Over the last decade, social media has become a component of the lives of nearly two-thirds of American adults [1
]. This is an almost ten-fold increase since 2005. It is particularly popular with adults aged 18–29 years with 90% reporting to use it. Although social media sites were designed for purposes not necessarily germane to education, some have started to become tools for teachers. In particular, research has shown that the website Pinterest has become a popular resource for teachers at all levels [2
]. In a survey of mathematics and English language arts teachers, 87% of elementary and 62% of secondary teachers reported that they consulted Pinterest when planning lessons [2
]. Moreover, these teachers consulted Pinterest more often than websites designed specifically for mathematics instruction such as corestandards.org, illuminations.nctm.org, and engageny.org. Overall, the only site more popular than Pinterest was Google.
Just what is Pinterest and why is it popular with teachers? In contrast to social networking sites, which focus on individuals interacting and exchanging information with each other, Pinterest is a kind of social bookmarking site. Users create, organize, and share content by creating visual bookmarks called pins. These visual bookmarks link to various online resources including webpages, pictures, and videos. Once a pin is created, it can be discovered by other users via keyword searches, saved to a collection of similar pins called a board, liked, or commented on. The act of saving a pin to a board is known as a repin. Users typically design Pinterest boards around a central theme (e.g., mathematical topic). This makes the boards a space for organizing online content as well as a means for providing other users with easy access to a collection of teaching ideas.
The visual layout of the Pinterest feed is designed to allow the user to easily browse through many pins quickly. However, the feed itself provides little information for evaluation of a particular pin. As shown in Figure 1
, within a feed, each bookmark contains basic information about a pin including an image from the linked content, a title, the name of the pin creator, and a number indicating repin activity. Apart from these details, no other information is provided within the feed.
Understanding the content of Pinterest is a critical issue in mathematics education. Given that mathematics teachers are already using Pinterest in their practice [2
], there is a need for our community to provide guidance to inform this decision-making process. Initial educational research concerning Pinterest has been focused on understanding how teachers are using the website [3
]. These studies can provide information on how individuals incorporate features of Pinterest into their practice. Missing, however, is an understanding of the mathematical content that the teachers are actually viewing when they use the site. To take initial steps in understanding Pinterest as a curriculum resource for mathematics, we conducted a research project focused on available negative integer resources.
Framing Our Work
Within this article, we adopt the lens of connectivism, which builds on principles from theories concerning networks, chaos, self-organization, and complexity. Drawing from this lens, we view learning as “a process that occurs within nebulous environments of shifting core elements—not entirely under the control of the individual” [7
] (paragraph 21). We view Pinterest, which is a space formed by networks of linked pins, as this kind of nebulous environment. Users have the ability to explore pins, but cannot modify the pins of others. At the same time, changes by individual users result in an overall state of flux for the network of pins. Thus, the core elements of Pinterest are continuously being transformed.
Learning within a changing environment such as Pinterest, requires a focus on careful decision-making. As noted by Siemens [7
], decision-making is a key component of the connectivism lens:
Connectivism is driven by the understanding that decisions are based on rapidly altering foundations. New information is continually being acquired. The ability to draw distinctions between important and unimportant information is vital. The ability to recognize when new information alters the landscape based on decisions made yesterday is also critical [7
] (paragraph 22).
As we have described, using Pinterest is primarily an activity of sorting through visual bookmarks. Making good decisions within this space requires quickly discerning information from pins and recognizing how it relates to one’s current understanding. Users seeking to understand the corpus of resources available for a given topic are left with the task of browsing through their feed, which, as we have described, provides only a few details about a pin including a picture, description, author, and the number of repins. Of these details, the number of repins is the only consistently presented numerical information.
Our choice to investigate negative integer resources available on Pinterest is intentional and based on knowledge of the difficulties associated with teaching and learning about integers, which have been shown to be notoriously challenging for all [8
]. Specific challenges with integers include a focus on procedures [12
], difficulty with subtraction [13
], and language issues [11
]. Although research has shown that young children are capable of reasoning with integers [16
], there are many examples of adults struggling with the content. Piaget [9
] pointed to the difficulty of integer operations for secondary and university students. Likewise, Bofferding and Richardson [12
] illustrated that preservice teachers often focus on procedures when solving integer addition and subtraction problems. Recent research has also pointed to the difficulties that secondary students have connecting integers and contexts [11
]. Drawing on a historical lens, mathematicians in the 1700s and 1800s modeled integer addition and subtraction on a number line, but struggled to do the same for integer multiplication and division [8
Part of the challenge with integers is rooted in the difficulty of physically representing negative integers [20
]. For example, although we may talk about two objects or 2 feet in width, the same cannot be said for −2. Consequently, the negativity of −2 needs to be attributed to an object, such as one physical chip representing −1, negatives on a temperature scale, or even conceptualizing borrowing 2 dollars as −2. The challenge of the physical embodiment of negative integers [21
] causes educators and researchers to draw on various models with integers (e.g., [22
]). We acknowledge that there are various interpretations of the word model [25
], and align the definition in this paper with Vig, Murray, and Star [26
], who also reported on the use of models with integers. To this end, we use the term mathematical model (i.e., model) to refer to “material, visual sketches, paradigmatic situations, schemes, diagrams, and even symbols” that help students manage, document, communicate, or interpret mathematical ideas and phenomena [27
] (p. 13). Much of the research with integers supports the use of the number line model [10
] and chip model [29
], though some researchers have also described models such as elevators [13
]. Research examining textbooks and curricula in the domain of integer operations [30
] has shown the use of number lines, chip models, and contexts as models for dealing with integer operations. Likewise, traditionally-printed curricula (e.g., Lappan CMP) supports number lines and chip models [31
] with integer operations. Importantly, research has also highlighted that all models for integer operations have affordances and breaking points [26
A further obstacle in teaching about integers is that although curricula and tasks exist that support conceptual understandings of integers (e.g., [28
]), it is a challenge to support teachers in developing the ability to discern between materials that are conceptually focused versus those that are procedurally focused. This is particularly the case for integer subtraction, where different number sentences support different types of reasoning [13
]. Integer subtraction is difficult because the “rules” for whole numbers no longer hold for integers—adding does not always make bigger, subtracting does not always make smaller, and the commutative property does not hold for problems such as 2–3 and 3–2 [12
]. Furthermore, subtraction is complicated by the number sentence type (e.g., −2 − −5 compared to −5 − −2 is more challenging) [21
]. Additionally, language presents challenges when working with integers. For example, identifying whether money referenced in a contextualized problem with integers is viewed from the perspective of the lender or borrower of the money [11
]. Similarly, it is challenging for students to coordinate what the words “more” or “less” mean with integers [15
Taken together, the challenges related to teaching and learning about negative integers make it likely that teachers may feel underprepared to teach the content and seek resources outside of the classroom for assistance in planning. In this search for resources, many may turn to Pinterest as a curriculum resource for pedagogical and content information. With this group of teachers in mind, we conducted a research investigation focused on understanding the scope and characteristics of available negative integer content on Pinterest. Our study was guided by the following research questions:
What are the characteristics of pins related to negative integers?
What association, if any, exists between the number of repins and the presence of errors in linked content (e.g., models, language, worked examples)?