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Full-Text Articles in Education

"I'M Really Just Scared Of The White Parents": A Teacher's Perceptions Of Barriers To Discussing Racial Injustice, Shimikqua Elece Ellis, Christian Goering Oct 2023

"I'M Really Just Scared Of The White Parents": A Teacher's Perceptions Of Barriers To Discussing Racial Injustice, Shimikqua Elece Ellis, Christian Goering

Curriculum and Instruction Faculty Publications and Presentations

Purpose - This study explores the perceived barriers that a Secondary English teacher faced when attempting to discuss racial injustice through young adult literature in Mississippi.

Design/methodology/approach- The authors rely on Critical Whiteness Studies and qualitative methods to explore the following research question: What are the barriers that a White ELA teacher perceives when teaching about racial injustice through The Hate U Give?

Findings- The authors found that there were several perceived barriers to discussing modern racial injustice in the Mississippi ELA classroom. The participating teacher indicated the following barriers: a lack of racial literacy, fears of discomfort, and an …


“Mi Conciencia Habla Inglés, Aunque Yo No Quiera”: Unearthing Sociopolitical Wisdom Through Translingual Poetry, Rachel Snyder Bhansari, Grace Gonzales, Patricia Venegas-Weber Sep 2023

“Mi Conciencia Habla Inglés, Aunque Yo No Quiera”: Unearthing Sociopolitical Wisdom Through Translingual Poetry, Rachel Snyder Bhansari, Grace Gonzales, Patricia Venegas-Weber

Curriculum and Instruction Faculty Publications and Presentations

In this study, we examine translingual identity poems written by three focal Latinx Teacher Candidates (TCs) in response to assignments in their Teacher Education Program (TEP). To interpret the focal TCs work, we bring together theories of raciolinguicized subjectivities, translingual literacies, and sociopolitical wisdom. Through thematic analysis, we argue that the use of translingual identity poems provided opportunities for TCs to draw on their emotions as semiotic resources and assert the connections of their identities to broader histories of marginalization and resistance. We also argue that when we, as teacher educators, engaged in the work of reflexively reading the poems …


Learning With Place As A Catalyst For Action, Catherine Hamm, Jeanne Marie Iorio, Jayson Cooper, Kylie Smith, Peter Crowcroft, Angela Molloy Murphy, William A. Parnell, Nicola Yelland Mar 2023

Learning With Place As A Catalyst For Action, Catherine Hamm, Jeanne Marie Iorio, Jayson Cooper, Kylie Smith, Peter Crowcroft, Angela Molloy Murphy, William A. Parnell, Nicola Yelland

Curriculum and Instruction Faculty Publications and Presentations

In response to dominant discourses of quality and an over-reliance on humancentric practice, the Learning with Place framework emerges as an innovative way to rethink practices, structures, and policies within education and beyond. ‘Learning with Place’ views the local Place as agentic, recognizing Place as inclusive of local First Nations knowledges and stories, histories and the more-than-human (for example, landforms, waterways, animals, insects, flora, and fauna). Through ‘Learning with Place’, deep relationships with the local Place are generated and these relationships become the catalyst for actions and decision-making regarding caring for/with local Place. This article offers an example of ‘Learning …


Teacher Preparation In The Shadow Of Loss: The Blurring Of Transacting, Transforming, And Transgressing, Anita L. Bright Aug 2021

Teacher Preparation In The Shadow Of Loss: The Blurring Of Transacting, Transforming, And Transgressing, Anita L. Bright

Curriculum and Instruction Faculty Publications and Presentations

In this narrative, autoethnographic piece, the author contends with the constructs of transactional, transformational, and transgressive forms of educational engagement and teaching, all coming to the fore in a time of tremendous sorrow, loss, stress, and transition. Looking to critical scholars and their works for guidance, the author describes the path into and through a course with teacher candidates, taken on mid-term after the unexpected death of a close colleague.


Authoring Dis/Ability Identities Mapping The Role Of Ableism In Teacher Candidate Identity Construction, Molly B. Siuty, Margaret R. Beneke Oct 2020

Authoring Dis/Ability Identities Mapping The Role Of Ableism In Teacher Candidate Identity Construction, Molly B. Siuty, Margaret R. Beneke

Curriculum and Instruction Faculty Publications and Presentations

Ableism, or the belief that abled ways of being and knowing are superior, perpetuates deficit views of ability differences, and constructs dis/ability as a problem in need of remediation so that individuals achieve “normalcy.” Ableism’s entrenched pervasiveness in education systems can be a significant barrier in teacher education when preparing critical educators who can work towards radical forms of dis/ability justice. In this paper, we argue that dis/abled teacher candidates can afford particular insight into the ways in which ableism operates in educational institutions and that dis/ability should be considered an asset to inclusive and socially just teacher preparation. Using …


Teaching Jihad: Developing Religious Literacy Through Graphic Novels, Melanie C. Brooks, Kelly Deits Cutler, Fida Sanjakdar, Daniel D. Liou Jan 2020

Teaching Jihad: Developing Religious Literacy Through Graphic Novels, Melanie C. Brooks, Kelly Deits Cutler, Fida Sanjakdar, Daniel D. Liou

Curriculum and Instruction Faculty Publications and Presentations

This study examined the representations of jihad in graphic novels to ascertain how its depictions may inform the development of religious literacy in secondary classrooms. Hegemonic constructions of jihad in theWest are commonly reduced to false binaries that shape non-Muslims’ extant beliefs and perceptions of Islam and Muslims. This raises concerns about the ways in which societal expectations shape knowledge formation in schools. Accordingly, this critical content analysis explored the depiction of jihad in three graphic novel memoirs, an increasingly popular medium of instruction in secondary classrooms. Our analysis identified three forms of jihad conveyed through the graphic novels, specifically: …


A Study Of Early Career Teachers' Practices Related To Language And Language Diversity During Mathematics Instruction, Erin Turner, Amy Roth Mcduffie, Amanda Sugimoto, Julia Aguirre, Tonya Gau Bartell, Corey Drake, Mary Foote, Kathleen Stoehr, Angela Witters Jan 2019

A Study Of Early Career Teachers' Practices Related To Language And Language Diversity During Mathematics Instruction, Erin Turner, Amy Roth Mcduffie, Amanda Sugimoto, Julia Aguirre, Tonya Gau Bartell, Corey Drake, Mary Foote, Kathleen Stoehr, Angela Witters

Curriculum and Instruction Faculty Publications and Presentations

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially early career teachers’ (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students’ mathematical vocabulary use and development. Yet, there was variability in ECTs’ focus on how to teach mathematical vocabulary, expectations for students’ precise use of mathematical terminology, and the …


The Ouroboros Of Rubrics: A Conundrum, A Case, And A Call, Anita Bright Nov 2018

The Ouroboros Of Rubrics: A Conundrum, A Case, And A Call, Anita Bright

Curriculum and Instruction Faculty Publications and Presentations

In this think piece, the author explores a conundrum and tension related to using rubrics to evaluate doctoral work. She ponders whether the use of rubrics provides beneficial ways for students to “crack the code” of academia, and/or whether the use of rubrics is perhaps a tool to engender conformity. With these competing ideas in mind, the author considers in what ways one might press for means to provide this on-ramp of access for students to the existing power structures, while at the same time seeking to change academia, to more equitably provide spaces for a range in ways of …


Using Problems Of Practice To Leverage Clinical Learning, Maika Yeigh Nov 2018

Using Problems Of Practice To Leverage Clinical Learning, Maika Yeigh

Curriculum and Instruction Faculty Publications and Presentations

Teacher preparation is a complex endeavor. Preparation programs are designed to transform regular humans into adept teachers through carefully constructed coursework and clinical experiences. University programs and the K-12 school systems both play important roles in the process; however, tensions have persisted between university coursework and clinical field work—a divide between "theoretical" and "clinical". The 2010 NCATE Blue Ribbon Panel Report issued a call to action, and asked teacher preparation programs to reconceptualize approaches to pre-service teacher learning by placing clinical experiences at the heart of the work in an effort to bridge traditional theoretical and clinical divides. This article …


Critical Literacy: Engaging First Graders In An Exploration Of Race Through Children’S Literature, Kelly Deits Cutler Oct 2017

Critical Literacy: Engaging First Graders In An Exploration Of Race Through Children’S Literature, Kelly Deits Cutler

Curriculum and Instruction Faculty Publications and Presentations

As an educator, I often hear teachers suggest that young children are not “ready” to tackle controversial topics such as race, racism, and racial identity. Reasons are oftentimes stated, such as “that’s not developmentally appropriate” or “they’re too young to understand that concept.” In direct contrast, the last sixty years of educational research indicates that children do understand the concept of race at a very early age (Clark, 1988; Derman-Sparks & Ramsey, 2011; Goodman 1952; Katz, 2013; Proshansky, 1966). Yet often adults, including parents and educators, do not recognize children’s ability to understand race. Most teachers--particularly White teachers--have difficulty talking …


English Learners' Positioning During Interactions With Monolingual English-Speaking Students, Amanda Sugimoto, Kathy Carter May 2017

English Learners' Positioning During Interactions With Monolingual English-Speaking Students, Amanda Sugimoto, Kathy Carter

Curriculum and Instruction Faculty Publications and Presentations

Increasingly, English Learners (ELs) are being educated in mainstream classrooms alongside English fluent students. Using a positioning theory framework, this multiple case study explored how ELs reflexively positioned themselves during interactions with their peers as well as how English fluent peers interactionally positioned ELs. Drawing upon multiple data sources, (i.e., observations, interviews, and artifacts), and using cross case analysis techniques, we found that ELs’ reflexive positioning was influenced by their language history and schooling context and peers’ interactional positioning moves limited ELs’ access to academic interactions. These findings pose important considerations regarding the academic and linguistic access of ELs in …


The Back Burner: A Case Study Of A Teacher’S Dilemmas When Working With English Learners, Amanda Sugimoto May 2017

The Back Burner: A Case Study Of A Teacher’S Dilemmas When Working With English Learners, Amanda Sugimoto

Curriculum and Instruction Faculty Publications and Presentations

Increasingly, mainstream classroom teachers are working with (ELs), however, little is known about what dilemmas these teachers face in their practice with ELs. Using a dilemmatic spaces framework, this case study explored the dilemmas a fourth grade teacher negotiated while working with ELs in her low-incidence school. Drawing upon multiple data sources, (i.e., observations, interviews, and artifact analysis), and using iterative and thematic analysis techniques, three dilemmas were identified. These included: (1) a lack of professional experience with ELs, (2) lack of support from the ESL teacher, and (3) conflicting administrative expectations. These findings pose important considerations for the teaching …


Communities Of Practice In Higher Education: Transformative Dialogues Toward A Productive Academic Writing Practice, Janelle De Carrico Voegele, Dannelle D. Stevens Apr 2017

Communities Of Practice In Higher Education: Transformative Dialogues Toward A Productive Academic Writing Practice, Janelle De Carrico Voegele, Dannelle D. Stevens

Curriculum and Instruction Faculty Publications and Presentations

Because faculty have advanced degrees, it is often assumed that they have perfected the skills needed to be productive, successful academic writers. In reality, many faculty struggle with the demands of academic writing and the resulting loss of energy for teaching and other aspects of their roles. This article reflects on the impact of an academic writing program through a community-of-practice lens. We describe the program and its elements, its development into a thriving cross-discipline writing community, the role of central program elements such as accountability and dialogue, and the benefits stemming from a learning-community emphasis across program elements


Evaluating Tech Tools For Literacy: A Research-Based Checklist, Todd Cherner, Peggy Hopper Mar 2017

Evaluating Tech Tools For Literacy: A Research-Based Checklist, Todd Cherner, Peggy Hopper

Curriculum and Instruction Faculty Publications and Presentations

With an emphasis placed on students reading and writing digitally, this presentation offers attendees a resource they can use to evaluate the literacy implications for using different apps and websites.


Involving Literacy And Technology: An Action Research Study To Improve Teacher Candidates’ Practice, Todd Cherner, Kristal Curry Mar 2017

Involving Literacy And Technology: An Action Research Study To Improve Teacher Candidates’ Practice, Todd Cherner, Kristal Curry

Curriculum and Instruction Faculty Publications and Presentations

As reflected in the new generation of “college- and career-ready” standards, developing students’ literacy abilities has become an educational initiative. In addition, software developers are continually releasing a range of educational website, apps, and programs intended to support student learning. The challenge then becomes how teachers can use these evolving instructional technologies to develop their students’ literacy abilities by combining them with their content and pedagogical knowledge. In this action research project, two teacher educators set out to study how their candidates used instructional technology during their internship for these purposes. In this article, the researchers will provide a background …


Educational Apps In The Blended Learning Classroom: Bringing Inquiry-Based Learning Into The Mix, Todd Cherner, Alex Fegely Jan 2017

Educational Apps In The Blended Learning Classroom: Bringing Inquiry-Based Learning Into The Mix, Todd Cherner, Alex Fegely

Curriculum and Instruction Faculty Publications and Presentations

With schools investing heavily in mobile technologies and emphasizing blended learning lessons, teachers are being required to create learning experiences that utilize these technologies to further prepare secondary students for college and the workforce. In this article, the authors first present a brief vignette intended to be representative of the emotions and pressures facing teachers as they prepare to teach with these new technologies. Next, the authors provide a framework teachers can use to create app-based lessons, which are lessons that use multiple apps to engage students in an inquiry-based learning experience. To provide further support, the authors include two …


Analysis Of Stakeholder Perceptions Of A Clinical Model Involving Co-Teaching And Extended-Field Experiences In An Inclusive Middle-Grades Setting, Barbara Ruben, Nicole R. Rigelman, Matthew Carl Mcparker Jun 2016

Analysis Of Stakeholder Perceptions Of A Clinical Model Involving Co-Teaching And Extended-Field Experiences In An Inclusive Middle-Grades Setting, Barbara Ruben, Nicole R. Rigelman, Matthew Carl Mcparker

Curriculum and Instruction Faculty Publications and Presentations

A qualitative study of the impact of a school university partnership in which eight teacher candidates from a two-year graduate program were placed together in a poverty level middle school was conducted. Teacher candidates in this particular program receive a master’s degree, as well as a teaching license in their content area and special education. Using primarily focus group interviews with school leaders, cooperating teachers in special education and content classrooms, and teacher candidates, we wanted to determine the influence of the partnership on all stakeholders. We read transcripts to identify themes and coded by those themes. Later, we tracked …


Novice Teachers’ Narratives Of Seeing The Spectrum From A Lense Of Social (In)Justice: Preservice’ Teachers’ Well-Remembered Events Of Gender-Based Pedagogical And Policing Practices In Elementary School Settings, Amanda Sugimoto, Kathy Carter Apr 2016

Novice Teachers’ Narratives Of Seeing The Spectrum From A Lense Of Social (In)Justice: Preservice’ Teachers’ Well-Remembered Events Of Gender-Based Pedagogical And Policing Practices In Elementary School Settings, Amanda Sugimoto, Kathy Carter

Curriculum and Instruction Faculty Publications and Presentations

Despite very recent and hard-earned progress in national and state legislation explicitly prohibiting discrimination and bullying based on gender identity, expression, or sexual orientation, new teachers continue to report that their professional preparation programs do not adequately prepare them to address both the subtle and serious classroom-based bullying scenarios which routinely marginalize a particular group of students, those who identify as lesbian gay, bisexual, transgender, or questioning (LGBTQ) students (Jennings, 2007). To be sure, we, as a teacher education community, need to push forward in our work to develop socially just teacher education curriculum and tasks which prepare teachers to …


A Detailed Rubric For Assessing The Quality Of Teacher Resource Apps, Todd Cherner, Cheng-Yuan Lee, Alex Fegely, Lauren Santaniello Jan 2016

A Detailed Rubric For Assessing The Quality Of Teacher Resource Apps, Todd Cherner, Cheng-Yuan Lee, Alex Fegely, Lauren Santaniello

Curriculum and Instruction Faculty Publications and Presentations

Since the advent of the iPhone and rise of mobile technologies, educational apps represent one of the fastest growing markets, and both the mobile technology and educational app markets are predicted to continue experiencing growth into the foreseeable future. The irony, however, is that even with a booming market for educational apps, very little research regarding the quality of them has been conducted. Though some instruments have been developed to evaluate apps geared towards student learning, no such instrument has been created for teacher resource apps, which are designed to assist teachers in completing common tasks (e.g., taking attendance, communicating …


“I Understand What These Students Are Experiencing”: Linguistically Diverse Preservice Teachers’ Narratives Regarding English Learners, Amanda Sugimoto Jan 2016

“I Understand What These Students Are Experiencing”: Linguistically Diverse Preservice Teachers’ Narratives Regarding English Learners, Amanda Sugimoto

Curriculum and Instruction Faculty Publications and Presentations

Preservice teachers enter their preparation programs with multiple years of experience in schools as k-12 students. Past schooling experiences, or their ‘apprenticeship of observation’ (Lortie, 1975), often shape preservice teachers’ understandings of schools, teaching, and learning. Teacher preparation programs must address these experiences and related preconceptions when preparing preservice teachers to work with students, specifically diverse student populations (Hammerness et al., 2005). While the majority of the teaching force remains White, female, and monolingual English speaking, the scholarly community has begun to focus on the preparation of diverse preservice teachers (e.g., Tsui, 2007). This study focuses on one such a …


Social Studies In The Modern Era: A Case Study Of Effective Teachers' Use Of Literacy And Technology, Kristal Curry, Todd Cherner Jan 2016

Social Studies In The Modern Era: A Case Study Of Effective Teachers' Use Of Literacy And Technology, Kristal Curry, Todd Cherner

Curriculum and Instruction Faculty Publications and Presentations

The purpose of this research project was to highlight the practices and philosophies of two effective—but different—social studies teachers who balance the demands of teaching in the modern era while honoring their own philosophies for teaching social studies. This project was ground in the theoretical framework provided by TPACK and used a case study methodology for its research design. While the pedagogical content knowledge of the participants was strong and technology was used abundantly for instructional purposes, this research raised questions regarding how teachers can most effectively use technology to enhance instruction by helping students conceptualize content knowledge and apply …


Building Anti-Bias Early Childhood Programs: The Role Of The Leader, Louise Derman-Sparks, Debbie Leekeenan, John Nimmo May 2015

Building Anti-Bias Early Childhood Programs: The Role Of The Leader, Louise Derman-Sparks, Debbie Leekeenan, John Nimmo

Curriculum and Instruction Faculty Publications and Presentations

An anti-bias early childhood care and education (ECCE) program puts diversity and equity goals at the center of all aspects of its organization and daily life. It involves much more than adding new materials and activities into the already existing learning environment. Rather, broad systemic changes are necessary. The learning environment and curriculum, as well as program policies, structures, procedures, and processes, all come into play. Change also includes the attitudes of the individuals who serve the children and families. In sum, it is "a process, not an event".


Putting The Heart Back Into Writing: Nurturing Voice In Middle School Students, Barbara Ruben, Leanne Moll Nov 2013

Putting The Heart Back Into Writing: Nurturing Voice In Middle School Students, Barbara Ruben, Leanne Moll

Curriculum and Instruction Faculty Publications and Presentations

To gain a deeper understanding of young adolescent motivation and developmental needs as the nation plunges ahead with the national Common Core Standards and their implications for writing instruction, the authors of this article pondered five questions as they studied their own middle school writing team: (1) What intrinsic motivators drive these young students to write? (2) What components create a nurturing writing environment? (3) How can we understand student motivation so that we can nurture student interest in writing within the constraints of large classes and mandates to address Common Core Standards? (4) For students who are already intrinsically …


Engaging Middle Level Teachers In Literacy Through Lesson Study, Susan J. Lenski, Micki M. Caskey Jun 2013

Engaging Middle Level Teachers In Literacy Through Lesson Study, Susan J. Lenski, Micki M. Caskey

Curriculum and Instruction Faculty Publications and Presentations

This is a presentation on the Lesson Study approach of teaching that was presented at a workshop during the annual meeting of the International Reading Association in Atlanta, Georgia, in May 2008.

A 2-page summary of the presentation is located as supplemental file below.


What Research Says About... The National Project On Common Planning Time, Steven B. Mertens, Vincent A. Anfara Jr., Nancy Flowers, Micki M. Caskey Jun 2013

What Research Says About... The National Project On Common Planning Time, Steven B. Mertens, Vincent A. Anfara Jr., Nancy Flowers, Micki M. Caskey

Curriculum and Instruction Faculty Publications and Presentations

What Research Says about... The National Project on Common Planning Time PDF version of a PowerPoint presentation given at the National Middle School Association Annual Conference, Indianapolis, IN, Nov. 6, 2009.


Queer Youth In Heterosexist Schools: Isolation, Prejudice And No Clear Supportive Policy, Olivia Jo Murray Oct 2011

Queer Youth In Heterosexist Schools: Isolation, Prejudice And No Clear Supportive Policy, Olivia Jo Murray

Curriculum and Instruction Faculty Publications and Presentations

In the wake of institutionalized homophobia afflicting public schools, the nation faces a unique opportunity to acknowledge and transform the assumption that all people are or should be heterosexual and gender-conforming. In this article, the author examines how people, as a nation, can reform schools to be more inclusive of diverse student identities, such as queer, by transforming educational policy to include the voices of marginalized youth. She begins by first describing federal legislation that excludes the protection of queer youth, subjecting millions of children to exploitation, humiliation, and condemnation within classrooms across the nation. Then, drawing from bell hooks …


A National Research Project Revitalizes And Strengthens A Sig’S Membership, Leadership, And The Quality Of Research In The Field, Steven B. Mertens, Vincent A. Anfara Jr., Nancy Flowers, Micki M. Caskey Aug 2011

A National Research Project Revitalizes And Strengthens A Sig’S Membership, Leadership, And The Quality Of Research In The Field, Steven B. Mertens, Vincent A. Anfara Jr., Nancy Flowers, Micki M. Caskey

Curriculum and Instruction Faculty Publications and Presentations

A recent moratorium has temporarily halted the creation of new Special Interest Groups (SIGs) in the American Educational Research Association (AERA). The AERA SIG Executive Committee, the official governance body that oversees approximately 160 SIGs, requested this moratorium, which was subsequently approved by AERA Council. The purpose of the moratorium is to allow the SIG Executive Committee to gather data to facilitate a more critical examination of issues related to SIGs, including low membership numbers, leadership challenges, and specific membership needs addressed by SIGs. This article offers the Middle Level Education Research (MLER) SIG as an example of a SIG …


Evaluation Of A Merged Secondary And Special Education Program, Ann Fullerton Dr., Barbara Ruben, Stephanie Mcbride, Susan Bert Apr 2011

Evaluation Of A Merged Secondary And Special Education Program, Ann Fullerton Dr., Barbara Ruben, Stephanie Mcbride, Susan Bert

Curriculum and Instruction Faculty Publications and Presentations

If classroom teachers are among the greatest determinant of student learning, then teacher preparation programs have a role to play improving educational outcomes for struggling learners. There are currently three established teacher preparation program models: (1) "discrete"; (2) "integrated"; and (3) "merged." In the "discrete" model, which is the most widely implemented of the three, general and special education programs are separate. In the "integrated" model, separate programs are retained but faculty work together to develop some courses and/or field experiences in which special education candidates learn about the general education curriculum while general education candidates learn about inclusive education. …


Research Summary: Assessment, Robert Michael Capraro, Mary F. Roe, Micki M. Caskey, David Strahan, Penny A. Bishop, Christopher C. Weiss Jan 2011

Research Summary: Assessment, Robert Michael Capraro, Mary F. Roe, Micki M. Caskey, David Strahan, Penny A. Bishop, Christopher C. Weiss

Curriculum and Instruction Faculty Publications and Presentations

Assessment is important for middle level teachers and their students. In fact, the National Middle School Association (NMSA) highlighted curriculum, instruction, and assessment in This We Believe: Keys to Educating Young Adolescents (NMSA, 2010). The intention of this summary is to establish assessment’s rightful position as one priority for middle grade teachers and their students. When used wisely and well, teachers obtain information about their students’ strengths and needs, and their students remain informed about their achievements. To begin, educators need an operational definition of assessment. Based on the work of many scholars (e.g., Delclos, Vye, Burns, Bransford, & Hasselbring, …


"Math In A Can": Teaching Mathematics And Engineering Design, Ronald B. Narode Jan 2011

"Math In A Can": Teaching Mathematics And Engineering Design, Ronald B. Narode

Curriculum and Instruction Faculty Publications and Presentations

Using an apparently simple problem, "Design a cylindrical can that will hold a liter of milk," this paper demonstrates how engineering design may facilitate the teaching of the following ideas to secondary students: linear and non-linear relationships; basic geometry of circles, rectangles, and cylinders; unit measures of area and volume; solving systems of equations with at least two variables; minimization of area to control materials costs and to prevent heat exchange; packing geometry to minimize space for transportation and storage and for controlling for heat exchange; golden ratio as a design aesthetic; ergonomic factors in design including considerations of comfort …