Reading Apprenticeship Inspired Assignment or Lesson
Reading Apprenticeship Inspired Assignment or Lesson
Using Benjamin Wardhaugh’s terminology [2010], a primary source is created “at the time.” Primary sources are our only direct sources of information about the historical period. They may be artifacts other than written texts, such as photographs or sound recordings. Wardhaugh gives Isaac Newton’s Principia Mathematica as an example of a primary source. Although modern readers will typically read a translation of Newton’s Latin original, reading Principia in its original language gives the reader the opportunity to read Newton’s ideas as he presented them. Primary sources require the reader to slow down and carefully consider not only what writers knew, but how they knew it and why they understood what they knew the way that their presentations suggest they did.
The Reading Apprenticeship (RA) framework is an excellent tool to further support and scaffold explicit instruction in reading historical mathematics. Overlaying RA routines on a PSP’s written materials can provide students with concrete mechanisms for discerning mathematical and historical meaning from the primary source excerpts in a PSP. In other words, the role of RA routines is to facilitate students’ engagement with the PSP materials and with one another during classroom discussion.
We consistently used “Talk to the Text” as an RA routine when working on PSPs throughout the semester.
(This text is taken from my paper published in 2023 in Convergence - Primary Source Projects and Reading Apprenticeship in Mathematics History: Using Primary Sources to Teach Mathematics.)
Week 8 - Introduce Talk to the Text in the context of the first PSP, From the Roots of Algebra. Instructor models the routine, then students follow up with an individual TTText on another text excerpt within the PSP.
Week 12, Day 1 - Students read aloud text from the second PSP, Gaussian Guesswork, one phrase at a time as a whole class. Instructor thinks aloud and annotates based on what the students read.
Week 12, Day 2 - Instructor reads aloud text from the third PSP, Agnesi on the Product Rule, one phrase at a time as a whole class. Students think aloud and annotate based on what the instructor read.
Week 14 - Students take turns reading and thinking aloud from the fourth and final PSP, Archimedes’ Measurement of a Circle. Instructor role is only to mark off each phrase so that students know “their” text excerpt to read and think aloud on.
We surveyed students at the end of the semester about their experiences with RA routines and PSPs. Anonymized responses can be viewed here.
Please see excerpts from student responses in the survey below (emphasis added).
I was able to use note-taking techniques involving asking questions and reinterpreting text to help make sense of the primary source sections in the PSP projects. These sections were difficult to parse using traditional direct reading techniques, so having alternate ways of making sense of them was helpful in interpreting them.
Writing out what we read in our own words was very helpful in terms of solidifying our understanding of the material (especially in al-Khwarizmi’s work). Also, doing this as a class helped us to all understand it correctly, because it was truly hard to understand alone.
Using Reading Apprenticeship routines, such as Talk to the Text, help me make sense of the PSPs because it helped me understand the ideas by writing down what I thought each section meant of a paragraph which helped me understand the big ideas one piece at a time.
Analyzing the PSP's using tools such as Talk to the Text had helped me break down what the original author was trying to say. Due to the different use of language from our modern sense compared to the time period of the author, it was difficult to make sense of the text all at once. So by analyzing the text piece by piece, I could recognize what the author was teaching.
The RA routines are part of the PSP lessons. It’s hard to say exactly how long it takes, since it’s just part of the lesson plan. Each of these PSPs took 1-2 class days to fully implement (1 hour 50 minute sessions).
Otero, Danny, "Completing the Square: From the Roots of Algebra" (2019). Pre-calculus and Trigonometry. 4.
https://digitalcommons.ursinus.edu/triumphs_precalc/4
Barnett, Janet Heine, "Gaussian Guesswork: Infinite Sequences and the Arithmetic-Geometric Mean" (2017). Calculus. 2.
https://digitalcommons.ursinus.edu/triumphs_calculus/2
Monks, Kenneth M., "Three Hundred Years of Helping Others: Maria Gaetana Agnesi on the Product Rule" (2023). Calculus. 23.
https://digitalcommons.ursinus.edu/triumphs_calculus/23
(Preprint) Clinkenbeard, J. & Bonsangue, M. “Archimedes’ Measurement of a Circle.” Geometry. 2024.
https://drive.google.com/file/d/1o7wvSnkHSj2U-s06CqaT-iiWdmtgP7Al/view?usp=sharing
Paper published in 2023 in Convergence - Primary Source Projects and Reading Apprenticeship in Mathematics History: Using Primary Sources to Teach Mathematics. The routines in the paper are Talk to the Text and a Metacognitive Reading Log. Sample student work is included as part of the paper. There is also a student survey that can be adapted for other course contexts.
Workshop from August 2024 MathFest session: On the Shoulders of Giants: Teaching and Learning Mathematics from Primary Historical Sources. Co-authored by J. Clinkenbeard with Edwards, A., Monks, K., Otero, D., Parker, A., and Saclolo, M. This workshop is for conference participants (mostly math faculty) to learn more about primary source projects and to be introduced to the RA pedagogy and sample routines within that context. RA routines included are: Articulating reading strategies; Think-Aloud; and Talk to the Text.
