Journal: Homeostasis and Having Kittens (9/8/2020)
Research Reflection: Teacher beliefs are not enough: A response to Campbell et al. (2004)

Tuesday 9/8/2020
Journal: Homeostasis and Having Kittens (9/8/2020)

Homeostasis is the brain’s desire to return to equilibrium. When the brain is in a state of equilibrium it can learn new things, creating new neural pathways between experiences.

Now that I’m three weeks into my doctoral program I’ve, in some ways, reached a sort of homeostasis. I’ve at least achieved a routine. Monday, Tuesday, and Wednesday evenings are reserved for my classes, while the rest of the week I am working on said classes. I’ve been utilizing the slow cooker so the family can eat dinner that I prepare during the day. I try to make sure to read scholarly work for at least an hour a day so I don’t fall behind.

Speaking of which, spending so much time reading research articles has been interesting, but continues to plague me with decision paralysis. The ur-premise of Necessary Conditions is that math teaching and learning is incredibly complex. It’s easy therefore to get into “research sprawl.” You try to read about a particular topic and find six more papers to follow up on. Pretty soon you’re like that classic Shell Centre task, “Having Kittens”: each paper you read can beget several more papers, which beget several more again. 

That said, I’m starting (key word: starting) to develop my final papers which may turn into the genesis of dissertation research. I’ll share them here, but please don’t hold me to them:

Potential Topics for EMAT5100 (Theory & Research in Learning and Development) :

  • Literature Review of Persistent Problem Solving, Productive Struggle, and their relationship to Inquiry
  • The Eight Common Core Standards of Mathematical Practice: What are they? How are teachers interpreting them? How can we teach them? How can we assess them?

Potential Topics for EMAT5800 (Culture, Power, and Identity in Math Education): 

  • Culturally Relevant Assessment (or, Assessing with a Lens of Social Justice)
  • A literature review of cradle-to-classroom teaching: How do early experiences with mathematics result in or inhibit a more diverse teaching talent pipeline?

If you have ideas or key papers for any of these topics, feel free to email me or add ‘em in the comments!

Thursday 9/10/2020
Teacher beliefs are not enough: A response to Campbell et al. (2004)

Campbell et al. (2014) is a voluminous study that correlates teacher knowledge, teacher pedagogical knowledge, beliefs and understanding about student mathematics dispositions, and student achievement. The researchers administered tests and questionnaires to teachers and math assessments to their elementary and early middle school pupils. The headline of the article is (I think), that student achievement on the assessments are correlated with their teachers’ high level of math content and pedagogical knowledge. This is a result shown in Ball et al. (200x) among other studies. 

However, there is another additional nugget of insight that I found particularly interesting and one that I need to chew on a bit more. The researchers also measured a factor around “teacher beliefs.” These are beliefs held by the teacher that adhere to peer-reviewed best practices. The authors define the “teacher beliefs” factor as the following three mindsets and teachers dispositions:

  1. Teachers should allow students to struggle (from Hiebert and Grouws, 2007)
  2. Teachers should explicitly model activities (from Battista, 2001)
  3. The teachers claim to know or desire to seek out students’ mathematical dispositions (from Goddard, Hoy, & Hoy, 2000)

(A quick aside: the first two factors often appear contradictory in professional development, conference presentations and TED talks, but oughtn’t be. This might be an entire separate post.)

Regarding teacher beliefs and students achievement, what I found particularly interesting was the following: Teacher beliefs about student capabilities had a significant impact on student achievement only if they also had a high level of prerequisite content and pedagogical knowledge.  

Teachers who had those nice and good beliefs didn’t actually move the needle in student achievement unless they had the requisite math knowledge (content and teaching). The reason I find this interesting is that much of our district level professional development, departmental PLCs, and even conference sessions focus laserlike on teacher beliefs. We’ve all been to sessions on growth mindset, grit, productive struggle, active caring, etc. These are very well productive, provided the attending teachers also have the math teaching chops. 
The next time you’re attending or delivering a session focused on teacher beliefs and mindsets and crucial that is to student growth, toss some mathematics in. That’s actually best practice.


Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing Mathematics for Teaching. American Educator, 29(1), 14-17,20-22,43-46.

Battista, M. T. (2001). How do children learn mathematics? Research and reform in mathematics education. In T. Loveless (Ed.), The great curriculum debate: How should we teach reading and math? (pp. 42–84). Washington, DC: Brookings Press.

Campbell, P. F., Nishio, M., Smith, T. M., Clark, L. M., Conant, D. L., Rust, A. H., DePiper, J. N., Frank, T. J., Griffin, M. J., & Choi, Y. (2014). The Relationship Between Teachers’ Mathematical Content and Pedagogical Knowledge, Teachers’ Perceptions, and Student Achievement. Journal for Research in Mathematics Education, 45(4), 419–459. 

Goddard, R. D., Hoy, W. K., & Hoy, A. W. (2000). Collective teacher efficacy: Its meaning, measure, and impact on student achievement. American Educational Research Journal, 37(2), 479–507.

Hiebert, J. S., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 371–404). Charlotte, NC: Information Age.