Education Commons^™

Instructional Decision Making In A Gateway Quantitative Reasoning Course, Deependra Budhathoki, Gregory D. Foley, Stephen Shadik

Numeracy

Many educators and professional organizations recommend Quantitative Reasoning as the best entry-level postsecondary mathematics course for non-STEM majors. However, novice and veteran instructors who have no prior experience in teaching a QR course often express their ignorance of the content to choose for this course, the instruction to offer students, and the assessments to measure student learning. We conducted a case study to investigate the initial implementation of an entry-level university quantitative reasoning course during fall semester, 2018. The participants were the course instructor and students. We examined the instructor’s motives and actions and the students’ responses to the course. …

Threshold Concepts In Quantitative Reasoning, Judith Canner, Jennifer E. Clinkenbeard

Numeracy

The idea of “threshold concepts” has been used to identify discipline-based concepts that are critical to that academic area. Threshold concepts are often difficult for students to assimilate in a meaningful way but, once done, can be powerful for the learner. In general, threshold concepts are 1) transformative to learner thinking; 2) bounded by the discipline; 3) integrative with other concepts; and 4) irreversible once understood (Meyer and Land 2003). This paper presents five threshold concepts in quantitative reasoning (QR) developed by transdisciplinary faculty workgroups that may be applicable for non-mathematics disciplines as well. They are as follows: 1) QR …

Using Formative Assessment To Build Coherence Between Educational Policy And Classroom Practice: A Case Study Using Inquiry In Science, Connie Cirkony, John Daniel Kenny

Australian Journal of Teacher Education

In this paper we argue that the complexity of education systems can lead to a lack of coherence in the implementation of policy. More effective educational change requires policy-makers and researchers to pay more attention to supporting teachers in classrooms. As an example, we consider decades of research attempts in STEM education to implement learning through inquiry and note there has been little change in teaching practices in classrooms. Using formative assessment in science education as a case study, we developed a rubric for teachers that embeds key aspects of the desired pedagogy. We argue this builds teachers’ confidence to …

Overcoming Challenges In Assessing Mathematical Reasoning, Sandra Herbert

Australian Journal of Teacher Education

Despite mathematical reasoning being necessary for in-depth understanding of mathematical concepts, many teacher experience difficulty in assessing it. Data were collected from 34 primary teachers at 4 Victorian government schools at two post- lesson reflective sessions following lessons with a focus on reasoning. These sessions facilitated teachers’ collaborative efforts to assess their students’ reasoning from students’ work samples. The data included transcripts of all the reflective sessions; written work samples; and associated completed rubrics. Analysis of these data enabled identification of seven challenges teachers experienced in assessing reasoning: Limited guidance provided by curriculum documents; Teachers’ knowledge of reasoning; Teacher noticing …

President's Message, Joanie Funderburk

Colorado Mathematics Teacher

Assessment refers to more than just high-stakes tests. Teachers assess students every time they ask a question, have students share work on the board, review a homework assignment, or solicit student questions during a lesson.

The Seesaw App: Providing Differentiated Assessment Opportunities, Tessa Ziser

Colorado Mathematics Teacher

I discovered the Seesaw app, which allows students to create drawings, videos, and pictures that become part of an online portfolio. Although it is not THE answer to assessment, it has become one of my (and my students’) favorites.

The Redesigned Sat Calls For A Conceptual Approach, Jeff Mccalla

Colorado Mathematics Teacher

Be intentional about including conceptual questions on every assessment that students take.

Probing For Bias: Comparing Populations Using Item Response Curves, Paul J. Walter, Edward Nuhfer, Crisel Suarez

Numeracy

We introduce an approach for making a quantitative comparison of the item response curves (IRCs) of any two populations on a multiple-choice test instrument. In this study, we employ simulated and actual data. We apply our approach to a dataset of 12,187 participants on the 25-item Science Literacy Concept Inventory (SLCI), which includes ample demographic data of the participants. Prior comparisons of the IRCs of different populations addressed only two populations and were made by visual inspection. Our approach allows for quickly comparing the IRCs for many pairs of populations to identify those items where substantial differences exist. For each …

Measuring Numeracy: Validity And The Programme For The International Assessment Of Adult Competencies (Piaac), Samuel L. Tunstall

Numeracy

A tension raised in recent scholarship is that between numeracy as a social practice and numeracy as a functional skill set. Such frameworks for conceptualizing numeracy pose a challenge to assessment because what individuals do with numeracy is not the same as what individuals can do (or express) in an assessment setting. This study builds on work related to numeracy assessment through a validity examination of a portion of a well-known assessment: the OECD’s Programme for the International Assessment of Adult Competencies (PIAAC). In following a path set out by standards for assessment, I ask: What does the PIAAC numeracy …

Assessment Instrument For Practicum Skills In Trimyristin Separation For Undergraduate Students, Naseer Ahmed, Senam Senam, Antuni Wiyarsi

Jurnal Inovasi Pendidikan IPA

Assessment of practicum plays an essential role in gaining knowledge and skill. Because practical work is an essential component of science courses, there were need to develop new instruments to examine practicum skill. To gain the purpose, Research and Development method used, Borg and Gall's model was adopted in this research. Observation sheets were used to obtain data. The qualitative data analysis technique was used to make coding. The data were described using descriptive statistics. It was used to determine the ability of students to practice in general, purposive sampling technique used for data collection. Products of practical's skills assessment …

Grading For Growth: Using Sliding Scale Rubrics To Motivate Struggling Learners, Dina Mahmood, Hugo Jacobo

Interdisciplinary Journal of Problem-Based Learning

In an effort to adopt more equitable and humanizing grading practices, this teacher inquiry explores how educators attempted to improve students’ views of learning and assessments by utilizing rubrics on a sliding scale. Using the sliding scale rubric approach to grading provided an opportunity for students and educators to rethink how learning is evaluated. The authors found that the logistics of using sliding scale rubrics as a grading tool does need to be refined and further evaluated; however, the belief that a student can receive a grade based on her or his individual starting point did have some positive implications …

Gaining Access To The Language Of Science: A Research Partnership For Disciplined, Discursive Ways To Select And Assess Vocabulary Knowledge, H. Emily Hayden, Anupma Singh, Michelle Eades Baird

Reading Horizons: A Journal of Literacy and Language Arts

To equalize access to science learning across genders and demographic groups, access to the disciplinary language of science is one place to start. The language of science is highly challenging and specialized, and difficulties acquiring this language contribute to disparities in science achievement across diverse student groups. This study used a pre-post design to analyze effectiveness of a brief classroom science vocabulary assessment designed to assess receptive and productive vocabulary knowledge across multiple sections of one 7^th grade science teacher’s class. Vocabulary was selected and analysis conducted by an interdisciplinary research partnership including the science teacher, a literacy specialist, …

Variations In Implementation Of Specifications Grading In Stem Courses, Mai Yin Tsoi, Mary E. Anzovino, Amy H. Lin Erickson, Edward R. Forringer, Emily Henary, Angela Lively, Michael S. Morton, Karen Perell-Gerson, Stan Perrine, Omar Villanueva, Marygeorge Whitney, Cynthia M. Woodbridge

Georgia Journal of Science

Specifications grading is an assessment strategy based on mastery learning, clear learning objectives, and frequent evaluations and feedback. Twelve instructors at a southeastern four-year public college implemented the specifications grading method across eight discrete courses in four STEM areas. In this modified assessment strategy, the students controlled their grades through multiple attempts, with limitations, on assessments of course objectives. The instructors designed and executed specifications grading in unique ways that aligned with their content areas, teaching beliefs, and individual teaching styles.

Preliminary observations suggest that, regardless of subject area, specifications grading can be used as an alternative to traditional assessment …

Alignment Between Learning Objectives And Assessments In A Quantitative Literacy Course, Younggon Bae, Samuel L. Tunstall, Kathryn S. Knowles, Rebecca L. Matz

Numeracy

In this analysis, we examine how course assessment items were aligned with learning objectives in a quantitative literacy course at Michigan State University. The alignment analysis consisted of mapping assessment items to a list of operationalized learning objectives from the course. Our analysis shows how often the learning objectives are represented in assessment items, how often they are paired with other learning objectives, and how influential they are in contributing to a student’s course grade. In addition, through comparisons across four assessment types (e.g., exams and homework), we show how each learning objective was assessed differently within each assessment type. …

Assessing Mechanistic Reasoning: Supporting Systems Tracing, Paul J. Weinberg

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

Reasoning about mechanism is central to disciplined inquiry in science and engineering and should thus be one of the foundations of a science, technology, engineering, and mathematics education. In addition, mechanistic reasoning is one of the core competencies listed in the Next Generation Science Standards (NGSS) Engineering Concepts and Practices (NGSS Lead States, 2013). Mechanistic explanations focus on the processes that underlie cause–effect relationships and consider how the activities of system components affect one another.

While some assessment work has been accomplished in engineering education, to date mechanistic reasoning is an area where limited assessment development has been accomplished for …

The Iterative Development And Use Of An Online Problem-Based Learning Module For Preservice And Inservice Teachers, Peter Rillero, Laurie Camposeco

Interdisciplinary Journal of Problem-Based Learning

Teachers’ problem-based learning knowledge, abilities, and attitudes are important factors in successful K–12 PBL implementations. This article describes the development and use of a free, online module entitled Design a Problem-Based Learning Experience. The module production, aligned with theories of andragogy, was a partnership between the recipients of a grant using PBL to enhance English language learner education and the Sanford Inspire Program. A multistage evaluation design was used in the iterative process of module creation. Starting with an initial white paper, the module’s conceptualization, development, pilot testing, and refinement are described, along with the current use statistics. The URL …

The Quantitative Reasoning For College Science (Quarcs) Assessment 2: Demographic, Academic And Attitudinal Variables As Predictors Of Quantitative Ability, Katherine Follette, Sanlyn Buxner, Erin Dokter, Donald Mccarthy, Beau Vezino, Laci Brock, Edward Prather

Numeracy

In this article, we explore the ability of demographic and attitudinal variables to predict student scores on the Quantitative Reasoning for College Science (QuaRCS) Assessment. Variables measured by the assessment include: students' academic choices and plans, attitudes and perceptions regarding mathematics, self-reported effort level, and basic demographics such as age, race/ethnicity, gender and disability status. As in previously published numeracy studies, we find significant score deviations according to gender, race/ethnicity, and disability status; however, the effect size of these correlations pale in comparison to the effect size of affective/attitudinal variables on QuaRCS score. A large number of variables with …

Pengembangan Perangkat Assessment Pembelajaran Matematika Pokok Bahasan Geometri Dan Pengukuran Smp/Mts, Robert Edy Sudarwan, Heri Retnawati

Jurnal Riset Pendidikan Matematika

Penelitian ini bertujuan untuk: (1) mengembangkan produk perangkat assessment pembelajaran pada pokok bahasan geometri dan pengukuran yang berorientasi pada aspek pengetahuan, keterampilan dan sikap peserta didik SMP/MTs kelas VII dan VIII sebagai hasil pengembangan berdasarkan kajian teori, pendapat ahli, dan pendapat pengguna dengan kualifikasi baik; dan (2) mendeskripsikan kualitas produk assessment pembelajaran pada pokok bahasan geometri dan pengukuran yang berorientasi pada aspek pengetahuan, keterampilan dan sikap peserta didik SMP/MTs kelas VII dan VIII berdasarkan aspek kevalidan, kepratisan dan keefektifan. Teknik analisis data yang digunakan untuk menghitung reliabilitas dengan menggunakan α-reliability, untukα ‰¥ 60 maka reliabel. Percentage of Agrements (PA) …

From Stem To Steam: Reframing What It Means To Learn, Nicole M. Radziwill, Morgan C. Benton, Cassidy Moellers

The STEAM Journal

Although involvement in art and design have been shown to play an essential role in catalyzing STEM research, true integration is still an area of active research. The realization of STEM education via STEAM lends itself to interactive and participatory dialogic art; this juncture provides a nonjudgmental space to cultivate the question-making aspect of inquiry, the ability to comfortably hold uncertainty, and a sensitivity to the process of discovery. Even though STEM education can (and often is) inquiry-based, assessments still tend to focus on whether knowledge or skills have been obtained, and this is no different than the current general …

The Levels Of Conceptual Understanding In Statistics (Locus) Project: Results Of The Pilot Study, Douglas Whitaker, Steven Foti, Tim Jacobbe

Numeracy

The Levels of Conceptual Understanding in Statistics (LOCUS) project (NSF DRL-111868) has created assessments that measure conceptual (rather than procedural) understanding of statistics as outlined in GAISE Framework (Franklin et al., 2007, Guidelines for Assessment and Instruction in Statistics Education, American Statistical Association). Here we provide a brief overview of the LOCUS project and present results from multiple-choice items on the pilot administration of the assessments with data collected from over 3400 students in grades 6-12 across six states. These results help illustrate students’ understanding of statistical topics prior to the implementation of the Common Core State Standards. Using the …

The Quantitative Reasoning For College Science (Quarcs) Assessment, 1: Development And Validation, Katherine B. Follette, Donald W. Mccarthy, Erin Dokter, Sanlyn Buxner, Edward Prather

Numeracy

Science is an inherently quantitative endeavor, and general education science courses are taken by a majority of college students. As such, they are a powerful venue for advancing students’ skills and attitudes toward mathematics. This article reports on the development and validation of the Quantitative Reasoning for College Science (QuaRCS) Assessment, a numeracy assessment instrument designed for college-level general education science students. It has been administered to more than four thousand students over eight semesters of refinement. We show that the QuaRCS is able to distinguish varying levels of quantitative literacy and present performance statistics for both individual items and …

Assessing Numeracy In The Upper Elementary And Middle School Years, Carol Ann Gittens

Numeracy

Numeracy is the ability or tendency to reason critically about quantitative information. The preponderance of published research on numeracy examines this construct among either pre-K or early elementary samples, students with developmental challenges, or is focused on post-secondary and adult cohorts. The numeracy skills of upper-elementary and middle school students is less documented and understood, most notably because of the lack of valid instruments that are developmentally appropriate for the age range. A numeracy scale for use among upper-elementary and middle school students is introduced in this paper. Scale validation was performed using a gender-balanced, racially / ethnically diverse sample …

Teacher, Researcher, And Accountability Discourses: Creating Space For Democratic Science Teaching Practices In Middle Schools, Cory A. Buxton, Shakhnoza Kayumova, Martha Allexsaht-Snider

Democracy and Education

This study explores the role of competing discourses that shape current practices in U.S. schools and how professional development efforts can support teachers and researchers in finding ways to reinsert more democratic processes into their collaborative work. We examine the case of one research and professional development project with the goal of supporting middle school science and ESOL teachers in fostering more meaningful science learning for all their students but especially their English language learners. Using Gee’s notion of big-D discourses and Fairclough’s notion of interdiscursivity, we trace how the Discourse of accountability, the Discourse of science teaching, and the …

Parts Of The Whole: Learn More, Learn Better, Dorothy Wallace

Numeracy

Building on previous columns in Numeracy, this column analyzes various teaching techniques in terms of their ability to build cognitive schema, extend existing schema, reinforce learning, move mean understanding of a group of students, and reduce variance in understanding of a group. We offer a pedagogical cycle as an example of how to address multiple learning goals using common teaching methods.

Motivation For Achievement And Attitudes Toward Mathematics Instruction In A Required Calculus Course At The Norwegian University Of Science And Technology, Donna Sundre, Carol Barry, Vidar Gynnild, Erin Tangen Ostgard

Numeracy

This study from the Norwegian University of Science and Technology (NTNU) examines students’ learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ) is advanced from current literature with two additions: (1) a course specific context using introductory college calculus students, and (2) participation of Norwegian students.

Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors’ aspirations. A significant increase in “Mastery Avoidance” and “Work Avoidance” was accompanied with a drop in “Mastery Approach” and …

Numeracy, Financial Literacy, And Financial Decision-Making, Annamaria Lusardi

Numeracy

Financial decisions, be they related to asset building or debt management, require the capacity to do calculations, including some complex ones. But how numerate are individuals, in particular when it comes to calculations related to financial decisions? Studies and surveys implemented in both the United States and in other countries that are described in this paper show the level of numeracy among the population to be very low. Moreover, lack of numeracy is not only widespread but is particularly severe among some demographic groups, such as women, the elderly, and those with low educational attainment. This has potential consequences for …

Parts Of The Whole: An Algebra Lesson, Dorothy Wallace

Numeracy

This column draws on research of Eon Harper to demonstrate how an understanding of his proposed stages of algebra acquisition would inform a systemic overhaul of algebra education. Harper's stages also explain why students may pass a series of algebra courses yet still be unable to make sense of calculus, as well as offering insight on what aspects of algebra support quantitative literacy.

Quantitative Reasoning In The Contemporary World, 3: Assessing Student Learning, Stuart Boersma, Caren Diefenderfer, Shannon W. Dingman, Bernard L. Madison

Numeracy

In this third paper in a series describing the Quantitative Reasoning in the Contemporary World course, the authors provide an adaptation of the Association of American Colleges and Universities quantitative literacy VALUE rubric. Describing achievement levels in six core competencies (interpretation, representation, calculation, analysis/synthesis, and communication), the resulting Quantitative Literacy Assessment Rubric (QLAR) is applicable to grading student work and has exhibited a high degree of reliability in two separate scoring tests (97% and 88% respectively). The distribution of the six core competencies across the 24 case studies in the authors’ quantitative reasoning casebook shows that interpretation, calculation, and analysis/synthesis …

Quantitative Literacy At Michigan State University, 2: Connection To Financial Literacy, Dennis Gilliland, Vince Melfi, Alla Sikorskii, Edward Corcoran, Eleanor Melfi

Numeracy

The lack of capability of making financial decisions has been recently described for the adult United States population. A concerted effort to increase awareness of this crisis, to improve education in quantitative and financial literacy, and to simplify financial decision-making processes is critical to the solution. This paper describes a study that was undertaken to explore the relationship between quantitative literacy and financial literacy for entering college freshmen. In summer 2010, incoming freshmen to Michigan State University were assessed. Well-tested financial literacy items and validated quantitative literacy assessment instruments were administered to 531 subjects. Logistic regression models were used to …

Quantitative Literacy At Michigan State University, 1: Development And Initial Evaluation Of The Assessment, Alla Sikorskii, Vince Melfi, Dennis Gilliland, Jennifer Kaplan, Suzie Ahn

Numeracy

Development, psychometric testing, and the results of the administration of a quantitative literacy (QL) assessment to undergraduate students are described. Three forms were developed covering a wide range of skills, contexts, and quantitative information presentation formats. Following item generation and revision based on preliminary testing and cognitive interviewing, a total of 3,701 consented undergraduate students at Michigan State University completed one of the three forms. Two of the forms contained 14 multiple-choice items, and one form contained 17 multiple-choice items. All forms were completed by students in less than 30 minutes. Evidence of validity and reliability were obtained for the …