*By Jesse Akman*

Perhaps no subject inspires more anxiety in students and instructors alike quite the way mathematics can. In research going back as far as the 1960’s, when surveyed, students report perceiving mathematics as “difficult, boring, not very practical, and abstract,” (Köğce, Yıldız, Aydın, & Altındağ, 2009). Moreover, mathematics is often portrayed or perceived as a purely cognitive function, relying solely on a dispassionate, calculating logic (Nicolaidou & Philippou, 2003). The perception of mathematics and students’ self-perceptions of mathematical ability are especially troublesome across lines of race, socioeconomic status, and gender (Catsambis, 1994), with students of color, students from low-income households, and female students reporting the lowest confidence in their abilities to do mathematics. These outcomes feed into harmful stereotypes about different groups’ abilities and preferences towards mathematics, which in turn, affects those same students’ confidence in their own capacities (Bieg, Goetz, Wolter, & Hall, 2015).

All these attitudes and misconceptions combine to cause math anxiety. Math anxiety is the fear and apprehension surrounding engagement with mathematics (Ramirez, Shaw, & Maloney, 2018), and it is considered distinct from other learning anxieties including test and state anxiety, with some going so far as to consider it a phobia (Oizzie & Kraemer, 2017). Furthermore, math anxiety is strongly related to low math achievement levels (Ma, 1999). Until recently, researchers believed that math anxiety’s onset came around the sixth grade (Ramirez, Shaw, & Maloney, 2018); however, recent studies suggest the seeds of math anxiety are sown much younger, with students as early as first grade reporting math-specific anxieties (Aarnos & Perkkila, 2012).

The question then becomes how does one prevent or mitigate the effects of math anxiety? While a multitude of interventions are possible, evidence suggests that learners’ mathematical confidence is ultimately raised through mathematical exposure (Everingham, Gyuris, & Connolly, 2017; Ramirez, Shaw, & Maloney, 2018). In other words, the best way to fight math anxiety is by doing math, particularly in low-stress environments, and there is evidence to suggest that the library can be an especially helpful tool for improving students’ math outcomes (Betne & Castonguay, 2008).

Librarians, however, are not immune to math anxiety; far from it, in fact. STEM anxiety is a common phenomenon in librarians (Baek, 2013), and anxiety surrounding mathematics is particularly acute in the population. As we’ve seen by now, however, librarians have all the tools and competencies needed to be effective STEAM instructors, and teaching math is no exception. In this chapter, we will examine what “math” can mean for library instructors; how to prepare for math instruction, including ways to understand your community’s math instructional needs; and explore some age-specific strategies and considerations for teaching math to different groups of children and adolescents.

#### What “Mathematics” Means for Library Instructors

As we have already seen, math is not exactly universally beloved by librarians. While more evidence may be needed to state conclusively, Baek (2013) suggests that much of this anxiety is a product of a sense of lacking qualification. Librarians often come from non-STEAM –especially non-math– backgrounds, and thus feel apprehensive about teaching math as “non-mathematicians.” Kliman, Jaumot-Pascual, and Martin (2013) suggest that mathematics is seen as “without context” (i e., divorced from the “real world”), and librarians’ math anxiety is often a result of a narrow or incomplete conception of what math really is.

Let’s briefly consider just what math is before turning towards the specifics of planning and leading math instruction in libraries. The traditional understanding of what counts as math is likely something akin to Dudley’s (2010) view of mathematics as “algebra, trigonometry, calculus, linear algebra, and so on: all those subjects beyond arithmetic,” (p.608); in essence, math is applied arithmetic and the more esoteric formulations beyond those subjects covered in primary school. While this definition is certainly not incorrect, it is limited, and there are more helpful ways to approach this question. Hersh and Ekeland (1997) offer a more organic articulation that might be better suited for our purposes: they argue that math is the name we give to a set of social objects. Rather than being a set of natural laws that are “out there” in the universe waiting to be discovered, math is instead a human-created system that we can use to understand the universe and solve problems. The rules, figures, concepts, and problems of math are occasionally grounded in some physical reality, but most often, they are shared social conventions. For example, we typically use the base-10 or decimal number system (with digits from 0-9) in everyday life, but some cultures use a base-8 system, and computer programmers use a base-16 (hexadecimal) system. There is nothing fundamentally more “natural” about base-10; we have just agreed as a society to use this system for most mathematical applications.

Understanding math as a human-created system may help alleviate math anxiety somewhat: if math is the name for a set of social objects and librarians already perform countless social tasks, then librarians likely already possess substantial knowledge about math and math instruction. Math is already part of every storytime, especially those with shapes, numbers, or sizes; math happens in every Lego club; math undergirds every makerspace. In short, libraries are full of math already, and librarians make that math happen. Our true challenge, then, is recognizing those objects and knowledges, and then channeling them into action.

#### How is Math Taught in K-12 Schools?

Before exploring how math can be incorporated into library programming and services, we will briefly discuss how it is currently taught in public K-12 classrooms. If you haven’t been in a K-12 setting since 2010 or so, math instruction likely looks very different now compared to what you experienced as a student. That is due to the national adoption of the Common Core State Standards, which has transformed math and Language Arts instruction in the United States.

Rather than teaching students the quickest way to solve mathematical problems, or the one “right” way to solve a problem, Common Core math aims to help students understand mathematical operations and the relationships among them conceptually. This often involves teaching students multiple approaches to the same mathematical operation, focusing on process as much as answers, and encouraging argumentation and logical reasoning. With that said, it’s important to understand that the Common Core is a set of standards – benchmarks for what students should know and be able to do at each grade level. Common Core is *not* a curriculum; it does not dictate what happens in individual classrooms to help students reach those standards. Many of the complaints about Common Core math shared on social media and in the news are really complaints about the materials used to teach the standards, rather than the standards themselves (search “Common Core math memes” if you’re not already familiar with these).

The center of the Common Core math standards is a set of eight Standards for Mathematical Practice that cut across all grade levels (http://www.corestandards.org/Math/Practice/). These standards, like the Next Generation Science Standards (NGSS), emphasize mathematical processes rather than specific operations or “facts:”

- Make sense of problems and persevere in solving them
- Reason abstractly and quantitatively
- Construct viable arguments and critique the reasoning of others
- Model with mathematics
- Use appropriate tools strategically
- Attend to precision
- Look for and make use of structure
- Look for and express regularity in repeated reasoning

Also like the NGSS, these standards have clear connections to the types of skills we already teach in the library. For example, YALSA Teens First Learning Outcomes such as “Teens are able to think flexibly” and “Teens are able to show perseverance” (http://bit.ly/2mg1x9U) align well with the first two standards above.

Although Common Core math has been in place for nearly a decade, the jury is still out on whether it has resulted in improvements to student learning. National research studies have found mixed results on this question, though Common Core proponents point to several reasons why the evidence may not yet point to its unqualified success: teachers are still getting used to the new curriculum, classroom materials continue to be refined and improved, and national tests such as the National Assessment of Educational Progress may not accurately measure the type of thinking that Common Core is trying to develop (Barnum, 2019). Regardless, it seems that for the time being, Common Core math is here to stay.

Now that we have discussed what math is and how it is taught in schools, we can move on to more specific strategies for incorporating math instruction into public library programming and services.

#### Getting Started

Before jumping into math programming at your library, it’s important to take stock of where you, your library, and your community are currently and what your needs are. One place to begin is by determining what resources you already have access to, both in the library and in the community, that might support math instruction.

As we saw earlier, you are almost certainly already doing math programming in your library. The question, then, is what materials are you using for that programming? Do you have Legos? Then you have the best geometry-instruction tools available (Hopwood, 2012). Do you have picture books that deal with counting? Then you have a math-themed storytime ready to go. As Sharma (2016) notes, what is or is not a math resource is entirely up to you and the context into which you place those items. Think carefully about what you already have and consider discussing those materials with other librarians to see how they may have used those same resources to design a math lesson plan before. Ultimately, the “math-ness” of any given item in your collection or inventory can be grown through resourcefulness and imagination.

Improving your collection of math-related resources does not have to involve a large financial expenditure for the library. Perhaps more than any other field, the STEAM disciplines have embraced the open source movement, meaning there are more low- and no-cost resources available to you than ever before. For older and more advanced learners, especially, there are options galore. If coding and computers are big in your area, consider investigating open source statistical programming languages like R or S, or larger, more comprehensive statistical computing packages like JASP – an open alternative to SPSS. Exploring community fora like GitHub can yield invaluable information about open source software to improve your math instruction. Additionally, there are open alternatives to consider for more common software, such as OpenOffice as a substitute for expensive Microsoft programs like Excel.

Furthermore, free lesson plans, textbooks, and other math instructional materials are increasingly available as the Open Educational Resources (OER) movement grows. This is especially true and important if the schools in your area have adopted the Common Core State Standards (CCSS) (Welz, 2017), as numerous digital libraries of OERs were created to help defray the cost of adopting these relatively new educational standards (Waters, 2013). As a “one-stop shop” for all your instructional material needs, OERCommons.org belongs in every instructional librarian’s bookmarked pages.

Librarians looking to grow their resource pool or attempt STEAM programming on an ambitious scale are in luck: as arguably the chief national educational priority of the new millennium, there are a host of grants and funding agencies dedicated to supporting STEAM programming in libraries. From private organizations such as PNC Bank, to nonprofit agencies like the Carnegie Foundation, to state and federal agencies (Anderton, 2012), there are an abundance of options for librarians in need of capital to grow or begin their libraries’ foundations for STEAM instruction. Consider beginning with highly reputable options such as the NEA Foundation, the National Science Foundation, or the US Department of Education’s Supporting Effective Educator Development (SEED) program.

Finally, perhaps more than any other STEAM discipline, librarians may want to think about what their local communities can do to improve the library’s math instructional capacities. Consider your local institutions: is there a university or college? You might want to contact the math department to gauge the faculty’s interest in a potential collaboration. One rising trend (Bushey, 2014) in library education is the growth of TEDx conferences, which feature fun, accessible presentations of educational content by subject experts. These events can be held for reasonable costs and are scalable from one-off talks to extensive conferences. If your area does not have an institution like this, you may still be surprised by what individual members of your community can offer. There are often retired math teachers or high-achieving students looking for volunteer opportunities, and your library might be the perfect opportunity for these interested parties. Ultimately, math resources in your community are just like the math resources in your collection: they are almost certainly there, you just need to turn a careful eye towards them!

With the beginnings of math instructional collection development and assessment in place, let’s now examine some strategies, limitations, and aims for library math instruction across different age groups.

#### Mathematics Programming for All Ages

Although math instruction may get much more complex at higher levels, it can begin with something as simple as learning concepts like “less and more” or counting to ten. This means that math instruction in the library can begin with programming for our very youngest users.

###### Preschool

Math education for preschool age children is one area where librarians may already be well prepared; moreover, this is one of the areas where library instruction in math can make the biggest difference for learners, as evidence suggests fostering math skills at this developmental stage is strongly correlated to long-term academic success (Park, Bermudez, Roberts, & Brannon, 2016). For learners in this age group, math instruction is often intended to develop students’ number sense (Baroody, Eilan, & Thompson, 2009), which has three sequential components: first, developing counting strategies using objects or words (i.e., inductive reasoning); next, reasoning skills that add patterns and relationships to those counting processes (i.e., deductive reasoning); and last, retrieval strategies that move those earlier skills to long-term memories which learners can more easily recall. Outside of number sense, mathematics instruction in this age range also focuses on fostering spatio-geometric sense and interest by emphasizing exploration of shape and size (Sarama & Clements, 2004). These three stages rely on skills which libraries and librarians regularly help develop.

With an understanding of the skills we are looking to develop, let’s consider a successful example of mathematics instruction for this age group to see some of the tools and techniques available to library instructors.

Spotlight: Mathematize Your Storytime

After attending a workshop sponsored by the US Department of Education, librarians Renea Arnold and Nell Colburn (2009) decided to “mathematize” their storytimes, and doing so offered major returns for minimal investments. Fundamentally, Arnold and Colburn made one change: they added a meta-awareness to their own storytime practice. They offer the example of singing *Twinkle, Twinkle Little Star*, a song almost every children’s librarian has used during at least one storytime. When you sing the song, do you make a diamond with your hands for the line “like a diamond in the sky?” If so, you are already doing the work to help grow spatial skills in preschool-age learners; the only change needed is a cognizance of your actions.

Arnold and Colburn offer three suggestions for librarians to begin “mathematizing” their storytimes: first, ask math questions. For example, when reading a story about animals, ask questions that compare size (e.g., which one is tallest? Who was the heaviest?). Second, use the language of math. This means not shying away from vocabulary like “equals” or “less than” when discussing a story. Consider the example of *If You Give a Mouse a Cookie*: after the story, ask your learners to compare “one cookie” with “two cookies” by saying which quantity is *greater than *the other. Finally, they suggest librarians help their learners see themselves as problem solvers, which gives you the opportunity to develop those deductive and inductive skills in addition to their spatio-geometric understandings. If, for example, a story relies heavily on repetition to advance the conflict of the plot, remind your learners of what happened previously, then ask them what they think will happen when the characters try again. Ultimately, Arnold and Colburn remind us that the goal for your lesson plan is not for you to think mathematically, but for your learners to think in terms of math while you think in terms of fun!

###### Elementary School

As children transition from preschool into primary school, the challenges posed by and approaches to mathematics instruction in the library change considerably. While preschool-age math instruction tends toward fostering mathematical literacies through abstract connections and properties (e.g., “shapes,” “sizes,” “numeracy,” etc.), math instruction for elementary school-age children tends toward further developing those skills through concrete, explicitly “mathematical” tasks (i.e., “math problems”) (Stein, Grover, & Henningsen, 1996). However, while the materials themselves are more definitively mathematical, the ideas they express are considerably more abstruse. A student, for example, can easily understand that the elephant in the story is larger than the cat; she can refer to the pictures, she may have a direct experience to reference, or the story itself might provide contextual clues with which the student can deduce the answer. That question becomes significantly more esoteric when presented symbolically using numerical representations of the animals’ respective sizes.

Complicating matters further, one now needs to reconsider the purpose of library mathematics instruction given these changes in form and content. In her literature review, Frederiksen (2009) found that libraries and librarians tend to see the role of their instruction as both supplement and complement to the curriculum and standards of their local schools. Moreover, since this is the age group in which math anxiety most commonly begins occurring, libraries and library instruction can be the relaxed, fun environment children need to overcome those anxieties and successfully internalize mathematical concepts (Spencer & Huss, 2013).

With the understanding that mathematics library instruction for this age group can reinforce and expand the local standards and curricula, as well as act as a low-stress environment to help ease math anxiety, let’s now examine a successful model of mathematics instruction for elementary school-age children in the library.

Spotlight: Makerspaces for Math Instruction with Elementary-Age Children

While not every librarian has access to one, the makerspace is a powerful tool for mathematics instruction, and the case provided by Diana Widdows (2017) is a great illustration of their value. As a former third-grade teacher, Widdows was determined to find a way to use her library space to both ease the burden of standardized test prep on primary school teachers, and to help learners actively engage with the materials they needed to understand. Her area’s school system used the Common Core Standards, so she knew her learners were expected to understand “math performance tasks.” In the Common Core Standards, performance tasks are multi-step questions or problems that ask learners to do a performance to demonstrate a proficiency or an expected understanding in a subject.

Given the needs of her learners and their other teachers, plus the expectations of their curricula and sets of standards, Widdows decided to have her learners use the library’s makerspace to bring several math performance tasks to life. Using the available tools and resources, learners translated those word problems into physical actions and playable scenarios, including running their own lemonade stand businesses and designing and building their own model cars. By placing abstract questions and tasks in concrete, interactive scenarios, Widdows was able to not only help learners better understand and perform these math performance tasks, she got her learners to go beyond the problems by collecting their own data to answer new and self-directed questions about their situations.

This example embodies nearly all the essential values and goals of library math instruction for this age range. Widdows concretized and gamified abstract mathematical concepts, thus removing much of the potential sources of anxiety for learners; she provided a complementary lesson for the math being taught in their classes; and she successfully supplemented her learners’ other math curricula by helping them dive deeper into the tasks at hand through further data collection and analysis.

###### Middle Grades

The differences in needs and considerations between elementary school-age children and those in the middle grades are subtle, but significant. The aims and purposes for library math instruction are generally similar between these two groups. Frederiksen’s (2009) findings seemed to be as applicable to learners in this age range as they were to their slightly younger counterparts; that is, library instruction for learners in this age range tends to be a matter of reinforcing and supplementing the school curricula for these learners. For librarians, the key difference, then, is that the subject matter at hand may be slightly more sophisticated and abstract.

Crucially, however, there are some additional affective and ethical concerns for teaching these learners one should consider. Students’ self-perceptions seems to become a major determinant of success in this demographic (Pajares, Britner, & Valiante, 2000), and this is the age at which learners begin to report seeing math as useless or impractical (Parajes & Graham, 1999). Two possible implications here for instructors are the potential inclusion of multi-goal lessons into a curriculum so learners can feel successful early and often in the process, and working to tie those lessons to “useful,” real-world situations. Moreover, learners in this age range can handle and benefit from multi-tiered problems (Van de Walle, 1998) as one of the desired math competencies for this demographic is an ability to answer problems requiring iterative thinking.

Finally, we should consider library math instruction for middle grade learners as it relates to our present technological and educational conjuncture. Responsible and proficient computer use is doubtlessly an important skill for learners, and evidence (Herro, Quigley, & Jacques, 2018) suggests that this age group is an ideal one for developing those understandings. These learners likely have the mathematical thinking capacities and the broader intellectual and emotional sophistication to begin handling both the technical and ethical aspects of computer use. Furthermore, as Spencer and Huss (2013) demonstrated, the library can provide the ideal, low-stress environment for grappling with ideas that are challenging to learners on both cognitive and affective levels.

Since we have now seen how the needs of middle grade learners closely align, but remain critically distinct from those of elementary-age learners, let’s revisit the model we examined for the latter group and see how one can adjust that program to better suit the needs of an older cohort.

Spotlight: Makerspaces for Math Instruction with Middle Grades

In her research on makerspaces in school libraries, Cynthia Houston (2013) provides a number of crucial points for us to consider. First, she mentions that with their emphasis on “doing” activities that offer hands-on and applied learning opportunities, makerspaces can make subjects such as math seem more “useful” than they might appear otherwise. Second, Houston notes that those same highly interactive makerspace lessons show the natural interdisciplinarity of STEAM topics, offering learners who might be resistant to math but love, say, art the opportunity to connect a difficult subject with their favored ones. Finally, Houston notes that the prominence of technology and digital learning in makerspace lessons offers older learners the opportunity to for meta-commentary on the ethical considerations that might inform those activities.

For instance, if an instructor were to borrow Robin Henry’s (2004) “Number Hunt” lesson plan where learners used the library’s print and digital collections to complete a math scavenger hunt, the instructor could reserve time at the end of the lesson for discussion about what “safe and smart” searching means in this context. Learners could consider some of the greater ethical considerations of internet searching like personal data privacy and misinformation. Moreover, a lesson plan such as this could be designed to guide learners towards these considerations by deliberately directing them towards misinformation as they searched. Students at this age have both the sensitivity needed to begin grappling with these serious and abstract concerns, but still need considerable guidance to safely navigate them, and libraries and library instruction are ideal settings for striking that balance.

###### Teens and Young Adults

Much like the leap from elementary-age to middle grade learners, the needs and considerations for math instruction for teenagers and young adults are like those of middle grade and elementary-age learners, but distinct in key ways. Perhaps the strongest similarity between teens and their younger counterparts are the benefits of contextualizing math instruction. Stressing math’s importance in life after primary school ends is particularly beneficial in math instruction for teens (Burress, Atkins, & Burns, 2018); for instance, Tyson, Lee, Borman, and Hanson (2007) found that exposure to math in a STEM-career focused context in high school is a powerful predictor for whether a student will obtain a bachelor’s degree in a STEM field.

Beyond career and higher-educational implications, however, library math instruction’s value for teens —especially today’s teenagers—is a matter of rectifying a social-contractual failure for which teens are now paying the price. As Harris (2017) noted in his exhaustive evidence survey, primary education in the 21st Century has been defined by two major federal policies: 2001’s No Child Left Behind Act (NCLB) and 2009’s Race to the Top (RTTP) program. While each policy differed in its specific requirements, enforcement mechanisms, and aims, Harris observed that they shared two common characteristics: an emphasis on standardized testing as a means of evaluation, and the push for universal learning standards. These two factors profoundly changed education for learners, shifting classroom time towards the dreaded “teaching to the test,” and a classroom focus on the subjects those tests measured – STEM and language arts. Perhaps unsurprisingly, however, Harris found that the increased quantity of math education was just that: pure quantity, and nearly no quality math instruction. For example, he found that much “math” instruction focused on successfully eliminating obviously incorrect answers on tests in order to increase the likelihood of randomly selecting the right answer to a problem. Furthermore, it is teens bearing the brunt of these negative consequences, as their education has been entirely within this framework, and since the compulsory portion of their education is ending, they may not see an alternative model.

This is where math instruction in the library can make a profound difference. Since the library was and is not subject to these mandates, it can provide the stimulation and exploration schoolroom instruction can no longer afford to offer. Moreover, as Pew Research Center (Horrigan, 2015) found, the people most likely to use the library or attend a library program are those disproportionately burdened by math anxiety and instructional inequalities: women, people of color, and low-income households. Thus, one of the greatest benefits of library math instruction –for all ages, but particularly teens and young adults– is that it provides the opportunity for *meaningful* math instruction; an opportunity increasingly rare in other educational settings.

With the role and importance of math instruction established, we should now consider one effective model for library math instruction for teenagers.

##### Spotlight: “Train the Trainers”

At Palo Alto’s Mitchell Park Library, Teen Services Librarian Gina Martinez developed an instructional program that benefits three of the age groups we examined by approaching teenage learners with a “train the trainers” philosophy: Teens teaching Kids Code (2015). Teens honed their coding abilities in certain languages and environments through library instruction, then partnered with younger learners to help children begin building their own coding skillsets through yet more library instruction.

By taking stock of which resources were available to her locally in the heart of Silicon Valley, Martinez created a lesson plan that helped teenagers develop cross-discipline STEAM skills, plus teaching and communication abilities. Teens received instruction grounded in a practical, “real-world” context, while also being afforded the opportunity to explore STEAM topics that they found purely interesting. The instruction they received was generalized enough to be covered at the class-level, but personalized and customizable enough that learners had license to explore areas that were solely of interest to them. Moreover, these young adults were shown trust and respect by being given the responsibilities inherent in leading younger children. Martinez’s lesson plan is the perfect exemplar for teen math instruction in the library: she balanced the sensitivities and considerations required for effectively engaging her learners, and she did so by using the needs of one of her communities to address those of another of her patron communities.

#### Putting the Pieces Together: An Interview with Kate Jacobson from Cobb County Libraries

Kate Jacobson, a Youth Services Librarian in Atlanta, Georgia, has been involved with the library’s ongoing workshop series GEMS: Girls in Engineering, Math, and Science for several years. While writing this chapter, I had the opportunity to speak with Jacobson at length about her experiences with the program. While you read her interview responses below, think about how topics discussed earlier in this chapter (such as math anxiety, inequities in math education, and connections between math and library content) are addressed through the GEMS series.

**What** **was the impetus for the Girls in Engineering, Math and Science (GEMS) Workshop?**

GEMS came about in 2013, and it was started by our then-digital services librarian. She grew up with a strong interest in STEAM, but her school didn’t really address that interest when she was in school. As she began her career as a librarian, she came across research showing that without stimulation, there is a decline in interest in STEM in girls after the age of seven, so she wanted to create targeted programming to address those issues. GEMS was for girls age 13-18, and in its first iteration, was a single-site program lasting 13 weeks. She recruited women from across the STEM disciplines to provide programming, mentorship, and career advice –and real job opportunities in a few cases– and this culminated in a “capstone” project.

After that first year, the timeframe was shortened, because with the increased interest in our community, we could not sustain a 13-week program. The second version of GEMS was a four-week series, and it focused specifically on 3D printing. We still partnered with women in STEM fields for programming, including faculty from local universities and a women in STEM organization. Our third year kept a similar model; however, each week had its own focus, rather than a single emphasis on 3D printing. Due to some staff turnover, we were unable to provide GEMS last year for the first time since it began, and the community response was huge. People have really come to love –and expect– GEMS. Apart from last year, the four-week, multi-focus format has been our model since then, although we hope to change some elements this year.

We received a very generous donation from our library foundation to provide this programming. We get a fixed amount for programming from the county each year, so those funds from our library foundation were crucial to GEMS’ success. Moreover, their donation allowed us to purchase STEM materials that we’ve been able to use throughout the year in our programs.

*What is your approach to designing math instruction for youth in a public library setting?*

I am an English major, so when I took my last math class in college, I was so happy. But when I got into my job at the library, STEM programming was really taking off, and we were expected to provide it. I’ll admit I had some resistance at first, because I was like, “no way! I thought I left that all behind!” But when I got to speak to some other librarians, I realized I could find a way to make this work for me.

The way I make math programming work for me is to combine it with something I feel comfortable doing, like art. Math and art together makes sense for me, so it provides a means for explaining mathematical concepts. A good example is symmetry: when I talk about symmetry, we do a program about snowflakes, and then we talk about other things in nature that show us symmetry. I don’t get hung up on what a “true” math lesson is. This approach is fun for me and them; it’s manageable for me; and we’re still learning.

In the past few years, we have strengthened our relationship with the local schools, and we are creating more math programming designed to be an extension of their math curricula. For example, we recently did “marshmallow geometry” to complement the kids’ shape lessons. We think this type of instruction will become a bigger part of what we do in the future, but for now, my primary focus remains creating math instruction that I can make sense of, and that emphasizes the math of “everyday life” through activities that are hands-on and interactive.

*Does your approach vary between age ranges? If so, how?*

In some ways yes, but in most ways, no. Obviously, the program I do for first and second graders will be different from the one I do with teenagers, both in form and content, but I try to make the general idea of my programs transferable to multiple age groups. My approach to the essential components of program design is to build a structure where the details can be simplified or complicated as my audience’s needs dictate, but the fundamental structure works for multiple groups.

Certain things are definitely age-group dependent though. With teenagers, for example, my hope is to reach a point in an instructional session where they are the ones leading the discussion or they’re asking me questions instead of me lecturing them. Teenagers, too, can handle a broader range of concepts, and can balance more ideas in one lesson. With younger ages, however, I only want to introduce one or two major concepts at a time so we can take our time and really explore those ideas. I also build a little bit more guidance and structure into lesson plans with younger groups.

So, my best-case scenario would be something like building a scalable plan for, say, geometry that conveys basics about shapes to my youngest ones, and complex ideas about design or applications to engineering for my oldest groups, but each program still follows the same general progression.

*Do you see any particular challenges to designing or implementing math programming for children in a public library setting? If so, what are those challenges?*

I’ve rarely met people who say math is their favorite subject, and as I said, I was pretty resistant to math programming in the beginning. Beyond not feeling like a mathematician, I think a lot of librarians believe that there just isn’t that much for them to do or say about math. When you first contacted me, even I had to go back to my old notes to make sure I had done enough math programs to really say something!

The thing I’ve realized over time is that the first challenge is breaking out of our misconceptions about what math is, or really, what math programming is or “has to be.” Math is already rolled into most other fields, so recognizing that I can teach math by making art was really freeing.

One of our best programs was a building challenge for teens. The kids all got some building materials –a few clothespins, some Popsicle sticks, things like that– and then a few different sized balls. They were then given increasingly difficult challenges where they had to use those materials to build a structure that was at least six inches tall and could support a ping pong ball; then they had to build one that was 12 inches tall and supported a tennis ball; then we might take away one of their building materials and ask them to do the last challenge again, and it kept going like that. I actually stole this idea from one of our presenters –she is a math researcher from Georgia Tech– because she was able to show that this challenge, which seemed mostly like a design and engineering challenge, couldn’t be done without an understanding of math. Even more than that, she explained to the kids that when she uses design thinking to navigate these questions –*can I still make this work without this piece? OK, what about when I need it to also have this feature?*– she is doing math. It was such a great way to get the kids to think about how math is a part of all the STEAM fields, and you’re doing math even when what you’re doing isn’t *just *math.

*How do you assess math programming?*

Our library system doesn’t use a formal assessment model anymore. We did at one point, but we no longer fill out forms or use certain techniques for assessment. But I do like to do my own informal assessment, just for my purposes. If something seems like it isn’t working, or afterwards I realize, “oh, I could have explained that better!” I want to have some record of it. I use a Google Sheet to track materials that I need, and I like to jot down those ideas there. I just want to know how I can improve my practice, and make programs where I leave and think, “OK, that was a success.”

*Do you have any recommendations or advice for those interested in designing and implementing math programs for youth in a public library setting?*

I would first say, “Be open minded, and don’t let a fear of math get in your way of trying!” Look for a way to make it fun for you, because the kids can tell when you’re not enjoying something, and if you aren’t, they definitely won’t. I also think it’s important that you not be afraid to ask for help and admit when you need some help, or you need a math refresher.

I really want librarians to know that these are their programs, and they can make math be whatever they need it to be. 22-year-old me would be shaking her head, but it’s like your high school math teacher told you: math really is a big part of your life, and whether you realize it, you do it all the time. Whenever you make measurements, that’s math; when you work with shapes, that’s math; when you do builder challenges with marshmallows and toothpicks, that’s math! Don’t be afraid to do a program about the “math-ness” of something other than math. Just be confident and comfortable with the material, and you can make the math programming that’s right for you successful.

#### Conclusion

Math anxiety is an unfortunate reality of math education, at least as presently constructed. It is likely that both you, the library instructor, and your learners at least occasionally struggle with it. The goal of this chapter was not to provide a cure for math anxiety, but rather to develop a program of math anxiety mindfulness to limit its effects on library math instruction. Our plan for combatting math anxiety involved situating math and math instruction in the right conceptual framework; identifying helpful library resources, and exploring options for collection expansion through low- and no-cost means; and examining the needs and considerations of different age groups, and matching them to exemplary programs. Successful math instruction, however, does not end with overcoming math anxiety.

As librarians, it is likely that mathematics is not and will never be your favorite subject (Kliman, Jaumot-Pascual, & Martin, 2013); however, it is also likely that you will encounter learners for whom math is a favorite subject. Moreover, a three-year longitudinal study of 20 schools found that students who rank mathematics as their favorite subject often feel as though they are alone in their preference, and thus, atypical or unusual (Attard, 2011). That study also found that regardless of preference, students saw a “good” math instructor as:

A teacher who is passionate about and enjoys mathematics. [A student] attributed this quality with increasing her own engagement with mathematics: ‘She just puts a lot of enthusiasm in maths and makes it really fun for us. She gets all these different maths activities. She just makes it really fun for us and I quite enjoy maths now because of that. (p.373)

Therefore, the final component of successful math instruction is bringing genuine enthusiasm for math to your lesson plans. Whether you find some property or branch of mathematics that sparks your own interest in the subject itself, or it is an enthusiasm for fostering love for mathematics in your learners, truly excellent math instruction comes from passionate math instructors.

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