You are here

Primary Source Projects and Reading Apprenticeship in Mathematics History: Summary and Application

Jennifer Clinkenbeard (California State University, Monterey Bay)


PSPs are a useful, classroom-ready resource for students and instructors to engage in learning mathematics via primary sources. Yet, students may still struggle to engage with the text, especially when they are still developing their own ability to read and comprehend written mathematics. Reading Apprenticeship routines can support students by providing the “missing piece” of explicitly teaching reading strategies, routines, and practices that are needed to make sense of a PSP. Used in concert, RA routines and PSPs can support student learning and engagement.

The RA routines presented in this paper are the “Talk to the Text” routine and metacognitive reading logs. These are introductory routines for instructors that can be used in a wide variety of settings. In the PSP tasks presented, the RA routines were mostly used to make sense of the original historical language in the PSPs before working through the guided reading tasks in the PSPs. These RA routines were particularly helpful for students when making sense of the transition from rhetorical to symbolic algebra, as in al-Khwārizmī’s and Bhāskara I’s work in the first and third examples, respectively. The second and third examples both utilize a metacognitive reading log approach, but with the difference that in the third example, the student is using the routine without being prompted by the instructor.

A brief description of additional RA routines that can be adapted to a variety of contexts, including PSPs, is given in Table 3 below. These routines are taken from Reading for Understanding: How Reading Apprenticeship Improves Disciplinary Learning in Secondary and College Classrooms [Schoenbach, Greenleaf, and Murphy 2016]. The sample student work and questionnaire responses presented in this article suggest that RA routines such as these and PSPs complement one another when used in the classroom.

Table 3. Additional sample RA routines.

RA routine

Brief Description

Think Aloud

The verbal version of Talk to the Text. Students experience being deliberately metacognitive by thinking out loud about their reading processes with a partner. Pairs and then the whole group consider the range of ways students interact with the text and how it helped them build understanding. [p. 105]

Twenty-five Word Abstract

Students write a twenty-five word summary to focus on what is most important in the text. Students take turns presenting their abstracts to group members, then write a group abstract of twenty-five words or less. Groups rate one anothers’ abstracts and choose a “best summary.” [p. 223]

Math Solution Summary Analysis by a Peer

Students trade solutions, read their partner’s solution, and answer the following questions: Can you follow the solution in math form? Written explanation? Does the answer seem reasonable? Has the original question been answered completely? Is there anything additional needed, or anything unimportant that should be taken out? Partners discuss and revise their work based on the feedback. [p. 220]

The RA examples presented here may help students be more effective and open to exploring primary sources as well as perhaps to seeing the value in doing so. Using RA as a tool for students to access primary historical sources in mathematics gives students an explicit framework for making sense of mathematical texts that they can also apply to modern textbooks. Using PSPs and RAs together is a timely strategy as the move towards “alternative” assessment methods that promote equity and inclusion gains momentum and support in our learning institutions. Such assessment methods are more likely to be adapted by instructors if they are both effective for student learning and manageable for the instructor to learn about and implement. Readers are encouraged to download the PSPs and RA routines presented in this article and to adapt these tools for their own classrooms. The samples of student work may offer insight into how the methods could be applied in the classroom and what instructors might expect when planning their own courses. 

Jennifer Clinkenbeard (California State University, Monterey Bay), "Primary Source Projects and Reading Apprenticeship in Mathematics History: Summary and Application," Convergence (November 2023)