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
- Inferring and Predicting
- Determining Importance
- 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:
- Problem Solving
- Reasoning and Proof
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:
- Carrying Out The Plan
- 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!
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)