Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
143
result(s) for
"Jacobson, Erik"
Sort by:
Preservice Teachers' Reasoning About Relationships That Are and Are Not Proportional: A Knowledge-in-Pieces Account
Past studies have documented students' and teachers' persistent difficulties in determining whether 2 quantities covary in a direct proportion, especially when presented missing-value word problems. In the current study, we combine a mathematical analysis with a psychological perspective to offer a new explanation for such difficulties. The authors illustrate how the combination of mathematical analysis and psychological perspective may be applied to data using empirical examples drawn from interviews during which preservice middle-grades teachers reasoned with varying degrees of success about relationships presented in word problems that were and were not proportional.
Journal Article
Field Experience and Prospective Teachers' Mathematical Knowledge and Beliefs
This study (n = 1,044) used data from the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the relationship between field experience focus (instruction- or exploration-focused), duration, and timing (early or not) and prospective elementary teachers' intertwined knowledge and beliefs about mathematics and mathematics learning. Findings suggest that field experience has important but largely overlooked relationships with prospective teachers' mathematical knowledge and beliefs. Implications for future research are discussed.
Journal Article
Workforce development rhetoric and the realities of 21st century capitalism
Increasingly, the provision of adult education (including literacy and training programs) is influenced by a rhetoric of workforce development that tasks education with closing a supposed 'skills gap' between the skills that workers have and what employers are looking for. This deficit model of education blames adult learners for their own condition, as well as for larger problems in the economy. In addition to arguing for broader goals for adult education, those in the field also need to question the economic premises of this rhetoric. A review of current economic conditions points to fundamental aspects of capitalism as the source of instability, which means that education and training programs have a limited ability to move large numbers of people out of poverty. For this reason, students and teachers in adult education should focus on developing structural analyses of the situation and push for substantive changes in the economy. [Author abstract]
Journal Article
Using Covariation Reasoning to Support Mathematical Modeling
For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical modeling, beginning algebra students must learn to use their understanding of arithmetic operations to make mathematical sense of problem situations and to relate this sense making to functions represented by equations, tables, and graphs. The word problems commonly used in beginning algebra courses give opportunities to practice mathematical modeling. Further, the ability to reason with quantities as well as numbers is an important capacity for students to develop. Two kinds of quantitative reasoning have a special relevance for beginning algebra students. The \"correspondence\" perspective deals with the question, How is one quantity related to another? A correspondence understanding of speed might be expressed as the rule that relates each value for time with a unique value for distance, such as the equation y = 25x, where x represents time and y represents distance. By contrast, the key question for \"covariation\" reasoning is, How does one quantity change as another quantity changes? A covariation understanding of speed would focus on how distance and time change together--that is, the distance covered increases by 25 meters as the elapsed time increases by 1 second. Both kinds of reasoning are important goals for algebra students. Correspondence is a fundamental piece of mature reasoning about functions, and covariation is critical for developing the rate-of-change concept. Presented in this article are two sessions from Ms. Holmes's classroom (the teacher's name is a pseudonym) in which seventh graders intuitively used covariation to begin to make sense of word problems. The passages show how students' covariation reasoning might surface in the classroom and illustrate some of the teaching strategies that Ms. Holmes used to support her students' reasoning. The sessions also provide a foundation for the discussion of classroom strategies, which summarizes research-based strategies for supporting students' use of covariation reasoning to build robust mathematical models.
Journal Article
Utilizing the M-Scan to measure standards-based mathematics teaching practices: affordances and limitations
The Mathematics Scan (M-Scan), a content-specific observational measure, was utilized to examine the extent to which
standards-based mathematics teaching practices
were present in three focal lessons. While previous studies have provided evidence of validity of the inferences drawn from M-Scan data, no prior work has investigated the affordances and limitations of the M-Scan in capturing standards-based mathematics teaching. We organize the affordances and limitations into three categories: the operationalization of the M-Scan, the organization of the M-Scan, and the M-Scan within the larger ecology of instruction. Our analysis indicates the M-Scan differentiates among lessons in their use of
standards-based mathematics teaching practices
by operationalizing the M-Scan dimensions at the lesson level, sometimes at the expense of capturing the peaks and valleys within a single lesson. Simultaneously, the analysis revealed how the application of the rubrics may be impacted by lesson transcripts. We discuss the theoretical organization of the M-Scan and its implications for researchers and practitioners applying the rubrics. Finally, we point to the affordances and limitations of the M-Scan within the larger ecology of instruction by considering curricular issues and two dimensions of instruction not highlighted by the M-Scan.
Journal Article
Race, Gender, and Teacher Equity Beliefs: Construct Validation of the Attributions of Mathematical Excellence Scale
Teachers’ beliefs can have powerful consequences on instructional decisions and student learning. However, little research focuses on how teachers’ beliefs about the role of race and gender in mathematics teaching and learning influence educational equity within classrooms. This gap is partly due to the lack of studies focused on variation within classrooms, which in turn is hampered by the lack of instruments designed to measure mathematics-specific equity beliefs. In this study of 313 preservice and practicing elementary teachers, we report evidence of construct validity for the Attributions of Mathematical Excellence Scale. Factor analyses provide support for a four-factor structure, including genetic, social, personal, and educational attributions. The findings suggest that the same system of attribution beliefs underlies both racial and gender prejudice among elementary mathematics teachers. The Attributions of Mathematical Excellence Scale has the potential to provide a useful outcome measure for equity-focused interventions in teacher education and professional development.
Journal Article
Measuring Mathematical Knowledge for Teaching Fractions With Drawn Quantities
Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study investigated the utility of an alternative called themixture Rasch modelthat allows for subgroups. The model was applied to middle-grades teachers' performance on pretests and posttests bracketing a 42-hour professional development course focused on drawn models for fraction arithmetic.
Journal Article
CAN PEDAGOGICAL CONCERNS ECLIPSE MATHEMATICAL KNOWLEDGE?
Mathematical knowledge for teaching (MKT) is often thought of as a transformed, mutually-influencing mixture of content and pedagogy. However when individuals' MKT does not integrate content and pedagogy, one type of knowledge can supersede the other, sometimes unconsciously. We exemplify this with Emma, a prospective elementary teacher, whose views on students' learning needs overshadowed her content knowledge. Specifically, Emma answered mathematical questions incorrectly, despite being aware of the correct answers, because she inadvertently gave more weight to pedagogical than to mathematical concerns. Implications for research and teacher education are discussed.
Journal Article
Prospective elementary teachers’ conceptions of multidigit number: exemplifying a replication framework for mathematics education
Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser’s (Educational Studies in Mathematics 75:241–251, 2010) study of prospective elementary teachers’ conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers’ conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology.
Journal Article