utilize connections, links, in conjunction with our rich metagcognitive strategies. Our work with New Performance Standards and the Workshop Model has proven that total student engagement combined with conversation that is rich in conceptual understanding produces student products that encourage students to converse and think thus promoting improved academic achievement. Research has shown that when students are actively engaged in the learning process academic achievement improves. Research has also proven that simply teaching by telling, lecturing, drilling, taking the pen or pencil out of a childs' hands to show them how to solve a problem or perhaps what word fits are methods that are embedded in the culture of mathematics teaching in the United States. This can be viewed with a lens of practicing the scales on a piano...rote, routine practice each day leaves little to no room for exporation. The old premise that it is easier to give a child the answer rather than guide students to self-explore does not equip our students with the skills that will enable them to solve real-world problems and become life long learners.

The concept that teachers need to teach math for understanding is the first step in changing the culture of mathematical conceptual understanding and problem solving in the U.S. One way to accomplish this goal and help our children soar is to weave together math, language, and cognition. When these areas are woven together they become stronger and more powerful thus enabling our teachers and students to develop richer conceptual understanding.

Arthur Hyde, Professor of Mathematics Education at National-Louis University has worked with K-8 teachers to investigate various ways to help their students become good mathematical problem solvers.

The integration of language, especially reading comprehension and mathematics has increased students cognition. We all are aware that Reading is the process of deriving meaning from written language. This is where the reader is able to engage or interact with the text to create meaning using the content of the text as well as how the text is structured. This applies not only to Reading but also to other content areas.

One of the paramount strategies that enable cognition to improve is through the use of vocabulary development. Holly and Linda have started us on a refresher journey into Vocabulary...A School-Wide Approach. I encourage each Math teacher to stretch vocabulary by including a Math Vocabulary Word Wall that is interactive. If space is an issue consider the use of a chart stand or chart that can be pulled out for use and housed in an accessible/visible location in the classroom...readily available for student use. The chart should be cumulative in nature in an effort to constantly review previous lessons. Remember, when a teacher places value on a strategy or artifact then students will value this strategy or artifact and its use will be frequent and powerful.

Research has identified effective cognitive strategies for students to use in reading comprehension (Harvey & Goudvis, 2007; Keen & Zimmermann, 2007; Miller, 2002), they include:

  • Making Connections

  • Asking Questions

  • Visualizing

  • Inferring and Predicting

  • Determining Importance

  • Synthesizing

  • Metacognitive Monitoring

The above strategies are all too familiar as part of Duval Counties Standards Based Curriculum. These same strategies can be adapted for math and will result in a deep conceptual understanding of abstract ideas. The National Council of Teachers of Mathematics (2000) identified five key cognitive processes in which students must engage in order to understand mathematical concepts:

  1. Problem Solving

  2. Reasoning and Proof

  3. Communication

  4. Connections

  5. Representations

Let's take a look at a tried and true strategy/tool used to for reading: The Reading K-W-L Chart:

  • K: What do I know?

  • W: What do I want to learn more about?

  • L: What did I learn?

Teachers adapted the K-W-L tool and formed the K-W-C Math Chart with great success in increasing their students cognition. This can be used during the Work Period of Math Investigation when students are in small groups. This can also be used as a type of Math Conference with a small group of students or as a one-on-one conference. The questions would be presented during the launch portion of Math Investigation or as part of the classroom Rituals and Routines. Here the teacher models the K-W-C questions for the whole class and encourages students to use the questions as they focus on reading story problems. Once the students are in small groups the dialogue continues allowing the questions to serve as a springboard or structure for the students' work and to assist students by connecting problems to prior knowledge. The Math K-W-C Chart:

  • K: What do I know for sure?

  • W: What do I want to find out?

  • C: Are there any special conditions that I have to watch out for?

This type of strategy also lends itself for students to conduct dialogue that will assist them with open-ended or extended response tasks. The study showed that the quality of the students' work improved significantly as demonstrated by their written responses.

The above experiment paved the way for the Braid Model of Problem Solving. This model incorporates seven reading comprehension strategies into four traditional phases of problem solving that consist of:

  1. Understanding

  2. Planning

  3. Carrying Out The Plan

  4. Looking Back

Let's take a look at how the adaption of Making Connections for Math helps students become more proficient at problem solving. We all know that Making Connections is interwoven in all aspects of reading comprehension. Making connections holds true when working with math problems. A teacher's goal should be to provide each child with a variety of connections as they try to solve problems. After all...there certainly is more than one way to solve a problem.

When we began our journey with New Performance Standards and the reading comprehension strategies we were introduced to the familiar connections in reading: Text-to-Self, Text-to-World, and Text-to-Text. If we adapt the same connections to math it will read like this: Math-to-Self (connecting math concepts to prior knowledge and experience); Math-to-World(connecting math concepts to real-world situations, science, and social studies); and Math-to Math (connecting math concepts within and between branches of mathematics or connecting concepts and procedures). Once this is embedded in our students thinking then they are readily able to identify different kinds of connections and bridges have been constructed that will help students cross over and reach greater understanding.

The Braid Model also took a look at the other comprehension strategies and adapted them to Math. The K-W-C process had students viewing the questions to decide what inferences they made and whether those inferences were accurate. Problem solving at its best!

Obviously reading is an integral component of math. Just as Read Alouds increase comprehension conversation, dialogue, questioning, etc., enhance successful learning for math concepts.

The United States is striving to raise the achievement of math for our students. In order to accomplish this goal we need to use a lens that infuses language and thinking into mathematics. This is not an easy task. Teachers and students are asked to realize that we are on a quest that will help us discover the importance of using all modalities, require us to ask relevant questions, and unfold the layers of cognition.

Teachers must be the catalyst to spur students into this new arena of learning. This is indeed a Brave New World! Alimacani's teachers are the bravest and will always strive to enrich their teaching with Research Based Practices that adapt reading strategies, language, and thinking to help Plant Seeds For Success in All Content Areas...It's All About Growth!

Educational Leadership
November 2007
VOL. 65 NO. 3

(Because I am still a novice and haven't figured out how to post credits or quote...I want to remain in compliance and verify credits so...portions that are italized come from the article...I will strive to improve on blogging skills...a journey worth unfolding)

No comments: