Theory of Cognition Course

St. Louis Park teachers Rose Korst and Mary Norris will premier a new course spring semester at St. Louis Park High School entitled "Theory of Cognition." The course has been designed as the bookend course for the school's International Baccelaurette (IB) capstone course--Theory of Knowledge.


Students in Theory of Cognition are sophomores who want to accelerate their skills in order to be successful in IB classes as juniors and seniors. Rose and Mary are keeping with the NUA philosophy of "Do not remediate kids--accelerate them."


Rose and Mary have extensive NUA and Thinking Maps training, so this pre-IB course will involve the explicit instruction of thinking skills and concentrate on the metacognitive processes involved in reading, writing and math.


The ultimate goal for the students will be for them to see a problem and be able to tell themselves: "These are the thinking skills that I can use to solve this problem." In other words, the teachers will help the students to learn how to "mediate their thinking for self-directed learning."


Besides using Thinking Maps ad other written forms of metacognition, students in Theory of Cognition with employ Socratic dialogue. For example, students will use Socratic defense with math problems. If two students have different approaches to solving a math problem, each will defend his or her approach with reasons why.


Mary and Rose invite area teachers to observe their class and provide them with feedback. They can be reached at norris.mary@slpschools.org or korst.rose@slpschools.org.

More Math Thinking Maps

Scott and Lizzy have really embraced using Thinking Maps in math classes this fall. Below is an example of how they have used the flow map to show the sequence of a variation problem.

Here's an example of a multi-flow map to prove a theorem.

Comparing Math Equations

As part of their math exam, students in Lizzy's class had to compare and contrast two equations by creating a double bubble map. Here is one student's answer:

Algebra Problem Takes Three Thinking Maps

Scott and Lizzy have been working this fall with Algebra students and using thinking maps to solve problems. The students went through a process of defining the problem with a circle map, classifying known information about the problem in a tree map, and then putting the equation steps into a flow map.

The teachers prompted the circle map creation with the question, "what do you need to define to solve this word problem?" "What distance" was the essential question, so that became the center of the circle map, and students defined "what distance" with all the details they knew from the word problem.

The second step was to classify the details into a tree map. Lizzy and Scott did not tell the students the categories, so many students struggled with this step. Upon reflection, Lizzy and Scott felt that the tree map categories should be worked out in a full class discussion so that students are not led too far astray. Here are the resulting tree maps:

Anticipation Guide to Engage Students

An anticipation guide is a set of true/false or agree/disagree statements that are presented to students prior to informational text (including math chapters), films, and guest speakers. The strategy sharpens a student's thinking skills while building curiosity. When information is memorable, student learning increases.


The steps:

1. The teacher writes several declarative statements that are based on the upcoming reading, film, chapter, speaker, etc. The best statements are possible yet open for debate.
2. Before the reading, students decide on their response. Students could complete the anticipation guide with just their own opinions and then check with a partner or group.
3. The group discusses some of the statements as a whole class, having students tell the reasoning behind the response. The teacher can prompt: "Why do you think so?
4. Students read the assigned material and change their answers so that they leave class with the correct answers to study.

Generally, anticipation guides are used with non-fiction texts so that students can reason with prior knowledge. With fiction, the author could take the reader anywhere. However, anticipation guides can be successful with fiction when the agree/disagree statements get at the big ideas or themes of the novel.


Here are some example fiction statements for anticipation guides:


Huxley's Brave New World--
A society's stability is hindered by people expressing their individuality.


Twain's Adventures of Huckleberry Finn--
A natural father's rights are more important than a child's welfare.


Shakespeare's Much Ado About Nothing--
Before deciding to marry someone, people need to agree with their parents' wishes.

This strategy is culturally responsive because students share their reasoning behind statements with small groups and the entire class. Since the reasoning is based on what students know, various cultural backgrounds will emerge. Hopefully, this leads to students appreciating other backgrounds and life experiences.

English 10 teachers used an Anticipation Guide during the first week of school where students agreed or disagreed with statements about life if high school. This activity worked well.

KC even created an anticipation guide of personal information as a way for students to get to know their teacher.

Math Thinking Strategies

Scott, the high school numeracy coach, and I have been meeting over the past few weeks to discuss ideas for Advanced Algebra. Since my math skills left me 25 years ago when I dropped Calculus II in college, these meetings have been a challenge for me.

However, my lack of knowledge may be paying off. Last week, Scott gave me a word problem to solve and asked me if I could use thinking maps to solve it. Being true to the belief that the brain thinks eight ways as represented by Hyerle's Thinking Maps, I set out on the task. I falsely started with a tree map and then realized I didn't even know the ideas to classify yet.

After backtracking to a circle map to define the problem, I felt much better about the problem. I then could make a tree map that classified the parts of the problem, which turned out to be the parts of the mathematical expression I needed to arrive at to solve the problem. The solution to the problem was just a quick flow map away.

I have to confess that it took me nearly 20 minutes to solve this one word problem from an Advanced Algebra sophomore class. Scott found my thoughts fascinating because I was talking out what I was thinking as I was making the Thinking Maps. Scott said that with students he never gets to hear the thought process; students usually just shut down and say, "I don't get it."

Scott and I came to the conclusion that my brain needed to go through the following three thinking processes to solve the problem:
1) a circle map to define
2) a tree map to classify
3) a flow map to sequence the stages of the mathematical expression

Since the problem solving process took so long (even with Scott asking me clarifying questions along the way), I wanted to test the idea that I had, in fact, learned something and could solve another problem. I wanted to show Scott that taking the time up front to get me to understand the process would pay off in the end when I made up time on future problems.

I went through the same three-step process with a second problem and arrived at the correct answer in only five minutes, and I had sketched out the three Thinking Maps. I was amazed at my ability to solve the second problem, and I was actually enjoying math.

After this session with Scott, I pulled out Hyerle's Thinking Map binder to look if he had addressed math problem solving steps. He had! I can't believe that I neglected to look there first, but in retrospect, I am glad I tried to construct meaning on my own. Hyerle proposed using the same three-step process that I had arrived at on my own--the circle map, the tree map and the flow map in that order. Arriving at that process independently further strengthened my belief that the brain does think in those eight ways.

Scott took my completed maps back to the math department. One teacher couldn't believe that I had thought that way to solve the problem. She felt I should have done it another way. Scott said that he realized then that people have different frames of reference when solving math problems and there are probably students sitting in the math classes needing to think out the problems with all the steps that I needed.

Writing in Math Class

Scott's math students are writing their robot stories on his blog, http://www.woelber.blogspot.com/. I love that students are writing for math classes as part of their homework. Now if only I could figure out how to teach math across the curriculm.


For more information on Scott's work as the EHS Numeracy coach, visit his blog at http://www.ehsnumeracy.blogspot.com/.

List Group Label Strategy

The List/Group/Label strategy offers a simple three-step process for students to organize a vocabulary list from a reading selection. This strategy stresses relationships between words and the critical thinking skills required to recognize these relationships.

List/Group/Label challenges students to . . .

• List key words (especially unclear and/or technical terms) from a reading selection.
• Group these words into logical categories based on shared features.
• Label the categories with clear descriptive titles.
  

Steps to List/Group/Label:

1. Select a main topic or concept in a reading selection.
2. Have students list all words they think relate to this concept. Write student responses on the whiteboard.
3. Divide the class into groups of 3 or 4 students. Have these teams join together related terms from the larger list. Have the teams provide "evidence" for this grouping—that is, require the students to articulate the common features or properties of the words collected in a group.
4. Ask the student groups to suggest a descriptive title or label for the collections of related terms. These labels should reflect the rationale behind collecting the terms in a group.
5. Finally, have students read the text selection carefully and then review both the general list of terms and their collections of related terms. Students should eliminate terms or groups that do not match the concept's meaning in the context of the selection. New terms from the reading should be added, when appropriate. Terms should be "sharpened" and the groupings and their labels revised, when necessary.

An alternative use of this strategy is for the teacher to provide the list of terms or vocabulary words for the students to organize. Then students can speculate about the topic to be read. These word lists can be copied on card stock for easier manipulation.

The finished, labeled categories can be presented in a tree map since the tree map is for classifying details and grouping ideas.

Using the List/Group/Label strategy develops critical thinking abilities and uses motivation to increase comprehension. The strategy engages students by building their curiosity and allowing them to activate their prior knowledge. Hilda Taba created this strategy because of people's interest in inductive thinking, making generalizations based on specifics. This cognition strategy is also based on Jerome Bruner's research on how people learn, organize and retain information.

Some teachers may feel that they need to teach all of the word definitions for students to be successful with this strategy; however, not knowing all of the definitions also adds to a student's curiosity and guessing definitions may increase student enjoyment in the task.

Math teachers have found success with this strategy when they have students List/Group/Label various terms, expressions and symbols.