Analyzing Students’ Errors in Solving Fractions in Developmental Mathematics Courses

JMutah

Jonah Mutua

Jonah Mutua is a Ph.D. Candidate in the Developmental Education program at Texas State University with a specialization in developmental math.  He earned his M.S. from the University of Texas at Dallas and taught mathematics for Dallas Community Colleges (2011-2012) and Huston-Tillotson University in Austin (2012-present). His research interests involve finding better and practical ways to teach fractions and quadratic equations to college algebra students.

Introduction

Students enrolled in developmental mathematic courses experience various challenges in learning mathematics in general, and, in particular, they struggle in solving fractions problems.  The American National Mathematics Advisory report (2008) states that “difficulty with the learning of fractions is pervasive and is a major obstacle to further progress in mathematics and other domains dependent on mathematics, including algebra” (p. 28).

Seigler and Pyke (2012) state that some of the properties of positive whole numbers arithmetic operations–which are taught before fractions are introduced to students–are not transferable in solving fraction problems, which is a major source of confusion among students. For example, positive whole numbers never increase with division, never decrease with multiplication, and they have unique successors.  None of these properties are applicable when solving fraction problems. Students often find it difficult to learn and apply new properties required to handle fractions.  Instead, they apply positive whole number properties in dealing with fractions and vice versa (Ni & Zhuo, 2005; Vamvakoussi & Vosniadou, 2010).

Another hurdle witnessed among children and adults as they struggle to master fraction concepts and procedures is the realization that the numerator and denominator should be handled together as a single unit and not as two separate and unrelated whole numbers. A study found that “students process the natural number parts of the fractions separately” (Kallai & Tzelgov, 2012).  For example, when students solve this problem  2/3 + 4/5 , they often add 2+4=6 and 3+5=8, and they obtain 6/8 (which is wrong) as their final answer. According to Siegler & Lortie-Forgues (2015), there is a positive and significant relation between students’ ability to accurately place a fraction or decimal on the number line and their general arithmetic ability.

Theoretical Framework

Procedural and conceptual knowledge theories guided this study. According to Lin (2010), procedural knowledge can be defined as the necessary steps required to solve problems. The use of procedures helps students to solve fractions without necessarily understanding the concepts behind the procedures. Siegler & Lortie-Forgues (2015) found that procedures are easy to memorize and apply, but they are not as flexible as conceptual understanding.

Fazioand, Lisa & Siegler (2011) defined conceptual knowledge as knowing why–showing understanding and the ability to sequentially explain why rules or procedures applied in solving fractions result to correct solutions.  Conceptual knowledge can be generalized to a class of problems and is not tied to a specific problem, (Fazioand, Lisa, & Siegler, 2011).

Research Questions

  1. What are the common errors committed by developmental mathematics students when solving fractions?
  2. Which fractions concepts do developmental mathematics students struggling with the most?

Importance of the study

Learning fractions has remained a challenging domain for students in developmental mathematics. This study seek to identify specific area in which students struggle while solving fractions. The study findings can be used to inform lesson planning so that “problematic” can be allotted more emphasis in terms of time and resources.

Research Method

Participant and Procedures

Three students were identified for this study based on the averages of their pretest and examination one scores, willingness to participate in the study and their availability. Benson is struggling with the basics of solving fractions. His pretest score was below 50%. Mary is an average student compared with students Benson and Loice. Her pretest score was between 50-60 %. Loice is the best of the three students in the study. His pretest score was 65-75 %. Each student solve three problems. All students in the study are freshmen, and they had never enrolled in this course before. This requirement was necessary to ensure a fair comparison among students at the end of the study.

 Research Findings

QUESTION 1: Which is greater: 5/12 or 9/16?

Benson: He converted both fractions into decimal and then compared the two before choosing is final answer. Benson was able to solve this problem and explain his solution logically.

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Mary: She compared 5 with 9; 9 was greater, then she compared 12 with 16; 16 was greater.  Therefore,  9/16 was greater than. Mary got the correct answer, but her explanation was wrong.

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Loice: She cited her previous instructor: “fractions are the reverse, the bigger the denominator, the smaller the fraction.” She compared 12 with 16 and decided that 5/12 was greater than 9/16 because 12 is smaller than 16. Loice’s answer was wrong.

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QUESTION 2: Solve x+ 1/6 = 5/8.

Benson: He isolated x by subtracting on both fractions. Benson converted the fractions on the right side into decimal numbers, and then he subtracted 0.167 from 0.625 to get his answer (0.458). Benson struggled in converting his final answer (0.458) into a fraction, but he did great work.

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Mary: She isolated x by subtracting on both fractions. Mary calculated the Least Common Multiple (LCM) of 6 and 8, then performed the subtraction on the fractions. Why find LCM? We find the LCM because I thought we needed to have it, but I don’t know why.”

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Loice: She isolated x by subtracting 1/6 on both fractions. Mary calculated the Least Common Multiple (LCM) of 6 and 8, then performed the subtraction on the fractions. Why find LCM? “We find LCM because you can’t solve a problem without the denominators being the same. It’s like comparing apples to apples.”

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QUESTION 3: Divide 5-1/8 by 2-1/6 , write your answer as a mixed number.

Benson: He was not able to proceed beyond changing the mixed fractions into improper fractions. “I have to stop because I do not know. I have forgotten how to divide mixed numbers.”

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Mary: She converted the mixed fractions into improper fractions she verbalized this acronym “keep change flip, (KCF),” which meant keeping the first fraction unchanged, change the division sign to multiplication, and find the reciprocal of the second fraction. Why do we find the reciprocal of the right side fraction? “I do the KCF because it’s what I was taught; it’s the rule when you divide fractions.”

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Loice: She identified fractions which were divisible by a common factor.  Loice simplified the fractions and she obtained her answer. She used fewer steps.Why do we find the reciprocal of the right side fraction? “I’m not sure why we get the reciprocal because I’ve just always done it this way.”

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Conclusions & Discussion

This study found that participants were struggling with both the procedural methods and conceptual understanding of solving fractions.  Participants committed errors in multiplying and simplifying fractions. This study found that students’ procedural skills in solving fractions were better than their conceptual skills.  Participants fared relatively well in addition and subtraction of fractions problems, but experienced challenges in dividing and comparing the magnitudes of two or more fractions.  Participants who were not proficient with fraction concepts were unable to solve problems when they could not recall the associated acronym or rules.  For example, students who could not recall how to find the least common multiple (LCM) of two fractions failed to answer question one. Division of fractions posed a major challenge to almost all participants. Although students tried to apply division of whole numbers rules to solve division of fractions, problems most of the rules were not applicable. The use of acronyms helped some students while others could not go beyond the first step. For example, students knew they were supposed to find the reciprocal of one of the fractions when dividing two fractions, but they were not certain whether to find the reciprocal of the left or right side fraction. There was a strong relationship between students’ abilities in explaining the necessary steps required in solving a problem and obtaining the correct answer.

References

Bettinger, E., & Long, B. T. (2005). Remediation at the community college: Student participation and outcomes. New Directions for Community Colleges, 129, 17-26.

Fazioand, Lisa & Siegler. (2011). Teaching fractions.  The International Academy of Education. http://unesdoc.unesco.org/images/0021/002127/212781e.pdf

Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: the origins and implications of whole number bias. Educational Psychologist, 40(1), 27e52. http://dx.doi.org/10.1207/s15326985ep4001_3.

Kallai, A. Y., & Tzelgov, J. (2012). When meaningful components interrupt the processing of the whole: the case of fractions. Acta Psychologica, 139(2012), 358e369. http://dx.doi.org/10.1016/j.actpsy.2011.11.009.

Lin, C. (2010). Web-based instruction on preservice teachers’ knowledge of fraction operations. School Science and Mathematics, 110(2), 59-70.

Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and Instruction, 28(2), 181e209. http:// dx.doi.org/10.1080/07370001003676603.

Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology.

Siegler, R. S., & Pyke, A. A. (2012). Developmental and Individual Differences in Understanding of Fractions. Developmental Psychology. Advance online publication. doi: 10.1037/a0031200.

 

Sparking Interest with Multimodal Assignments in Integrated Reading and Writing

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Amber Sarker and Carolyn Caudle

Amber Sarker is beginning her third year of doctoral coursework with Texas State University, pursuing a PhD in Developmental Education with a focus on literacy. Amber has worked in a variety of educational settings, including elementary school, undergraduate courses, online environments, museum programming, and teaching adult second language learners. She has been a member of The Education Institute for two years, which has provided opportunities to co-create professional development, revise curriculum standards, and co-author grant proposals. Amber’s research interests are campus climate, postsecondary literacies, solidarity with students, and educational allyship with LGBTQ+ populations.

Carolyn Caudle is pursuing a Master’s degree in Developmental Education with a focus in literacy from Texas State University. Carolyn began her career teaching kindergarten and fell in love with literacy education after watching children swell with pride when reading their first word. After taking a few years off work while her children were young, Carolyn decided to go back to college and shift her focus to literacy at the post secondary level. She has special interest in improving students’ self-efficacy and boosting confidence within reading and writing.

Integrated Reading and Writing (IRW) has become an increasingly popular option for Developmental Education literacy courses. While reading and writing should continuously be the focus of each assignment and text (Holschuh & Paulson, 2013), embracing students’ digital literacies is an additional relevant and needed component of IRW instruction. The need for instructors to acknowledge and build on students’ digital skills is a result of academia’s shift from students being assigned static texts to complex hybrid texts (Lea and Jones, 2011). Moreover, multimodal meaning making, or comprehending a message using a variety of modes, occurs in a variety of cultural practices, and as a result, emphasizing this in the IRW classroom would benefit students greatly (Cope & Kalantzis, 2009). In order to provide context for this aforementioned research, this article briefly describes how an IRW course can use Adobe Spark to showcase connections students make in their personal lives in comparison to a novel read in class.

Cope and Kalantzis (2009) stated that embracing multiliteracies allows students to not simply restate ideas, but become “transformers of meaning” (p. 115). The ability of students to transform meaning using digital literacies is the central focus of the IRW lesson we are proposing. Our suggested assigned novel for an IRW course is Love and First Sight by Josh Sundquist. This novel is about a high school student, Will, who has been attending schools for the visually impaired his entire academic career, but decides to transfer to a mainstream high school. The text details his struggles and triumphs in this new environment. After reading the novel, students would identify a time in their own life when they were challenged with an unfamiliar environment and were required to navigate using a new literacy. They would then be asked to chronicle their own “fish out of water” experience using the free application Adobe Spark. Using this digital program, students could share their story using images, sound, and text to create a professional multimodal presentation.

College students are adept at navigating multimodal texts and resources. Unfortunately, this integration of technology often does not transfer to the classroom. To further prepare our students, embracing multimodal technology and making it the cornerstone of our instruction is paramount (Yu, 2014). Our suggested Adobe Spark storytelling project stresses the importance of New Literacies in an IRW course and suggests a method utilizing visual and auditory modes that can be used to augment instruction.

Cope and Kalantzis (2009) explained, “Experiencing the known involves reflecting on our own experiences, interests, perspectives, familiar forms of expression and ways of representing the world in one’s own understanding” (p. 125). By using Adobe Spark to connect a text to their own lives, students are able to digitally represent their world to their peers. The intersection of students’ experiences and the experiences of characters allows for an opportunity to understand varied perspectives and representations of ideas. Additionally, using Adobe Spark allows students to pre-record their presentation, allowing for a chance to revise the message intended for the viewer.

By creating experiences where students can use digital literacies to convey information, educators provide opportunities for students to “critique, resist, challenge, and change discourses” (Leander & Bolt, 2012, p. 33).  Moreover, by using multimodal presentations, students are able to interact and communicate with peers in an engaging way (Jewitt, 2014). In addition, using a platform such as Adobe Spark allows students to interact with an engaging tool in order to connect the meaning made from the text to a larger audience. Implementing varied uses of technology in an IRW course allows students to better understand the intersection of discourses and digital literacies.

References

Cope, B., & Kalantzis, M. (2009). “Multiliteracies”: New literacies, new learning. Pedagogies, 4(3), 164-195. doi:10.1080/15544800903076044

Holschuh, J. L., & Paulson, E. J. (2013). The terrain of college reading. College Reading and Learning Association.  Retrieved from http://www.crla.net/index.php/publications/crla-white-papers

Jewitt, C. (2014). Different approaches to multimodality. In Author (Ed.), The Routledge handbook of multimodal analysis (2nd ed., pp. 31-43). London, GBR: Routledge.

Lea, M. R., & Jones, S. (2011). Digital literacies in higher education: Exploring textual and technological practice. Studies in Higher Education, 36(4), 377-393.

Leander, K., & Boldt, G. (2013). Rereading “A pedagogy of multiliteracies”: Bodies, texts, and emergence. Journal of Literacy Research, 45(1), 22-46.

Yu, E. (2014). Let developmental students shine: Digital writing. RTDE 3(2), 99-110.

 

 

Implementing Contextualization into the IRW Classroom: Making IRW “Worth It”

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Jessica Slentz Reynolds

Jessica Slentz Reynolds is a third-year doctoral student in developmental education with a focus on developmental literacy at Texas State University. She earned a M.A. in English from Texas A&M University—Corpus Christi, where she also taught Composition and Developmental Writing as an adjunct instructor. She has been a Writing Consultant for the CASA Writing Center since 2011 and continues to tutor students online. Her research interests involve postsecondary literacies, integrated reading and writing, diversity in developmental education classrooms, and writing centers.

Last fall, I was inspired by The Education Institute’s (TEI) Self-Change Power Project to integrate contextualization into my Integrated Reading and Writing (IRW) course. Contextualization, in short, is the teaching of basic skills within a disciplinary topic (Perin, 2011). According to Perin (2011), contextualization can increase students’ intrinsic motivation and level of engagement in the classroom because it allows the subject to be deemed useful and interesting to learners. After reading Perin, I was reminded of the seminal work on IRW by Bartholomae and Petrosky (1986) where they argued that IRW courses should not be a study skills course consisting of workbooks and diagramming sentences, but IRW should help students acquire the necessary literacies to be successful in both academic and workplace discourses.

After making the connection between Perin’s (2011) work on contextualization and Bartholomae and Petrosky’s (1986) theory on IRW, I decided to modify the Self-Change Power Project to help students achieve the learning objectives for the expository unit of the semester: the Discourse Community Analysis (DCA). It is common for IRW instructors to assign an expository unit centered around the students’ future careers; however, I like to provide an opportunity for students to familiarize themselves with their future careers in a way that transcends a basic description of their potential professions. Since IRW is a reading and writing course, I use the expository unit to help students understand the various literacies in their chosen fields of study. The students complete a 6-week DCA project, where they not only research the many facets of communication within their potential careers, but they also observe and participate within these communities. The students must present—through either traditional essay format or by a formal presentation to the class—the goals, types of communication, language, membership, and the significance of literacy within their selected communities (Wardle & Downs, 2011).

These questions guided the expository unit to make IRW “worth it”:

  • Does assigning a DCA on students’ future careers lead to students having a stronger understanding of academic and workplace literacies?
  • Does implementing a comprehensive project that focuses on students’ individual goals increase motivation for students to complete the IRW course?
  • Could an alternative version of the Self-Change Power Project accomplish these goals?

The following is a brief timeline of activities leading up to the final product for the DCA project. These components are a direct reflection of the Self-Change Power Project guidelines.

  • Students brainstorm and research types of communication, language, behaviors, and various literacies of their future careers.
  • Students decide what types of communication, language, behaviors, and various literacies of their future careers they want to observe, participate in, and monitor for 4-5 weeks.
  • Students participate in their selected communities and keep a journal about their experiences. They are prompted to write about what they observed, how they participated within the community, and how literacy is an integral aspect of their community.
  • In the last week of the unit, students showcase through writing, class discussion, and photographic evidence their processes and experiences participating in their chosen discourse communities.
  • Students submit their completed DCA project for a grade via essay or in-class presentation.

This DCA project aligns with what Goen & Gillotte-Tropp (2003) referred to as the six principles of an IRW program: integration, time, development, academic membership, sophistication, and purposeful communication. Based on feedback from two sections of IRW, I received an overwhelming amount of positive responses from students who completed this project. Students stated that the project helped them decide if their selected major was the right path for them; the act of observing, understanding, and researching their communities forced students to use a variety of skills and resources they had not yet used in college; and, finally, students reported that it made them see the benefits to taking an IRW course.

 References

Bartholomae, D., & Petrosky, A.R. (1986). Facts, artifacts and counterfacts: Theory and method for a reading and writing course. Upper Montclair, NJ: Boynton/Cook.

Goen, S., & Gillotte-Tropp, H. (2003). Integrating reading and writing: A response to the basic writing “crisis”. Journal of Basic Writing, (22)2, 90-113.

Perin, D. (2011). Facilitating student learning through contextualization: A review of evidence.  Community College Review, 39(3), 268-295. doi: 10.1177/0091552111416227

The Education Institute. (2016). The Education Institute. Retrieved from http://www.tei.education.txstate.edu/

Wardle, E., & Downs, D. (2011). Writing about writing. Boston, MA: Bedford/St. Martin’s.

 

 

 

 

 

The Many Legacies of Dr. Claire Ellen Weinstein, Part 1 Tribute: Learning Frameworks Courses

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Dr. Claire Ellen Weinstein

“Much have I learned from my teachers, more from my colleagues, but most from my students.” ~Talmud, Ta’anit 7b

Dr. Claire Ellen Weinstein was Professor Emeritus at the University of Texas at Austin. Dr. Weinstein is renowned for groundbreaking research on learning strategies, her Model of Strategic Learning, and as senior author of the Learning and Study Strategies Inventory. Dr. Weinstein’s research and practice in strategic learning has helped to define strategic learning courses, curriculum, and instruction across the U.S. and abroad, and especially in Texas; her legacy lives on in her many students and her students’ students. Of particular interest for this tribute (Part 1) is her college-level, 3-credit, learning frameworks course, Individual Learning Skills (EDP 310), offered through the Educational Psychology Department at the University of Texas at Austin since 1975.

EDP 310 is designed to help students learn how to learn. The course enrolls students of all levels, but especially those who enter the university under special circumstances or who experience academic difficulty. Course content is driven by Weinstein’s Model of Strategic Learning, inspired by systems theory and Gestalt psychology, which emphasizes that strategic learning emerges from the interactions among elements within four major components: skill, will, self-regulation, and the academic environment.  Weinstein attributes many of her ideas about strategic learning to one of her mentors, Wilbert J. McKeachie, and his research at the University of Michigan on strategic teaching (Weinstein, 1994; Weinstein, Acee, Jung, Krause, Dacy, & Leach, 2012).

In 1999, the Texas Higher Education Coordinating Board authorized formula funding of up to three credit hours for courses following a learning frameworks curriculum, which must include, “…1) research and theory in the psychology of learning, cognition, and motivation, 2) factors that impact learning, and 3) application of learning strategies” (Hill, 2000, para. 4). The policy change was a result of two learning framework course studies, one from the University of Texas at Austin (based on EDP 310—Individual Learning Skills) and the other from Texas State University (based on EDP 1350—Effective Learning), which presented statistically significant improved student retention and graduation rates for students successfully completing multiple sections of these learning frameworks courses as compared to other students not enrolled (Hill, 2000).

Learning frameworks courses provide instruction on learning strategy applications and inform students of theoretical frameworks that underpin each strategy drawing from educational neuroscience, metacognition, behaviorism, and constructivism—among many others. Most “study skills” courses teach students specific techniques and methods in isolation, such as content mapping, comprehension monitoring, and textbook annotation, focusing on acquisition of a skill but not comprehensive understanding of why and how learning can be enhanced by using that technique. Learning frameworks courses help students to assess their own learning strengths and weaknesses so that, once introduced to theories and strategies, students can understand the reasons for engaging in specific studying behaviors. Practicing learning strategies with their other course content is essential for the transfer of this knowledge (Hodges & Agee, 2009; Hodges, Sellers, & Dochen, 2012).

While learning frameworks courses are offered throughout U.S. postsecondary institutions, Texas has been at the forefront; approximately 90% of 2-year institutions and 75% of 4-year institutions offer multiple sections of these courses. Many of Texas’s 2-year institutions now require all first-year students to enroll in the course while 4-year institutions more typically offer the course to special populations such as conditionally-admitted students or students on academic probation. High schools are also now beginning to offer learning frameworks courses as dual-credit courses (Acee & Hodges, 2017).

Dr. Weinstein was a pioneer in postsecondary access and success; she knew that every student could learn, and she dedicated her life to that end.  Learning frameworks courses are one of her many legacies. We honor her memory as we continue to expand the reach and effectiveness of these courses and help students to become more strategic and self-regulated lifelong learners.

Authors

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Russ Hodges, Ed.D.

Dr. Russ Hodges is Associate Professor in the Graduate Program in Developmental Education in the Department of Curriculum and Instruction at Texas State University. He earned his Ed.D. in developmental education from Grambling State University and his M.Ed. from University of Louisiana in Monroe. Dr. Hodges’ research focuses on postsecondary student success, postsecondary student success courses, interventions for students diagnosed with AD/HD, and demographic changes in higher education. The learning framework model that he co-developed serves as a curriculum model for many postsecondary learning framework courses throughout Texas and the nation. Dr. Hodges has held state and national leadership positions including president of the College Reading and Learning Association (CRLA) and chair of the Council of Learning Assistance and Developmental Education Associations (CLADEA). He is an active scholar, having published three books, many journal articles, book chapters, and conference papers along with four research grants totaling just over 1 million dollars. He is also a frequent invited speaker for conferences for postsecondary faculty and staff development.  Dr. Hodges has received many awards, including the Lifetime Achievement Award from the College Academic Support Programs conference, and outstanding service awards from both CRLA and the National Association for Developmental Education (NADE).  In 2009, Dr. Hodges was named National Fellow for CLADEA—his field’s most prestigious honor. 

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Taylor Acee, Ph.D.

Dr. Taylor W. Acee is Associate Professor in the Graduate Program in Developmental Education in the Department of Curriculum and Instruction at Texas State University. He earned his Ph.D. and M.A. in educational psychology at The University of Texas and his B.S. in psychology at the University of Pittsburgh. His program of research is focused on cognitive, metacognitive, motivational, and affective factors that contribute to and detract from student success in postsecondary education. In his research, Dr. Acee targets variables that are causative, account for a meaningful amount of the variation in student success, and are amendable to change through educational intervention. He is internationally known for his collaborative work on personal relevance interventions, academic boredom, and strategic learning assessments and interventions. His research activities have resulted in over 30 refereed publications, 5 funded research grants totaling over $800,000, and various other scholarly activities.

References

Acee, T. W., & Hodges, R. (2017). [Learning framework courses in Texas]. Unpublished raw data.

Hill, M. A. (2000, March 31). Funding for “Learning Framework” courses [Memorandum to Chief Academic Officers, Public Senior Universities]. Austin, TX: Texas Higher Education Coordinating Board.

Hill, M. A. (2000, March 31). Funding for “Learning Framework” courses [Memorandum to Chief Academic Officers, Public Senior Universities]. Austin, TX: Texas Higher Education Coordinating Board.

Hodges, R., & Agee, K. (2009). Program management. In R. F. Flippo &  D. C. Caverly (Eds.), Handbook of college reading and study strategy research (pp. 351-378). New York: Routledge.

Hodges, R., Sellers, D., & Dochen, C. W. (2012). Implementing a learning framework course. In R. Hodges, M. L. Simpson, & N. A. Stahl (Eds.), Teaching study strategies in developmental education: Readings on theory, research and best practice (pp. 314-325). Boston, MA: Bedford St. Martin’s.

Weinstein, C. E., Acee, T. W., Jung, J., Krause, J. M., Dacy, B. S., & Leach, J. K. (2012). Strategic learning: Helping students become more active participants in their learning. In K. Agee & R. Hodges (Eds.), Handbook for training peer tutors and mentors (pp. 30-34). Mason, OH: Cengage Learning.

 

Using Tableau Theatre in the Integrated Reading and Writing Classroom

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Tamara Harper Shetron and Kristie O’Donnell Lussier

Tamara Harper Shetron is a fourth year doctoral student in developmental education with a focus on literacy, learning supports, and postsecondary education for students with intellectual and developmental disabilities. She has a back ground in music and theatre, and brings an interdisciplinary approach to her teaching and research.

Kristie is in her fourth and final year of doctoral study at Texas State. Her teaching and research focus on integrated reading and writing, educational experiences of linguistically diverse students, and sociocultural aspects of teaching and learning. Kristie loves to travel and plans to see every continent someday. 

This article describes the process and results of a research experiment using tableau theatre with an integrated reading and writing class in the Spring of 2016.  Tableau is an instructional technique in which  students physically recreate ‘frozen statues’ of a literary event from their reading.  Our research goal was to find out if this contextualized learning experience would enhance motivation, engagement, and learning through the use of total body engagement (Asher, 1969), which stimulates brain activity, a prerequisite for learning (Hinton, Fischer, & Glennon, 2012; Rinne, Gregory, Yarmonlinskaya, & Hardiman, 2011; Toshalis & Nakkula, 2012), and currently one of the top needs in the Developmental Education (DE) classroom (Saxon, Martirosyan, Wentworth, & Boylan, 2015).

First, we introduced the tableau concept using a scene we thought students would be familiar with, a job interview.  Next, having established the conceptual dynamics and reflective learning postures, the IRW students then transitioned to using tableau techniques with scenes from their reading, “The Lottery” by Shirley Jackson.  We distributed copies of the story with the final paragraphs removed and taped under each student’s desk with the name of a different character from the story assigned to each.  Students were instructed to finish reading the story from the perspective of that character.  Next, using these randomly assigned characters, we created tableaus of the final dramatic stoning scene.  We created additional replications of the scene rotating through character assignments obtained through a mock lottery similar to that in the story.  Having grown accustomed to the task through the initial activity, students became highly engaged, and offered very little resistance to the activity.

The final portion of the experiment was to analyze student’s written responses to the activity.  Overall, student responses demonstrated a deep understanding of the story and an ability to understand the multiple perspectives of characters.  Two students responses in particular showed a depth of personal  engagement with the text far above what we had expected.  They were inventive, creative, and while remaining true to the original story, wove in themes of agency, democratic decision making and power redistribution, and even Christ/substitutionary death.

“Tessie Hutchinson was stoned to death, or so they thought,” “She laid there so life-less…she gained strength and limped away to safety..she has been working out to get stronger and faster,” “ Tessie planned to hurt everyone who was apart [sic] of her stoning,” “She was like a [sic] invincible woman.”

In a second student’s rendition, the town votes to end the lottery, but in an unexpected shift, votes to hold one last lottery, immortalizing Tessie as the final ‘winner.’  This highly descriptive emotional roller coaster ride is then given an unexpected twist when Tessie’s husband offers to die in her place.  This student showed in-depth engagement with the story and its characters, and also added philosophical thoughts about the lottery “For every rock, no matter the shape or size that hits their loved one, a fraction of his or her soul leaves their body.”

This sample of our research demonstrates that, indeed, tableau theatre can be a very engaging and motivating instructional technique for an Integrated Reading and Writing class.

References

Asher, J. J. (1969). The Total Physical Response Approach to Second Language Learning*. The modern language journal, 53(1), 3-17.

Hinton, C., Fischer, K.W., & Glennon, C. (2012). Mind, brain, and education. Teaching and learning in the era of the common core: An introduction to the project and the nine research papers in the Students at the Center series. Retrieved from www.studentsatthecenter.org.

Rinne, L., Gregory, E., Yarmonlinskaya, J., & Hardiman, M. (2011). Why arts integration improves long-term retention of content.  Mind, Brain, and Education, 5(2), 89-96.

Saxon, D.P., Martirosyan, N.M., Wentworth, R.A., & Boylan, H.R. (2015).  NADE members respond: Developmental education research agenda: Survey of field professionals, part 2. Journal of Developmental Education, 38(3), 32-34.

Toshalis, E. & Nakkula, M.J. (2012). Motivation, engagement, and student voice. Teaching and learning in the ear of the common core: An introduction to the project and the nine research papers in the Students at the Center series.  Retrieved from www.studentsatthecenter.org

Transforming Instruction with Technology

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Nathalie Vega-Rhodes

Nathalie Vega-Rhodes is currently a professor of mathematics and the mathematics technology coordinator at Lone Star College – Kingwood. She specializes developmental education redesign and focuses on researching and create valuable resources for students and instructors. Prior to her time at Lone Star, Vega-Rhodes taught mathematics and college student success courses at other institutions around the Houston area. Vega-Rhodes earned a Bachelor of Arts degree in mathematics with a minor in geology from the University of Houston and a Master of Science degree in mathematics from the University of Houston-Clear Lake. In her spare time, she enjoys reading, traveling, and scuba diving.

Technology is advancing exponentially in our world; its use is growing in our classrooms whether we want it to or not.  Beetham and McGill (2012) observed that technology is “transforming what it means to work, study, research, express oneself, perhaps even to think.”   Bowen (2014) agrees and would further add that this growth has made course design and pedagogy more important than ever.  Given this current and irreversible trend, we must harness the benefits of this tool to enhance learning in the classroom.

As instructors, it’s incumbent upon us to leverage technology to engage students as well as organize our courses in a clear and concise manner.  Learning management systems (e.g. Moodle, Desire2Learn, Blackboard, etc.) at most institutions are a means by which instructors can manage learning and connect with students.  Clearly-named modules, checklists and release restrictions ensure access to relevant information and keep students on track.  Additional features such as Intelligent Agents allow instructors to define criteria for automated and personalized communication at critical points throughout the semester.

Other options for creating dynamic courses are college-supported software programs such as Softchalk or Webex.   For example, Softchalk can be used to create interactive lessons, while Webex can be used to meet with students virtually, thereby eliminating the age-old problem of providing timely feedback for students who are not present in a traditional face-to-face classroom.  Instructors and students can share screens to discuss concepts or work out examples, either one-on-one or in a group.  An added benefit of these software programs is that they can be integrated with most learning management systems, making for a seamless student experience.

While proper organization is unquestionably important, by itself it is insufficient.  One of the problems that instructors have traditionally faced is lack of available information, which means that instructors may not always know when to intervene or what interventions are necessary.  A valuable tool to solve these problems is the analysis capabilities in online homework systems. Easily accessible reports can be used to track progress and determine challenging concepts for individual students or the entire class.  This data can be used for evaluating current assignments or improving future courses.

In addition to online homework systems, an easy and convenient way to engage students is by harnessing the capabilities of pervasive smartphone or tablet apps.  A few favorites include Attendance (easy recording/reporting of student attendance), Show Me (easy video creation), Notability (note-taking), and Google Voice (texting/phone calls without sharing a personal phone number). Each of these apps have the potential to increase efficiency with everyday tasks.

In summary, these tools, when coupled with thoughtful implementation, can truly impact teaching and learning.  McLoughlin and Lee (2008) stated that “technological resources provide opportunities for a range of interactions, communicative exchanges, and sharing, but it is not possible to base an entire sequence of learning episodes based on tools.”  Indeed, I am able to do more and better for my students since the immediate feedback allows me to tailor specific solutions based on each student’s needs.  I look forward to increased productive interactions with my students using innovations, both present and future.

References

Bowen, J. A. (2014). The teaching naked cycle. Liberal Education100(2), 18-25.

Littlejohn, A., Beetham, H., & McGill, L. (2012).  Learning at the digital frontier: a review of digital literacies in theory and practice. Journal of Computer Assisted Learning, 28(6), 547-556. doi:10.1111/j.1365-2729.2011.00474.x

McLoughlin, C. & Lee, M. J. W. (2008). The three p’s of pedagogy for the networked society: Personalization, participation, and productivity. International Journal of Teaching and Learning in Higher Education, 20(1), 10-27.

How to Contextualize Math Using Infographics

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Patricia Helmuth

Patricia Helmuth is an Adult Numeracy Consultant and Educator. She teaches two HSE classes, does one-on-one tutoring (in partnership with the Center for Workforce Development), and is a Professional Development Team Member for the Adult Program at Sullivan County BOCES, NY. In addition to working with students, she enjoys sharing her “numeracy adventures” at the regional, state, and national level by presenting at conferences and writing for adult education web-based resources. She currently serves as the newsletter editor for The Adult Numeracy Network.

In a traditional math classroom, where math topics may be taught in isolation, students watch the instructor model a procedure on the board and then students are expected to memorize, repeat, and practice the procedure. The trouble is, many students have difficulty connecting the procedure to real-life applications. This disconnect that students experience is evidenced in ABE/HSE classes, as well as on college campuses in developmental math classes. According to Models of Contextualization in Developmental and Adult Basic Education, “…students who want to be nurses, EMTs, firemen…. are stuck in a course that doesn’t work.” Conversely, when math is contextualized, students can develop conceptual understanding of the math.  “Research supports the fact that students understand math better when it is contextualized. It motivates and increases the students’ willingness to engage (Tabach & Friedlander, 2008) and provides concrete meaning to the math (Heid et all, 1995).” – (2015 Center for Energy Workforce Development)

In light of this research, and the implementation of the Common Core State Standards and the release of the Workforce Innovation and Opportunity Act, adult education instructors are being called upon to make changes in classroom practice that will adequately prepare students to pass new high-stakes exams and enter college and the workforce with marketable skills. How can adult educators do all this given the short amount of time that adults typically spend in class?

A great place to start is by using a variety of authentic infographics that connect to the social studies, science, or career readiness that you are already teaching. By using infographics, you are combining content knowledge, math skills, and analyzing and interpreting graphic information into one lesson! While infographics may be new to some of us in adult education, they are not new to our students. They see them all the time in the real world so it is imperative that they develop skills to decode them. Besides all that, they are fun! Students are drawn into a conversation when you display an infographic and simply ask:

  • What do you notice? What do you wonder?

Students at all ability levels can participate in a lesson that is introduced like this. Furthermore, when students share out their observations and questions it serves as a formative assessment and enables the instructor to connect what students already know with the whatever math concept the instructor has in mind to draw out of the infographic.

For specific lesson plans and ideas on how to do this, go to:

In the Adult Education classroom today, we need to do more than present our students with workbooks that include traditional examples of maps, charts, and graphs.  We need to use what our students see all around them every day: infographics.

References

Center for Energy Workforce Development (2015). Contextualized math for the energy industry. Retrieved from http://www.cewd.org/contextualized-math/

Education Development Center (EDC). (2012). Models of Contextualization in Developmental and Adult Basic Education. Retrieved from EDC website: http://bit.ly/1KAnllT

 

Doing Different in the Mathematics Classroom

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Stephanie Cockrell Andrews, Ed.D.

Dr. Stephanie Cockrell Andrews is a mathematics professor and the mathematics department lead faculty at Lone Star College-Kingwood (LSC-K).  She has earned degrees from East Texas Baptist University, Stephen F. Austin State University, and Sam Houston State University. This is her 28th year in education, where 15 of those years were in public education as a secondary mathematics teacher and counselor.  Stephanie was a 2006 Project ACCCESS fellow with the American Mathematical Association of Two-Year Colleges (AMATYC). She has received the Faculty Excellence Award at LSC-K and the Educational Leadership Doctoral Award at Sam Houston State University.  She is a member of the Delta Kappa Gamma Society International for Key Women Educators. 

In the report, Closing the Gaps by 2015: 2009 Progress Report, the Texas Higher Education Coordinating Board (THECB, 2009) stated, “Texas must take bold steps for the future success of its people” (p. ii). Being the math chair, my president was always stressing to me that we needed to increase student success (A, B, or C) in our developmental courses, to get more students to and through our gateway mathematics course—and to do it all faster! Add in the definition of insanity—attributed to several, including Einstein (Howes, 2009)—of “doing the same thing over and over again and expecting different results,” and I was determined to do something that was bold and different.

So, during 2013 – 2014, I taught Foundations of Mathematical Reasoning (FMR) and Statistical Reasoning (SR) using the curriculum from The Dana Center at The University of Texas in Austin, and it rocked my academic world. I am a dedicated, traditional algebra teacher, and I have received awards for teaching, but when I taught these courses, my life and the lives of my students changed. The New Mathways Project (NMP) courses are based on principles including to provide relevant and rigorous mathematics, help students complete college-level math courses faster and use intentional strategies that help students grow as learners (The Charles A. Dana Center, 2013).

I have always been told that, while I am teaching, I should include real-world problems, interdisciplinary activities, collaborative work, active learning, productive struggle, reading and writing. I could not get all of this included much less included well, but NMP incorporates all of these skill—all based on proven practice! I did it with NMP!  I saw it work for me and be transformational for my students.

Even though this is controversial, I believe what I experienced teaching these courses is a strong rationale that this can be done and should be done. The courses are rigorous, involve collaborative learning; are saturated with real-world problems that the students get excited about (e.g., blood-alcohol-level formula for order of operations); teach students to be much better college students and well-informed citizens; and are much more closely aligned with degree programs than college algebra for non-STEM majors.

Testimonials from students include a video from Holly at https://utexas.box.com/s/vmr9xlba4kxv66csehm35obdsm716yml.

And an article by Kaleena Steakle at https://www.theguardian.com/pearson-partner-zone/2016/aug/31/approaching-math-differently-to-change-lives.

I have been working the last two years for The Dana Center helping other professors in our state and nation implement the NMP materials, but this week, I started back in the classroom! I have three, full FMR classes, and I am extremely excited to see how the students will grow this semester and be propelled to the next steps of their careers.

References

Howes, Ryan. (2009, July 27). The definition of insanity is…perseverance vs. perseveration. Retrieved from https://www.psychologytoday.com/blog/in-therapy/200907/the-definition-insanity-is

Texas Higher Education Coordinating Board. (2009). Closing the gaps by 2015: 2009 progress report. Retrieved from http://www.thecb.state.tx.us/reports/pdf/1852.pdf

The Charles A. Dana Center. (2016). The New Mathways Project curricular materials. Retrieved from http://www.utdanacenter.org/higher-education/new-mathways-project/new-mathways-project-curricular-materials/

 

Breaking Out of the e-Learning Courseware Box: Integrating Social Media

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Steven S. Vrooman, Ph.D.

Dr. Steven S. Vrooman is a Professor of Communication Studies, Chair of the Department of English and Communication Studies, and Director of General Education at Texas Lutheran University. Following his B.A. in English at Loyola Marymount University, he earned his M.A. and Ph.D. in Communication from Arizona State University. He spoke at TEDxSanAntonio on how our brains work like Twitter. He is the author of The Zombie Guide to Public Speaking and writes The MoreBrainz Blog, which offers help for public speaking and pedagogy. He can be reached via email at svrooman@tlu.edu.

We are sure e-learning works, although we often act as if all online practices are the same as we continue to investigate online vs. face-to-face modes and find them equivalent. The finding remains the same over the course of ten years (Schaik, Barker, & Beckstrand, 2003); Mativo, , & Godfrey, 2013), yet each online course seems to have different designs.  Additionally, although we also believe that social media is good for learning, Facebook, to take one platform, sometimes works (Kivunja, 2015) and sometimes does not (Moran, Seaman, & Tinti-Kane, 2011), and my reading of the studies seems to indicate that it depends on what we use it for and how.

In reviewing the growing literature on e-learning and social media and the various course practices that bridge them, it is clear, as with PowerPoint an educational generation ago, that when we drill down to exact practices, some things work (see, I’m sure, the past fifteen years of each of our teaching, right?) and some don’t (Adams, 2006). Specific analysis of specific practices is the only way forward. To paraphrase McLuhan, it’s not the medium, it’s the pedagogy.

To that end, I have used the following social media practices in class:

  1. Blogs: Students post data analysis, drafts, final projects and peer review them, publically.
  2. Public Blog Comments: Alumni/outside experts invited to critique student work.
  3. Discussion via Facebook Event: Including alumni/experts.
  4. Students Publicized Work: They did work on Instagram and shared it & blog work via Twitter, Facebook and LinkedIn.

Qualitative assessment of the outcomes of these results suggested the following positive outcomes:

  1. Better Work: Public work is better work, especially when outside voices tell them to improve it and students are promoting it.
  1. Engagement: Social media, used in certain ways, can increase engagement more than courseware, which can feel like a waste-of-time, count-my-comments-for-the-grade echo chamber.
  1. Portfolio: Students can retain their entire work to show progression or just the final versions to demonstrate their expertise.
  1. E-Learning Bonuses: Most gamified elearning practices work better on social media than in courseware. For example, debates have more at stake and engage the public. Creative projects get a larger audience and thus bigger reaction.
  1. Skillset Development: For my communication studies majors, social media skills are key. For other majors, they are more important than you might think.
  1. Alumni Engagement: Many LOVED the opportunity to reconnect with professors and students in this way and share their new skills and perspectives. Mentoring happened in many cases. And it set the stage for increased inclusion of those alumni in face-to-face events with students.

It also revealed the following challenges:

  1. Age:
    1. Nontraditional students: They had troubles: unwilling/critical of social media, self-doubt due to lack of familiarity, higher privacy concerns.
    2. Traditional students: They had troubles: difficulty adjusting to violation of “fun” space, difficulty with academic self-promotion.
  1. Sign-Ups:
    1. Technical Difficulties: Fewer than with courseware & easy to Google answers to, but signing up for accounts is surprisingly very hard for them.
    2. Secondary Accounts: Younger students often do not want classwork in their personal accounts, but second email addresses are often required for multiple accounts. Managing multiple accounts is easy for some platforms (Twitter) but hard in others (Instagram, Facebook, LinkedIn).
  1. Oversight: Hashtags are not enough to find their work. You need them to @ you or you won’t see everything.
  1. Content ABOUT Social Media is Needed: Things like how-tos, technical difficulties, privacy, etiquette, bullying/flaming, etc. probably need class time/resources to go over (however, offloading classtime experiences into social media helps offset this).

References

Adams, C. (2006). PowerPoint, habits of mind, and classroom culture. Journal of Curriculum Studies, 38, 389-411.

Kivunja, C. (2015). Innovative methodologies for 21st century learning, teaching and assessment: A convenience sampling investigation into the use of social media technologies in higher education. International Journal of Higher Education, 4 (2), 1-26.

Mativo, J. M., Hill, R. B., & Godfrey, P. W. (2013). Effects of human factors in engineering and design for teaching mathematics: A comparison study of online and face-to-face at a technical college. Journal of STEM Education: Innovations & Research, 14, 36-44.

Moran, M., Seaman, J., & Tinti-Kane, H. (2011). Teaching, learning and sharing: How today’s higher education faculty use social media. Babson Survey Research Group. ERIC: ED535130.

Van Schaik, P., Barker, P., & Beckstrand, S. (2003). A comparison of on-campus and online course delivery methods in Southern Nevada. Innovations in Education & Teaching International, 40, 5-15.

 

Acceleration in Mathematics (AIM)

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JP Anderson, Ph.D., & Kristen Foxley

JP Anderson (Ph.D., Rice) and Kristen Foxley (M.S., University of Houston—Clear Lake) have been teaching math for over 20 years. They share not only a passion for teaching, but for running as well, and have been running together for the past 10 years. Both JP and Kristen were part of the original design team for AIM and have been co-teachers since its beginning in 2012.  In addition to working with students, they enjoy providing professional development for faculty on ways to incorporate active learning in the classroom and presenting on AIM at conferences at the local, state, and national level. 

Nationwide, over 40% of students enter college needing one or more developmental courses. Unfortunately, traditional methods of remediation are not successful in preparing students for success in credit-bearing courses. In Texas, for example, only 12% of community college students who begin in developmental math courses will pass a gateway math course, such as college algebra, within 2 years (Complete College America, 2016). Although counterintuitive to some practitioners, many colleges have improved success through accelerated course offerings (Jaggars, Edgecombe, and Stacey, 2014), with corequisite models showing particular promise (Complete College America, 2016).

After implementing such a model, Acceleration in Mathematics (AIM), in Fall 2012, San Jacinto College has seen a significant improvement in student success. A study of seven long semesters’ data showed that 64.1% of AIM students passed college algebra with a grade of C or better, compared to 44.8% in traditional college algebra classes. This is especially notable since the majority of AIM students who are placed into developmental math courses are one or two levels below college algebra. Moreover, AIM narrowed the success gap for Hispanic students—approximately half of our student population—from 6% to less than 1%. In addition to AIM’s impact on students’ cognitive learning and academic success of students, a separate study showed improvements in their attitudes, feelings, and mindset regarding their mathematical abilities (Campbell, 2015).

Acceleration in Mathematics is a one-semester corequisite pairing of math courses that allows students who are not college ready in mathematics to complete all developmental requirements as well as college algebra in a single semester. Students who take AIM sign up for two classes: a three-contact-hour developmental course and a four-contact-hour college algebra course.  A typical AIM section meets Monday through Friday for a total of seven hours each week. AIM is team-taught by two instructors, one experienced in teaching traditional college algebra and one who specializes in developmental math instruction, both of whom are in the classroom for all class meetings and who share equally in the teaching duties.

  • Just-in-Time Remediation. Unlike traditional multi-semester or accelerated sequential remediation models, which teach basic skills weeks or months before they are needed in college algebra, AIM integrates these skills right before they are needed in the college algebra curriculum. For example, simplification of radical expressions is introduced just before the quadratic equation.
  • Streamlining. AIM focuses on learning objectives prescribed by the Texas Higher Education Coordinating Board. Some skills that have been part of the traditional developmental math curriculum, but which are not needed for college algebra, such as rationalizing the denominator, have been eliminated.
  • Active Learning. Daily lessons alternate brief lectures with small-group practice activities. To maximize student interaction and foster a sense of community, instructors use a technique called “clock partners” to pair students with a different practice partner each day.
  • Low-Stakes Assessment/Prompt Feedback. AIM students turn in daily homework assignments of approximately 25 questions. A portion of the problems are graded, and the assignments are returned the following day. Answer keys are available online for the ungraded problems. Students are tested every other week, for a total of seven unit tests and a final exam. Each unit test counts only 9% of the semester grade, making it possible for students to recover from one or two setbacks.
  • Cumulative Review. Every homework assignment and exam contains review problems to help students maintain essential skills throughout the semester.
  • Learning Resources. AIM students have online access to instructor-authored videos providing examples of all topics and worked-out solutions to the exam review sheets. San Jacinto College’s Student Success Center has a designated AIM table for on-campus tutoring. Also, thanks to the strong sense of class community, AIM students often form study groups on their own.

AIM has proven most successful for students required to take college algebra for their associate’s degree. To support students who would benefit from an alternative math pathway, however, the college has begun offering corequisite courses for developmental students seeking credit in a statistics or quantitative reasoning course. Early results show that these pathways show similar promise.

References

Campbell, P.S. (2016). Self-Efficacy in a Co-requisite Model of Developmental Mathematics and College Algebra: A Qualitative Analysis of Student Perceptions (Doctoral Dissertation). Retrieved from https://ttu-ir.tdl.org/ttu-ir/handle/2346/66121

Complete College America. (2016). Corequisite Remediation: Spanning the Completion Divide. Retrieved from http://completecollege.org/spanningthedivide/

Jaggars, S. S., Edgecombe, N., & Stacey, G. W. (2014). What we know about accelerated developmental education. New York, NY: Columbia University, Teachers College, Community College Research Center.