Week 5: What’s the relationship between teaching and learning?

Ah, the old age question of education.  There’s an inside saying among the math teachers at our school… we can teach students things, but we can’t make them learn!  We jokingly relate it to the “you can lead a horse to water” idiom, but we would like to change the phrase “but you can’t make them drink” to “we will DUNK them (hand gesture of pushing a head down)”.  We, of course, knowingly say this because we would like our students to learn the material we teach them, but math is not everyone’s favorite subject, or liked subject, or widely used subject (beyond 8th grade math).  So how do you have students learn math?  I (obviously?) teach math.  How do I get students to buy into and be motivated to learn math?  If I knew, I would be the next multi-billionaire.  🙂

After reading the chapter on teaching in Invent to Learn, I have come to some interesting, depressing, and insightful aha moments.  I am an instructionist.  I teach facts, show how to solve problems, and have students practice. (Martinez, 2016)  I suppose math lends itself to this type of teaching, and most textbooks I have seen have a similar approach.  The depressing aha moment is that I have what is called “habitus”.  I look back on my learning of math and base most my instruction on this.  I suppose I don’t realize that everyone is not like me, or wired like me, or thinks like me.  How can a student not understand a math concept the way I taught them?  I learned it that way!  I need to modify my instruction to create more avenues for learning.  I hope making is one of them.  It brings tactile, motor, and problem solving skills together.

What is my teacher identity?  I’ve never given much though about this, though it is real.  There are multiple definitions of teacher identity.  The one I can relate to is described by Randolph A. Philip.  He wrote a chapter titled Mathematics Teachers’ and Beliefs and Affect. “Teachers know; teachers believe; teachers feel; teachers participate; teachers belong.”  All these describe a teacher’s identity.  I cannot describe all aspects of this to define MY teacher identity, but it’s good to know that I do feel it can be modified and expanded. A view that is shared by Bjuland at the conclusion of his study of an elementary teacher’s teacher identity. (2012)

I do look for ways to improve ways to teach math at the high school level.  I give thoughtful reflection on what works in class, and what doesn’t.  I try new things to determine value, effectiveness, and success.  After 21 years of teaching math, you would thing I have exhausted ideas… NOT!  For that matter, found the perfect pedagogy for teaching upper level math… NOT!  But I do believe there will be a way to have students learn math that will not be dependent on the math instructor as sole provider of information.  I tend to believe that students DO feel this way.  “You have to teach me.”  “It’s your job.”  “That’s what you get paid for.”

If there was way for any individual to learn content easily (K-12 education), it would make our lives easier, wouldn’t it?  I am beginning to like phrases like “teacher as facilitator”.  Begin having more student-centered learning.  Having more maker spaces.  Having students excited about learning.  That’s what education should be. It’s not about the teacher.  It’s about the student.  Someday…


peanuts-math-cartoon               cartoon6371cartoon5.gif


Martinez, Sylvia Libow; Stager, Gary S.. Invent To Learn: Making, Tinkering, and Engineering in the Classroom (Kindle Locations 1658-1662). Constructing Modern Knowledge Press. Kindle Edition.

Bjuland, R., Cestari, M., Borgersen, H. (2012). Professional Mathematics Teacher Identity: analysis of reflective narratives from discourses and activities. [electronic file]. J Math Teacher Educ, DOI 10.1007/s10857-012-9216-1. Retrieved from http://brage.bibsys.no/xmlui/bitstream/handle/11250/138188/Cestari_2012_Professional.pdf?sequence=1&isAllowed=y

Philipp, R. (unknown date). Chapter 7: Mathematics Teachers’ Beliefs and Affects. Teachers and Teaching. [electronic file]. Retrieved from http://www.sci.sdsu.edu/crmse/STEP/documents/R.Philipp,Beliefs%26Affect.pdf



2 thoughts on “Week 5: What’s the relationship between teaching and learning?

  1. Gerald,
    I share your feelings about being an instructionist and teaching the way my brain works, which is in a structured and linear fashion. I shared in my post that 99% of my teachers from kindergarten through college taught using direct instruction in a model where they were the experts. That is what I’m comfortable with, and I realize that these classes are pushing me to mix things up a bit to appeal to my students’ many different learning styles. I feel like we as teachers have to modify our teaching to make learning more engaging to our students so that they are motivated to learn and are excited by it. It is hard to do so when we have to teach to the standards and deal with behaviors also. I agree with you that Making seems to have real possibility as a way of promoting problem solving skills with our students, and if they are engaged, negative behaviors should decrease. Your thoughts about how you can’t make kids learn made me think of a web site I ran across of how one teacher changed her math teaching practices to help her students who didn’t feel successful in math class: http://www.coolmath.com/0-teacher-success-area-prealgebra-algebra-precalculus. I appreciate knowing that I’m not alone in trying to assimilate this new knowledge with my habitual way of teaching.


  2. Gerald-
    Your post made me smile. I like how you are able to put so much of your personality in your writing. I wrote about my first experience with changing my “habitus” for EDET 637. I was teaching freshman biology and couldn’t use the textbook due to the gross amount of misinformation printed in it. I was forced to modify my teaching style to fit my resources. Here is a link describing the process:
    This doesn’t mean that I don’t feel that direct instruction doesn’t have a place in the classroom. In fact, I asked for special permission to be trained in Reading Mastery, an SRA direct instruction reading program, when I was teaching primary students in the Lake and Peninsula School District. In that situation, the curriculum and the instructional method were highly effective. I think effective teaching is mostly about knowing your students and their needs, then doing your best to provide for what they need. The simple fact that you are saying, “Hey, I’ve been doing this for more than 20 years, I think I know best,” speaks volumes about the type of teacher you are.
    P.S. I love the cartoons at the bottom of the post!

    Liked by 1 person

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