Logic and Critical Thinking

The question is

As for Chapter 5-Logic and Critical Thinking, please read through the chapter and respond to the summary question #4... How might a high school math teacher use Alice in Wonderland?

Please respond to the following excerpt found on page 127 in relation to our current educational system of assessments.

"His (Piaget) work appealed to many educators who believe that children must be active in their own learning. Educators began to distinguish "developmental learning" from "rote learning," the former being described as active and making a lasting difference in how students approach problems and new situations, the latter described as passive, temporary, and useless for further learning."

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Have fun!

Peer 1(sara)

My recollection of Alice in Wonderland is vague.  It has been a very long time since I have seen the movie, mainly because it scares me!  I am pretty sure I did not read the book for the exact same reason. So I am going to try and stick to the “how might” of the discussion question, rather than digressing into “why would anyone want to” J  Noddings describes in Chapter 5 how Alice in Wonderland can be used to teach formal logic and thereby teach critical thinking.  Noddings summarizes a passage from the story that could be used to illustrate the reasoning involved in solving a proof, much like one would do in Geometry.  While I can no longer remember all of the story’s the dialogue, to provide additional examples for use in teaching Math, I think the big picture for educators is to move beyond the obvious.  Many times when we go visit our nieces and nephews we manage to work math into our conversations (my husband is a math teacher, he can’t help it!).  Whether it is how much younger I am than their parents, how many balloons are on the cover of the book, or how many pieces of pizza each person gets, we take everyday situations and turn them into learning opportunities.  I think this idea ties in nicely with Dewey and his desire to see educators select materials and experiences that will be interesting to the students, moving beyond traditional textbooks for the content and examples.

Our current educational system of assessment relies heavily on standardized testing.  These tests require students to respond to multiple choice questions, selecting the one response that is correct.  I think these tests fall in between Piaget’s developmental learning and rote learning, if we placed it on a spectrum.  I see developmental learning as knowing what, how, why, and why not.  Rote learning is a basic stimulus-response reaction.  Standardized tests do not reflect the depth of knowing that a student might have; conversely, it does not reflect the depth of knowing a student might be lacking.  However, given that the problems on the standardized test will not be the exact same as what the students have practiced, the student will need more than just basic rote learning.  Educators who are proponents of formative as well as summative assessment are better able to capture the developmental learning (or lack thereof), but this practice is not necessarily pervasive in the educational system.

Peer 2(kim)

I am surprised to know the book, Alice in Wonderland, is mathematic fairy tale, which means that there are quite many mathematic principles in the story. It is easier for us to understand the fact if we knew that the writer, Lewis Carrol, whose real name was Charles Lutwidge Dodgson, was a famous writer and mathematician. I believe that it is great for teachers to introduce math in the connection with real world to help students think in more creative way. Story telling math is getting very popular in my country as well to make students creative, breaking away from studying and preparing only for an exam. In this sense, even high school teachers will absolutely be able to use this story when they teach math. Teachers can teach not only math formula, and principles but also the real purpose of learning them, who found them, and even how they are used in the real life by connecting their teaching with a story. Students will absolutely have more fun to learn the lesson as well if they are learning math principles, such as ageometricalfigures, height and weight changes, different movement of the hour and minute hand of a watch, etc. while they are learning the story.

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When I look back to my old school days, one of the first things came to my mind is taking exams. I studied very hard and memorized lots of different knowledge to prepare for those exams. However, I forgot the knowledge right after the exams. Whenever I repeated the routine process of memorizing information, taking exams, and forgetting things, I felt hopeless and I thought that I studied only for the exams. Unfortunately, this practice is still quite dominant in my country, even though there are many changes going on to asses not only the memorization of knowledge from rote learning but also the real understanding of a subject based on their developmental learning. As we all know, the ‘washback effect’ is great in teaching area, which means that the assessment is influencing a lot to the way of teaching and learning activities. If we can assess students not by only the multiple choice questions but by more various ways like connection, true/false questions, and essay tests, etc., students will also be ready for their learning base on the developmental learning.

Peer 3(Paige)

I had never really thought of the connection of Alice in Wonderland with math until I read it in this book. This was a great way to use reasoning in a math class at a higher level without using numbers.  Sometimes students do not see how a skill that is taught is transferable to other disciplines. This is a prime example of using deductive reasoning and logical problem solving.  Any time we can teach the actual skill (not just an answer) to be used for future problems throughout the curriculum, we are providing structure that will allow increased future student achievement. The examples of Alice in Wonderland also reminded me of the different story problems such as “If Suzie is 10 year older than Bill and Mark is twice Karen’s age….” These were always challenging, however when you were able to tackle one, there truly was a sense of accomplishment. Children do need to be active in their own learning.  There is a difference in development learning and rote learning; however in my opinion they both are necessary to a certain degree to achieve.   Sometimes beginning to learn a particular topic, you may need to memorize specific key facts that can be used as a basis in your application or higher level of problem solving.  Students need to be able to apply their knowledge in various situations, therefore being active in their learning.  Education has started to focus more on “justification, explanation, application” of the subject material instead of multiple choice questions/rote learning.    Having students share their metacognition is critical to determine their true understanding and even their developmental learning. Both developmental and rote learning will be necessary at times.  My mind immediately thinks about learning foreign languages.  There is a huge amount of rote learning that takes place initially.  There really isn't a good way to relate "hola means hello" outside of just memorizing it.  I think our goal is to use rote memorization minimally, and then start working towards higher levels of learning.

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