Education Commons^™

More Than Free Textbooks: Labor And Pedagogy In Implementing Open Resources In A Trigonometry Course, Caleb Holloway

Journal of Humanistic Mathematics

This paper reports the implementation of open educational resources (OER) in a university trigonometry class, with an emphasis on the pedagogical considerations and academic labor involved. To date these two matters have been underreported in the literature on OER. I provide an account of the work involved both in choosing an open textbook and in creating hundreds of accompanying homework exercises for an online learning platform. I also present the pedagogical lens that informed this implementation, discuss how it informed my adoption of an open textbook, and provide specific examples of how it guided the creation of these exercises. Based …

Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos

Journal of Humanistic Mathematics

We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …

Hearing Silence: Understanding The Complexities Of Silence In Democratic Classrooms And Our Responsibility As Teachers And Teacher Educators. A Response To "Creating A Democratic Mathematics Classroom: The Interplay Of The Rights And Responsibilities Of The Learner.", Kersti Tyson, Allison Hintz, Andrea English, Diana Murdoch

Democracy and Education

This response to Priya Prasad’s and Crystal Kalinec-Craig’s article on the interplay of the Rights and Responsibilities of the Learner aims to engage with and add on to the authors’ exploration of learners overexercising or opting out of their rights. While grappling with these challenges alongside the authors, our curiosity deepened about a significant and understudied facet of democratic classrooms: silence. Through this response, we consider the multifaceted dimension of silence and how a focus on silence may help us more fully understand the tension between learners’ rights and responsibilities to self, each other, and the collective. Specifically, we engage …

Pre-Service Elementary School Teachers’ Perceptions Of Themselves As Learners Of Mathematics And Science, Diana L. Moss, Rachel Wilson, Danielle Divis

Journal on Empowering Teaching Excellence

Access the online Pressbooks version of this article here.

This study investigated how prospective elementary teachers view themselves as learners of mathematics and science during their last year in a teacher preparation program at an American university. Using drawing and reflections as the method for collecting data, prospective teachers were prompted to draw themselves and reflect on learning mathematics and draw themselves and reflect on learning science prior to and after their mathematics and science methods courses. Drawings (n = 147) were coded according to the presence or absence of several themes including physical objects, teachers, students, and environment. …

The Impact Of Personal And Service-Related Factors On The Perceived Academic Success Among College Students, Ronnie Davis, Geraldine Doucet, Terayana Lamb, Sonya Sneed, David Fletcher

The Journal of the Research Association of Minority Professors

In recent years, student completion of the first year and second-year college curriculum has become a significant barrier to student success and retention especially at Historically Black Colleges and Universities. Despite low pass and retention rates, many degree programs in the U.S. require at least one college-level mathematics course, and the failure in this math course has contributed disproportionately to the failure to complete the first- and second-year curriculum.

The purpose of this study was to examine the predictability of the relationship between selected personal, academic, and service-related factors and the perceived academic success in mathematics among college students. Specifically, …

Middle School Students Generating Mathematical Problems From A Real-Life Situation, David Coffland, Ying Xie

Journal of Humanistic Mathematics

In this study, we examined the effect of different presentation formats of a realistic situation on students’ mathematical problem-posing behavior. We divided thirty-six middle school students into two groups, gave them a pretest, and then showed them a realistic, problem-posing situation in Artifact or Video format. We used Silver’s core dimensions of creativity, namely fluency, flexibility, and originality, to measure participants’ problem-posing activity. The results for the fluency measures showed that the Artifact group wrote more questions than the Video group but the same number of mathematics problems. The Video group posed problems in more mathematical domains than the Artifact …

The Impact Of Covid-19 On Mathematics Education Curriculum, Kristen Ferguson

The Journal of Purdue Undergraduate Research

No abstract provided.

Teaching Statistics For Social Justice - An Autoethnographic Research Report, Sheffield L. Dacia, Sierra Brooks, Basil M. Conway, Ha Nguyen

Georgia Educational Researcher

The following autoethnography was completed by two graduate students at University A learning to enact teaching for social justice while building content underpinnings in statistics at University B. The authors present a research base for teaching for social justice followed by a description of their lesson, observations during enactment, and reflection of change in beliefs about teaching for social justice afterward. Findings in this study are shared from the authors’ personal perspectives through the enactment of teaching a lesson for social justice in an undergraduate statistics course at University B. Implications provide encouragement that the inclusion of social justice topics …

Parts Of The Whole: The Last Column: Freire's Pedagogy Of Liberation, Dorothy Wallace

Numeracy

The educational theory of Paolo Freire is briefly summarized for instructors of quantitative reasoning, with a focus on what it means to give students “agency.” Some examples are given of how to implement his basic ideas.

Students Studying Students And Reasoning About Reasoning: A Qualitative Analysis, Salvatore J. Petrilli, Grant Clark, Nicholas Demarco, Jack Esposito, Brianne Giuliano, Sara Greiss, Emily Harris, Alessia Merritts, Kyle Murray, Mateusz Piekut, Brian Seidl, Scott Shannon, Nicole Silva, Christina Sullivan, Brittany Willoughby, Yile Zhou

Journal of Humanistic Mathematics

In this work, a faculty member takes a journey along with students as they enhance their understanding of how people solve mathematical problems through a mainly qualitative statistical project. Student authors of this paper registered for a problem solving seminar led by the faculty author, and then created and analyzed self-built assessment tools to explore problem solving techniques. Here we share our findings and recommendations, which we hope will inspire others to explore novel pedagogical techniques in the teaching of mathematical problem solving. We incorporate into our presentation ur voices, reflecting on how we and others solve problems.

Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge

Journal of Humanistic Mathematics

Parents and educators have powerful opportunities to introduce children to big mathematical ideas, when those ideas become necessary. Children are capable and curious. They don’t need to be sheltered from big mathematical ideas. Bring out mathematical ideas when kids are ready, or when they are needed. This article describes one such instance, when I helped my six-year-old son move beyond zero in the negative direction when subtracting.

Parts Of The Whole: Logical Categories Of Learning: Why Teaching Qr Is Hard, Dorothy Wallace

Numeracy

This column introduces the reader to an essay by anthropologist Gregory Bateson on the nature of learning. In that essay, he stratifies the learning process into categories based on what aspect of the student’s understanding is required to change in order to accomplish a given learning task. A discussion of the first three categories is followed here by examples from quantitative reasoning tasks and a further example from the ongoing discussion in the community of what numeracy entails. Bateson’s classification of learning into “logical categories” sheds light on what the goals of numeracy ask of both student and teacher, as …

The “Soft Bigotry Of Low Expectations” And Its Role In Maintaining White Supremacy Through Mathematics Education, Laurie Rubel, Andrea V. Mccloskey

Occasional Paper Series

In this study, we offer an analysis of the phrase the "soft bigotry of low expectations" and considers its role in rhetoric about U.S. mathematics education policy and practice, especially in regards to Critical Mathematical Inquiry. From the phrase’s origins in a speech given by President George W. Bush in 2000, to its current use on social media, this phrase offers a lens into white supremacy and "tools of whiteness" (Picower, 2009), and their persistence in U.S. schooling paradigms, especially about mathematics. We analyze specific, recent instantiations of the phrase on blogrolls and Twitter, in addition to more implicit …

Collaboration And Critical Mathematical Inquiry: Negotiating Mathematics Engagement, Identity, And Agency, Frances K. Harper

Occasional Paper Series

When faced with the challenge of supporting students to do the “messy” mathematical work necessary for exploring social justice problems through critical mathematical inquiry, teachers might rely on more procedural or direct instruction. Because how students learn matters as much as what they learn, this can inadvertently limit students’ engagement with mathematics. Instructional strategies designed to foster equitable collaboration can support critical mathematical inquiry by promoting norms for equitable student engagement and mathematics identity development. As teachers and students negotiate what counts as mathematics engagement and who has access to mathematics, students’ authority over mathematics and social justice issues increases.

Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois

Journal of Humanistic Mathematics

Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry …

The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli

Journal of Humanistic Mathematics

In this article I describe Adelphi University's Mathematics Orientation Seminar, a new course that was introduced into the mathematics major to help students find their passion in mathematics and to strengthen the educational community within our department. I discuss quantitative and qualitative results of surveys among students in the Mathematics Orientation Seminar in Fall 2016 and Fall 2017, which suggest that this might be a useful course for other institutions to utilize within any major. Finally, I explore faculty perspectives and describe what I believe to be the final version of this course.

Disciplinary Learning From An Authentic Engineering Context, Catherine Langman, Judith Zawojewski, Patricia Mcnicholas, Ali Cinar, Eric Brey, Mustafa Bilgic, Hamidreza Mehdizadeh

Journal of Pre-College Engineering Education Research (J-PEER)

This small-scale design study describes disciplinary learning in mathematical modeling and science from an authentic engineeringthemed module. Current research in tissue engineering served as source material for the module, including science content for readings and a mathematical modeling activity in which students work in small teams to design a model in response to a problem from a client. The design of the module was guided by well-established principles of model-eliciting activities (a special class of problem-solving activities deeply studied in mathematics education) and recently published implementation design principles, which emphasize the portability of model-eliciting activities to many classroom settings.

Two …

Cross Faculty Collaboration In The Development Of An Integrated Mathematics And Science Initial Teacher Education Program, Sharon P. Fraser, Kim Beswick, Margaret Penson, Andrew Seen, Robert Whannell

Australian Journal of Teacher Education

This paper describes a collaborative project involving mathematicians, scientists and educators at an Australian university where an innovative initial teacher education (ITE) degree in mathematics/science was developed. The theoretical frameworks of identity theory and academic brokerage and their use in understanding the challenges associated with the early stages of collaborative projects is described. Data from reflections and interviews of the participants after involvement in the project from one to three years are presented to illustrate these challenges. The paper concludes with a description of the importance of the academic broker in overcoming identity challenges and facilitating cultural change for academics …

On "Icky" Data, The Political Classroom, And Towards Equity And Social Justice In Mathematics Education: A Conversation With Tonya Bartell, Samuel L. Tunstall, Oyemolade Osibodu, Tonya Gau Bartell

Numeracy

Tonya G. Bartell, ed. 2018. Towards Equity and Social Justice in Mathematics Education (Switzerland: Springer International Publishing) 341 pp. ISBN 978-3319929064.

This brief interview with Tonya Bartell introduces Towards Equity and Social Justice in Mathematics Education to the Numeracy audience. The interviewers also discuss with Tonya connections between quantitative literacy and mathematics for social justice, particularly in the context of US K-12 schooling. Tonya shares her perspective on topics ranging from the placement of quantitative literacy in K-12 mathematics education and how one might get started in incorporating a social justice lens into their teaching to paradigms for research …

Review Of Towards Equity And Justice In Mathematics Education, Edited By Tonya Gau Bartell, Emily Lardner

Numeracy

Tonya Grau Bartell, editor. 2018.Toward Equity and Social Justice in Mathematics Education. (Cham, Switzerland: Springer International Publishing). 341 pp. ISBN 978-3-319-92906-4 (also available as an e-book).

Toward Equity and Social Justice in Mathematics Education is a welcome addition to ongoing conversations about what mathematics should be taught and how it should be taught at both the college and pre-college level. Although the primary audience for the volume will be math educators and researchers, readers of this journal will discover intersecting interests, concerns, and strategies.

Exploring Authenticity Through An Engineering-Based Context In A Project-Based Learning Mathematics Activity, Bradley Bowen, Bryanne Peterson

Journal of Pre-College Engineering Education Research (J-PEER)

As education works to reconnect student learning to something more than standardized testing, project-based learning (PBL) has become a popular way to increase student engagement while providing more authentic applications of student knowledge. While research regarding PBL is bountiful, little has been done to connect this body of research with student perceptions regarding its classroom application, especially concerning authenticity and student engagement. This research focuses on the topic of ‘‘task authenticity’’ as a means to improve student outcomes. Two groups of seventh-grade students were presented the concept of slope and y-intercept in the context of engineering-based activities. The research …

Actualizing The Rights Of The Learner: The Role Of Pedagogical Listening, Allison Hintz, Kersti Tyson, Andrea R. English

Democracy and Education

This response to Crystal Kalinec-Craig’s article on the Rights of the Learner (RotL) aims to take up and build on the author’s ideas about how the RotL framework can promote equitable mathematics teaching and learning. Specifically, this response examines how listening is implied in the work of teachers who support young mathematicians as they exercise their rights to be confused, claim mistakes, and say and write what makes sense. In doing so, we seek to highlight some of the opportunities and challenges that can emerge for teachers attempting to support all learners to actualize these rights.

The Demands Of The Rights Of The Learner, Elham Kazemi

Democracy and Education

In this response to Kalenic-Craig’s (2017) article, “The Rights of the Learner: A Framework For Promoting Equity through Dynamic Formative Assessment,” I consider what implications the RotL framework has for the work that teachers and students must do in learning environments where these rights flourish. The RoTL emphasizes student sensemaking and communication in the classroom. Given the realities of classrooms as racialized, gendered, and classed spaces, this emphasis on communication demands critical consciousness for both teachers and students.

Six Propositions Of A Social Theory Of Numeracy: Interpreting An Influential Theory Of Literacy, Jeffrey Craig, Lynette Guzmán

Numeracy

We share our experiences comprehending social theory as it applies to numeracy scholarship. We build on existing arguments that social theory—explicitly acknowledging the presence and influence of histories, power, and purposes—offers something important to scholars who study and discuss numeracy. In this article, we translate the six propositions of one particular social theory of literacy into propositions about numeracy, then we explore the meaning of each proposition, its connections to existing scholarship, and its implications. This article emerges from two literature reviews: one on social theories (especially their application to and development in literacy) and one on numeracy. We bring …

Tinkering With Logo In An Elementary Mathematics Methods Course, Keri Duncan Valentine

Interdisciplinary Journal of Problem-Based Learning

With an increased push to integrate coding and computational literacy in K–12 learning environments, teacher educators will need to consider ways they might support preservice teachers (PSTs). This paper details a tinkering approach used to engage PSTs in thinking computationally as they worked with geometric concepts they will be expected to teach in K–5. Experiences programming in Logo to construct authentic artifacts in the form of two-dimensional geometric graphics not only supported PSTs’ understanding of core geometric and spatial concepts, but also helped them to make connections between mathematics and computational literacy. Artifacts and discourse are discussed as they relate …

Parts Of The Whole: Hands On Statistics, Dorothy Wallace

Numeracy

In this column we describe a hands-on data collection lab for an introductory statistics course. The exercise elicits issues of normality, sampling, and sample mean comparisons. Based on volcanology models of tephra dispersion, this lab leads students to question the accuracy of some assumptions made in the model, particularly regarding the normality of the dispersal of tephra of identical size in a given atmospheric layer.

Why I Believe People Need Painting By Numbers, Jason Makansi

Numeracy

Jason Makansi.2016. Painting By Numbers: How to Sharpen Your BS Detector and Smoke Out the Experts (Tucson AZ: Layla Dog Press). 196 pp. ISBN 978-0998425900.

This piece briefly introduces my Painting By Numbers, which aims to take the core messages of the QL/QR community from academic and professional circles to the rest of the citizenry. I describe the book in the context of the critical need for the most basic numeracy tools to help consumers of news, information, and analysis—delivered through traditional and contemporary social media outlets—determine where a reported numerical result lies on the scale from utter nonsense …

Disrupting Dominant Discourses: A (Re)Introduction To Social Practice Theories Of Adult Numeracy, Helen M. Oughton

Numeracy

The role of dominant discourse in constructing a deficit view of adult numeracy is examined, using reports from recent international surveys of adult skills as illustrative examples. Social practice theory is introduced as an alternative perspective for examining the ways adults actually use numeracy in their daily lives and work. This perspective suggests the test items used by large-scale surveys such as PIACC are only proxies for real-life numeracy skills, and that performance in such tests may misrepresent the numeracy skills of adults. Instead, social practice theory suggests that adults may have informal, situated numeracy practices that serve them adequately …

Effects Of The Instruction With Mathematical Modeling On Pre-Service Mathematics Teachers’ Mathematical Modeling Performance, Gulzade Karaci Yasa, Ilhan Karatas

Australian Journal of Teacher Education

The purpose of the study was to investigate the effects of the instruction with mathematical modeling on pre-service mathematics teachers’ mathematical modeling performance. The participants were 24 pre-service elementary mathematics teachers. A mixed method approach was used to conduct the research. Each week, the participants were given two mathematical modeling problems and solved them as a group. After that, each group shared their solutions with the class so that there was an opportunity to focus on different solution methods. The data was collected via a pre and a post mathematical modeling test. SPSS package program was utilized in order to …

The Rights Of The Learner: A Framework For Promoting Equity Through Formative Assessment In Mathematics Education, Crystal A. Kalinec-Craig

Democracy and Education

An elementary mathematics teacher once argued that she and her students held four Rights of the Learner in the classroom: (1) the right to be confused; (2) the right to claim a mistake; (3) the right to speak, listen and be heard; and (4) the right to write, do, and represent only what makes sense. Written as an emerging framework to promote equity in the mathematics classroom through divergent formative assessment, the RotL assumes that students can take more explicit ownership of their learning, both in writing and in oral communication. Foregrounded in the literature, this paper discusses how the …