As noted in my initial statement of interest, my research interests lie in three major overlapping areas: teachers’ use of digital mathematics curriculum materials, students’ use of digital visualizations and manipulatives in mathematics learning, and the relationship between elementary mathematics and computational thinking. For the sake of keeping the historical overview manageable and coherent, in the first section below I focus on the first of these interests – teachers’ use of curriculum materials and how the increasing availability of technology has influenced related research. In the second section, I continue to focus on curriculum materials but also briefly discuss current approaches to research my other two areas of interest.
Changes in research over the last 25 years
The development and dissemination of curriculum materials has been a common strategy for influencing classroom instruction for many years, dating as far back as the 1960s (Ball & Cohen, 1996). This strategy became particularly prevalent in mathematics classrooms after the 1989 release of the National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards for School Mathematics (the Standards). This document detailed new, ambitious standards for the mathematics content to be learned and problem-solving goals to be attained by all students. The release of the document then prompted the National Science Foundation to fund the development of curriculum materials designed to help students and teachers reach the Standards (Senk & Thompson, 2003).
The development of a multitude of Standards-based curriculum materials led to a long tradition of research on how use of curriculum materials affects classroom practice and student learning. Early research on the influence of Standards-based materials tended to take a positivist, experimental approach, using curriculum materials as the independent variable and student achievement as the dependent variable. A study by Reys, Reys, Lapan, Holliday, and Wasman (2003) exemplifies this style of research. Reys and colleagues compared the performance of students on the mathematics portion a state-mandated achievement test according to whether their teachers used traditional or Standards-based curriculum materials to guide their instruction. When significant differences existed in the measures of achievement, the differences were in favor of the students using the Standards-based materials.
Although many such studies showed similarly positive results, the increases in student achievement were not as large or consistent as researchers and developers had hoped. In response, Ball and Cohen (1996) proposed that a factor limiting the influence of curriculum materials was the lack of attention to the role of the teacher. They argued that teachers necessarily make adaptations to curriculum materials as they enact them in their classrooms. Research on use of curriculum materials subsequently shifted from a focus on whether curriculum materials directly influence student achievement – a positivist frame – to a focus on ways in which teachers interpret curriculum materials as they teach – an interpretivist frame. A study by Choppin (2011) is a good example of the latter. Choppin provided a rich description of the ways in which three teachers interpreted and adapted the same set of curriculum materials. He found, for example, that none of the three teachers tended to add or subtract tasks from the lessons presented in the curriculum materials, but they all adapted tasks by adding scaffolding for students as needed. Additionally, only one of the three teachers described adaptations based on student thinking; the others spoke of practical reasons for their adaptations. Studies like Choppin’s contributed to the field’s understanding of the factors that influence the ways in which teachers enact curriculum materials, including their particular classroom contexts, beliefs about teaching, and mathematics knowledge.
Recent research on use of mathematics curriculum materials continues to mostly use an interpretivist frame, focusing on how a small number of teachers interact with the materials and providing detailed descriptions of their process of enactment. The increase in access to technology in schools and classrooms, however, has led to an interesting trend in curriculum research. Namely, several researchers focused on the ways that technology can position teachers as creators of curriculum materials as well as interpreters. A number of studies illustrate this current trend. For example, de Araujo, Otten, and Birisci (2017) described one teachers’ creation of videos that replaced the print textbook when she enacted a flipped classroom model. Relatedly, Gueudet, Pepin, Sabra, and Trouche (2016) studied a group of teachers who collectively developed an e-textbook via an online discussion platform. Moreover, Hoyles, Noss, Vahey, and Roschelle (2013) deliberately designed a set of curriculum materials to be open-ended and invite teachers’ adaptations, positioning the teachers as co-creators of the materials. They studied the ways in which the adaptable materials led to teachers’ further design work as they enacted the materials in their classrooms.
Thus, over the last 25 years or so, research on the influence of mathematics curriculum materials has evolved considerably. Early in this period, studies minimized or ignored the role of the teacher (Reys et al., 2003). Later, studies began to recognize and describe the influence of the teacher in curriculum enactment (Choppin, 2011). Recently, studies have begun to highlight how technology can change the role of the teacher in relation to curriculum materials – usually showing a shift in teachers’ roles from interpreter to creator (de Araujo et al., 2017; Gueudet et al., 2016; Hoyles et al. 2013).
Contemporary approaches to research
As stated above, the development and dissemination of mathematics curriculum materials is often for the purpose of promoting widespread change in classroom practice. This remains true for the case of digital curriculum materials, and so modern studies of teachers’ use of these materials tend to share a theme of investigating how to help all teachers – not just the most skilled or most enthusiastic teachers – to make changes to their practice that take advantage of the transformative technology features of the materials. Researchers, however, take varying approaches to exploring how to support widespread use.
One approach is to involve teachers in the design and development of the curriculum resources. Hoyles et al.’s (2013) study, mentioned in the historical overview above, is one example of this approach; this research group promoted teacher involvement in the resource design by deliberately making the tool open ended and adaptable. In a related approach, Hansen, Mavrikis, and Geraniou (2016) co-designed a manipulative with teachers through a series of professional development workshops and field testing in the teachers’ classrooms. Both research groups reported their results in terms of how teacher involvement in design led to changes in teacher practice, and offer suggestions at the end of their articles about how their processes might be replicated in the development of other curriculum resources to encourage teachers to use them in transformative ways.
A second approach to researching ways to support widespread change in teacher practice is to study teachers who may be less enthusiastic about the prospect of using technology in their teaching. Drijvers, Tacoma, Besamusca, Doorman, and Boon (2013) took this approach. They choose to study teachers who they termed mid-adopting, or those who are not early, enthusiastic adopters of technology but rather later adopters who are willing to try technology but skeptical of its utility. Drijvers and colleagues argue that the early adopters who are the research participants in many studies are an “important minority,” but “[f]or a widespread integration, these mid-adopters are the critical group” (Drijvers et al., 2013, p. 987). Their research focuses on developing ways to support these teachers.
Lastly, a third approach to supporting widespread change via use of curriculum materials is to examine how communities of practice can provide ongoing support for teachers. A study by Pepin, Guedet, and Trouche (2017) exemplifies this approach. In their study, Pepin and colleagues examined how several teachers used digital resources to develop their design capacity, both individually, and collectively via online discussion forums. In the conclusion of the article, Pepin et al. argued that the availability of online resources, including the discussion forums, led teachers to develop new design principles for their instruction. Although the researchers do not explicitly state this, I interpret this claim to have implications for widespread change in teacher practice. Specifically, teachers’ development of new design principles would seem to be evidence that the online discussions – something widely available to teachers – could support widespread changes in classroom practice.
I now briefly address contemporary approaches to research in my other areas of interest: digital mathematics manipulatives, and the integration of computational thinking into mathematics instruction at the elementary level.
I have identified three complementary approaches to the study of digital manipulatives in and their influence on student learning. First, some researchers have chosen to directly examine the relationship of specific affordances of the manipulatives (e.g., linked representations) to varying types of student outcomes, including achievement (Moyer-Packenham & Westenskow, 2013) and discourse patterns (Anderson-Pence & Moyer-Packenham, 2016). Second, in a parallel approach to studies of curriculum materials, some researchers focus studies of digital manipulatives on the ways in which teachers use them in instruction, rather than linking the manipulatives directly to student outcomes (Moyer-Packenham, Salkind, & Bolyard, 2008). Lastly, other researchers have suggested digital manipulatives as a direct replacement of their physical counterparts and examined the effects of those replacements on student learning (Bouck et al., 2017).
Similarly, I have identified three approaches to the study of computational thinking (CT) and its relationship to mathematics, although it should be noted that not all of these studies focus specifically on the elementary level. First, some researchers have focused their studies of CT integration on teachers, examining their experiences in professional development (PD) workshops and their subsequent ways of applying what they learned in PD (Duncan, Bell, & Atlas, 2017). Second, other researchers have approached the study of CT integration by designing and testing specific instructional activities that attempt to address both CT and other subjects (Tatar, Harrison, Stewart, Frisina, & Musaeus, 2017). Lastly, some researchers have examined conceptual and theoretical parallels between mathematics and computer science and how these parallels might impact instruction in each discipline (Hazzan & Zazkis, 2005). Although this last approach does not directly address the process or effects of integrating instruction, the results of such studies, in my opinion, provide useful information for future integration efforts.
References
Anderson-Pence, K., & Moyer-Packenham, P. (2016). The Influence of Different Virtual Manipulative Types on Student-Led Techno-Mathematical Discourse. Journal of Computers in Mathematics and Science Teaching, 35(1), 5–31.
Ball, D. L., & Cohen, D. K. (1996). Reform by the Book: What Is -- or Might Be -- the Role of Curriculum Materials in Teacher Learning and Instructional Reform? Educational Researcher, 25(9), 6–8, 14.
Bouck, E. C., Park, J., Sprick, J., Shurr, J., Bassette, L., & Whorley, A. (2017). Using the virtual-abstract instructional sequence to teach addition of fractions. Research in Developmental Disabilities, 70(June), 163–174. https://doi.org/10.1016/j.ridd.2017.09.002
Choppin, J. (2011). Learned adaptations: Teachers’ understanding and use of curriculum resources. Journal of Mathematics Teacher Education, 14(5), 331–353. https://doi.org/10.1007/s10857-011-9170-3
de Araujo, Z., Otten, S., & Birisci, S. (2017). Teacher-created videos in a flipped mathematics class: digital curriculum materials or lesson enactments? ZDM - Mathematics Education, 49(5), 687–699. https://doi.org/10.1007/s11858-017-0872-6
Drijvers, P., Tacoma, S., Besamusca, A., Doorman, M., & Boon, P. (2013). Digital resources inviting changes in mid-adopting teachers’ practices and orchestrations. ZDM - International Journal on Mathematics Education, 45(7), 987–1001. https://doi.org/10.1007/s11858-013-0535-1
Duncan, C., Bell, T., & Atlas, J. (2017). What do the Teachers Think ? Introducing Computational Thinking in the Primary School Curriculum. In Proceedings of the Nineteenth Australasian Computing Education Conference (pp. 65–74).
Gueudet, G., Pepin, B., Sabra, H., & Trouche, L. (2016). Collective design of an e-textbook: teachers’ collective documentation. Journal of Mathematics Teacher Education, 19(2–3), 187–203. https://doi.org/10.1007/s10857-015-9331-x
Hansen, A., Mavrikis, M., & Geraniou, E. (2016). Supporting teachers’ technological pedagogical content knowledge of fractions through co-designing a virtual manipulative. Journal of Mathematics Teacher Education, 19(2–3), 205–226. https://doi.org/10.1007/s10857-016-9344-0
Hazzan, O., & Zazkis, R. (2005). Reducing Abstraction : The Case of School Mathematics. Educational Studies in Mathematics, 58(1), 101–119.
Hoyles, C., Noss, R., Vahey, P., & Roschelle, J. (2013). Cornerstone Mathematics: Designing digital technology for teacher adaptation and scaling. ZDM - International Journal on Mathematics Education, 45(7), 1057–1070. https://doi.org/10.1007/s11858-013-0540-4
Moyer-Packenham, P. S., Salkind, G., & Bolyard, J. J. (2008). Virtual Manipulatives Used by K-8 Teachers for Mathematics Instruction: Considering Mathematical, Cognitive, and Pedagogical Fidelity. Contemporary Issues in Technology and Teacher Education, 8(3), 202–218.
Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of Virtual Manipulatives on Student Achievement and Mathematics Learning. International Journal of Virtual and Personal Learning Environments, 4(3), 35–50. https://doi.org/10.4018/jvple.2013070103
Pepin, B., Gueudet, G., & Trouche, L. (2017). Refining teacher design capacity: Mathematics teachers’ interactions with digital curriculum resources. ZDM - Mathematics Education, 49(5), 799–812. https://doi.org/10.1007/s11858-017-0870-8
Reys, R., Reys, B., Lapan, R., Holliday, G., & Wasman, D. (2003). Assessing the Impact of Standards- Based Middle Grades Mathematics Curriculum Materials on Student Achievement. Journal for Research in Mathematics Education, 34(1), 74–95.
Senk, S. L., & Thompson, D. R. (2003). School Mathematics Curricula: Recommendations and Issues. In Standards-Based School Mathematics Curricula: What Are They? What Do Students Learn? (pp. 3–27). New York: Routledge.
Tatar, D., Harrison, S., Stewart, M., Frisina, C., & Musaeus, P. (2017). Proto-computational Thinking: The Uncomfortable Underpinnings. In P. J. Rich & C. B. Hodges (Eds.), Emerging Research, Practice, and Policy on Computational Thinking (pp. 63–81). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-52691-1