Math Lessons for Life

Looking back at what I have learned over these past several weeks of Intermediate Math Methods, I realize that I've gained some specific math knowledge, as well as quite a bit of general knowledge that could be applied to any aspect of teaching.  I have appreciated this aspect of our instructor's teaching-- it is not all just about math. 

My top five "take-aways" are:

1. There is more than one way to solve a problem.  As teachers, we need to allow our students the opportunity to discover the method that brings true meaning to them.  We also must provide opportunities for them to discuss and share their learning so that they might be able to enrich the understanding of those around them.
2. Learning that is based on real-world problems motivates students to dig deep for answers.  Offering them relevant problems allows students to see the authentic need to apply what they know and find a solution. 
3. Technology can expand one's ability to represent data and mathematical concepts.  It is vital to incorporate it into the classroom, particularly the math classroom.
4. Manipulatives can bridge the gap between the concrete and the abstract.  By bringing manipulatives into the math classroom, we no longer ask students to learn something beginning with the abstract concept.  They are valuable for all types and ages of learners, though some learners certainly benefit more than others from their use.
5. One must be patient while developing from an acorn into an oak tree.  It takes time to become  a teacher who is comfortable and proficient enough to adapt the curriculum to genuinely meet the needs of your class.

And if I had to add one more, it would be that while my goal for teaching is that the students understand the content, I cannot measure their understanding, so it is not a proper word to use in my teaching objectives.

My suggestions for improvement of this course come from re-reading the course purpose (or objectives) in the syllabus:

Purpose
The purpose of this class is to understand math as a way to understand the world while also understanding how the concerns of science, math, technology, and society are integrated.  You will also learn (1) to design lesson, unit, and year-long plans based on Washington’s Math Standards requirements as well as national standards, (2) to formally and informally assess students’ science or mathematics content knowledge and (3) adapt instruction according to students’ needs and learning.

I believe that we covered a part of #1-- but I do not feel quite ready to design year-long lesson plans!  I would like to have become more familiar with the state and national standards.  I also feel a bit under-prepared in the area of formally and informally assessing students' mathematics content knowledge.  And I feel least prepared in the third area of being able to adapt instuction according to students' needs and learning.  I think that we could have had more instruction and practice in differentiating instruction as well as in current methods/standards of assessment.  I would gladly have traded an assignment in those areas for the i-Touch application reviews, which were incredibly time-consuming, and relatively useless.  I did find the virtual manipulatives review to be useful, and will certainly use that as a tool to differentiate my instruction.

Many lessons learned... for math, and for life.  Thanks, Robin!