Feedback on Isaak deMaio's dissertation

Constructs:

• Frayer model
• van Hiele levels of geometric thought

“What are the relations between students’ van Hiele levels of reasoning on triangle congruence proofs, as demonstrated in their Frayer Model work, their proof-writing achievement, and their performance on Interim and JMAP assessments?”

1 What are students’ van Hiele levels of reasoning, as demonstrated in their Frayer Model work[,] on triangle congruence proofs?
2 To what extent do students’ van Hiele levels of reasoning, as demonstrated in their Frayer Model work, predict or relate to their performance on formative and summative assessments?
3 What is the relationship between students’ mastery of geometric vocabulary, as evidenced by Frayer Models, and their overall performance on unit assessments and progression through van Hiele levels?

From results chapter:

1. To what extent does explicit instruction combined with the use of Frayer Models for key vocabulary terms influence students’ ability to access Euclidean geometry concepts and curriculum?
2. In what ways do students demonstrate understanding and application of geometric vocabulary through Frayer Models in classwork and assessments?
3. What is the relationship between students’ mastery of geometric vocabulary, as evidenced by Frayer Models, and their overall performance on unit assessments and progression through van Hiele levels?

Research questions

It seems that different questions make different assumptions:

• RQ1 treats van Hiele levels as a latent variable which can be measured by Frayer Model work.
• RQ2 asks (van Hiele -> formative) and (van Hiele -> summative), operationalized as (Frayer -> formative) and (Frayer -> summative)
• RQ3 asks (Frayer -> formative) and (Frayer -> summative)

The research questions presented in the results chapter are different from those in the introduction.

Language and thought

This research is really about the relationship between language and mathematical thought. We have a confound if the assessment of mathematical thought is in linguistic terms. This is embedded in:

“The Frayer Model … may provide students with the language necessary to articulate their understanding, thereby fostering deeper conceptual connections” (p. 17).

“the Frayer Model provides students with the linguistic precision necessary to engage in higher-order thinking and proof-based reasoning” (p. 30).

Does language allow articulation of existing understandings, or does it support construction of understandings? Piaget and Vygotsky, both cited in the literature review, engage this question substantially.

Methods

There are too many measures. Can you explain the difference between how you assess Frayer model scores and van Hiele scores? Figures 3 and 4 suggest that van Hiele levels are treated as latent varialbes meansured using Frayer scores as observed varialbes. But then the regression of van Hiele level on Frayer scores doesn’t make sense to me.

Results

Table 9 has the core findings. How do we know there are not confounds (as suggested by the clustering algorithm).

Minor issues

• Duplicated text, first paragraph of lit review, p. 10
• The connection to science of reading is tenuous. that’s more about how people learn to read, specifically phonics.