Student achievement in mathematics continues to be compared internationally, with the results indicating that students in other developed countries are outperforming students from the United States. Mathematical modeling is an expectation in both the new Common Core State Standards and the Programme for International Student Assessment (PISA). This study seeks to find the differences in expectations for students in mathematical modeling between the United States and Singapore, which is one country that regularly outperforms the U.S. on international assessments. Since teachers and students regularly use textbooks for curriculum, homework, and other resources, this study compares two textbooks from the U.S. with the high school series adopted in Singapore. More specifically, the aim of this study is to compare frameworks of mathematical modeling and code to-be-solved problems in algebra textbooks using characteristics common to all frameworks. While the U.S. textbooks explicitly state which word problems address the expectation of mathematical modeling, the Singapore program does not have this attribute. So, an equivalent chapter (in objective and number of to-be-solved problems) in all three textbooks will be coded for evidence of the expectations of mathematical modeling. The results of this study indicate that no standard framework for mathematical modeling exists, but there are multiple areas of overlap. This study found that the ratio of word problems to numerical problems was comparable in the three textbooks, although the U.S. algebra textbooks used in a one-year course had the same number of to-be-solved problems as the four-year Singapore series. Results also indicate that to-be-solved problems in the Singapore textbook series do not provide students with more explicit mathematical modeling instructions than do the U.S. textbooks. This study also found that the interpretation of to-be-solved problems differed according to the experience of the rater. None of the textbooks in this study provided to-be-solved problems that asked students to engage in the mathematical modeling cycle as delineated by any of the four frameworks.

Applying mathematics to real world problems, mathematical modeling, has risen in priority with the adoption of the Common Core State Standards for Mathematics (National Governors Association and the Council of Chief State School Officers, 2010). Teachers are at the core of the implementation of the standards, but resources to help them teach modeling are relatively undeveloped. This multicase study explored the perspectives of teachers regarding mathematical modeling pedagogy (the modeling cycle), instructional materials, and professional collaboration, with the assumption that understanding teachers’ views will assist authors, publishers, teacher educators, and administrators to develop better support for modeling instruction. A purposeful sample of six high school mathematics teachers from a variety of school settings across the country was interviewed using a semi-structured protocol. A conceptual framework developed by applying the theories of Guy Brousseau (1997) to the modeling literature guided the analysis. Qualitative methods including elements of grounded theory were used to analyze the data and synthesize the study’s results. The research showed that teachers structure their instruction consistently with the modeling cycle framework, but it also uncovered the need for additional detail and structure, particularly in the initial steps when students make sense of the problem and formulate an approach. Presenting a modeling problem is particularly important and challenging, but there is inadequate guidance and support for this teaching responsibility. The study recommends the development of additional materials and training to help teachers with these steps of the modeling cycle. Furthermore, teachers find that modeling problems are engaging, and they help students make sense of mathematical concepts. Teachers would employ modeling problems more often if they were more available and convenient to use. The study recommends that features for an online depository of modeling materials be researched and developed, including a course-based, chronological organization, a diverse variety of materials and formats, and tapping teachers to contribute their lessons.

The Common Core State Standards are a set of challenging learning goals in English language arts/literacy and math and their use in special education has been a controversial topic. On the one hand, many special education advocates have been pleased that the standards were written for all students, including students with disabilities. On the other hand, many special education teachers have been concerned that an overemphasis on the Common Core State Standards is limiting their students’ access to the full benefits of an Individualized Education Program, which is the central component of special education that makes it so special. Recent research conducted on teachers across the United States has shown that, overall, they believe that the Common Core State Standards are beneficial for students. However, there is a gap in the research documenting the specific views of special education teachers. It is important to understand their experiences because they have the unique task of balancing the general education curriculum with individualized instruction that may include skills not covered by the Common Core. This study aims to address this gap by answering several key questions about the experiences of special education teachers who use the Common Core State Standards with students with disabilities. A total of 476 special education teachers from across the United States were surveyed. This study found that they have a moderately strong understanding of the standards and they frequently used them to guide their teaching. The results of this study showed that while the majority of these teachers echoed the general belief that the Common Core State Standards are beneficial for students without disabilities, they did not believe that they are beneficial for students with disabilities. Strikingly, 86.9% did not believe that the standards provide adequate information about their application to students with disabilities. Of concern, 70.9% reported that, when using these standards, they are unable to address their students’ individualized goals—especially in the areas of social and functional skills. Moreover, when asked if they believed that the Common Core State Standards would help their students to be prepared for independent life, 79.1% said “no.” These results yield important information regarding current practice using the Common Core State Standards in special education and suggest important implications for teacher training courses related to the Common Core State Standards and students with disabilities as well as how the Common Core State Standards document and guidance materials may be revised to better meet the needs of students with disabilities.

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We will combine hands-on science investigations with supporting literacy activities to help students conduct original research on animal behaviors and communicate their findings.

We will combine hands-on science investigations with supporting literacy activities to help students build conceptual models of photosynthesis.

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