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© 2014 Pacific Crest
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Applying the LPM: Math and Metacognition
P
urpose
The role this topic plays in quantitative reasoning
When we engage in metacognition, the act of thinking about our own thinking, and step back from doing
to determine how and why we actually do what we do, we strengthen all aspects of our own learning and
growth. Mathematicians love thinking, understanding, exploring, and knowing their own mind (see the
profile of a math graduate in the resources for this activity).
In several critical ways, this entire course is about metacognition and increasing your awareness of your
own thinking, especially when it comes to learning and applying mathematics.
As you continue to explore and use the Learning Process Methodology (LPM), you may realize that
you have not thought that much about how you learn and think. This book uses the LPM in every
activity and, as you’ve already learned, the LPM helps you to increase your awareness of how you learn
mathematics so that you can improve your ability to learn mathematics.
In working with this book, you will be exposed to many different methodologies. As you use them, you
will strengthen how you analyze a piece of knowledge, contextualize it, and finally generalize it so that
you can apply it as a successful strategy in learning mathematics. The point is to learn to transfer new
knowledge and apply it to solve problems in new and different contexts.
Unfortunately, when it comes to mathematical learning, many people start with the self-defeating belief
they can’t learn mathematics. Contrast this with many other disciplines where students are interested,
engaged, and feel comfortable and confident as learners. If we take the self-defeating belief away (after
all, that belief is always unjustified), learning mathematics is not very different from learning in other
disciplines; the LPM works effectively as a strategy in nearly any context. This activity will focus on
applying the LPM for learning in quantitative areas as well as quantitative problem solving.
L
earning Goals
What you should learn while completing this activity
1. Learn to be your own researcher when it comes to your thinking and your mind’s performance.
2. Effectively use the LPM for mathematical learning by strengthening critical thinking skills.
3. Focus on your own thinking process in relation to learning and problem solving in order to elevate
your level of learner knowledge.
4. Learn ten techniques to address the top challenges in learning mathematics.
D
iscovery
Finding out for yourself
What has made learning mathematics difficult for you? Do some brainstorming and ask others what
gave them trouble when it came to learning mathematics. Put together a list of
Top 10 Stumbling Blocks
for Learning Mathematics
. Bring this to class.
Now shift focus and think about something in mathematics (a topic, idea, process, etc.) that you already
understand and fill out the following Metacognition form.