Search

Results from an experiment in Fall 2013 of 902 incoming students at this university are reported. In this experiment, after students were given a basic math assessment to ensure they had the necessary math skills to take a principles of economics course, they were randomly allocated to a treatment or control group to test whether there was a significant impact of test format, calculator use, and calculator type on students’ scores. The interaction of calculator use/type and test format was also tested. The results from this experiment suggest that each treatment had a significant positive impact on students’ assessment scores, with much variation depending on the type of question asked and the level of performance. JEL Classifications: A22, C23

To support continuous professional development model in the teaching and learning of mathematics, many districts and schools have begun hiring elementary mathematics coaches and/or specialists (MCSs). However, limited large-scale empirical research exists that determines how the use of MCSs affect student learning and achievement. Kristin E. Harbour and Evthokia Stephanie Saclarides begin to fill in this gap by using data from the National Assessment of Educational Progress to explore the relationship between the presence and responsibilities of elementary MCSs and 4th-grade student achievement in mathematics. Based on their findings, they share practical implications for districts and administrators to consider.

In this synthesis, we reviewed 65 studies involving elementary students (i.e., grades 1–5) identified with mathematics difficulty (MD) in which authors implemented a mathematics intervention. Of these studies, we identified 33 group designs, 9 quasi-experimental designs, and 23 single-case designs. We aimed to synthesize performance differences between students with MD with and without reading difficulty (RD). We identified three categories of students for analysis: Students with MD+RD, MD-alone, or MD-nonspecified (i.e., no reading information provided). Overall, 80% of studies included students with MD-nonspecified, and the interventions for these students demonstrated strong effects. For the limited number of studies with students with MD+RD or MD-alone, intervention effects were strong for students with MD+RD and variable for students with MD-alone. In the three studies directly comparing the performance of students with MD+RD versus MD-alone, we noted differential patterns of performance. To tailor interventions to student need, more research must be conducted to understand whether students with MD with variable reading profiles respond differentially to mathematics intervention.

Informed by a constructivist-based, student-adaptive pedagogical approach, this study explores the benefits of teacher–learner discourse moves for the mathematics learning of students with learning disabilities (LD). During a constructivist teaching experiment for nurturing the multiplicative reasoning and problem solving of five third-grade students with school-identified LD, we analyzed the global trends and detailed dynamics of teacher–student interactions with statistical discourse analysis. We found that the teacher’s discourse moves to support each individual student’s problem solving helped engage them in mathematical reasoning, which improved their problem-solving performance. Thus, this study contributes to knowledge in the field of special education by (a) specifying ways in which discourse-oriented mathematics instruction can help each student with LD and (b) showcasing a novel statistical analysis of teacher–student discourse.

This mixed-methods study explored the pedagogical practices of Prospective Elementary Mathematics Specialists (PEMSs) as they completed a university K-5 Mathematics Endorsement program. Participants were 13 elementary teachers at an urban, high-needs charter school. Data were collected via individual interviews, written reflections on enacted teaching practices, two observations of classroom teaching practices, and a 36-item Cognitively Guided Instruction Teacher Knowledge Assessment. The findings show the PEMSs were connecting their learning during program courses with instructional practices in their classrooms, as 85% were implementing standards-based learning environments (SBLEs) at a high level, with the classroom event of providing their students opportunities to make conjectures about mathematical ideas as a relative struggle. The PEMSs described pedagogical shifts across the program, providing insights into these changes, along with how particular program components contributed, with the emergent themes of skepticism, trying it on, shifters, and need more support.

A basic understanding of math, numeracy, and related concepts are critical skills for functioning independently in society. Individuals with disabilities often struggle with basic math, which impedes their ability for independent living. Augmented reality (AR), which builds on the evidence-based principles of video modeling, is a promising teaching strategy of providing math instruction to individuals with disabilities. This article provides a practical framework (with step-by-step instructions and examples) for practitioners wishing to implement AR as a teaching strategy for secondary students with disabilities.

English learners (ELs) experience difficulty with mathematical problem solving because word problems require complex processes beyond basic math skills, such as the use of linguistic information, identifying relevant information, and constructing the appropriate problem statement. This study used a combined multiple baseline design and criterion changing design to assess the effectiveness of a paraphrasing intervention on the problem-solving performance for nine third-grade students who are ELs and at risk of mathematical disabilities (MD). Although the magnitude of the Tau-U effect sizes was in the small range, the visual analysis indicated that all students displayed increasing trends in problem-solving accuracy as a function of the paraphrasing intervention. The results were discussed in terms of providing continual support toward maintaining intervention outcomes.

The Individuals with Disabilities Education Act stresses the importance of educating students with disabilities (SWDs) in the least restrictive environment, often with peers who do not have disabilities. Prior research has examined the extent to which SWDs are included in general education classrooms, but not the characteristics of the peers with whom SWDs are educated. We examined the math classmates of fourth- and fifth-grade SWDs from one state. On average, SWDs were grouped with twice as many other SWDs, about four per class, than students without disabilities. Students with learning disabilities had fewer peers with disabilities in their classrooms than students with other disabilities. Students with intellectual disabilities, autism, or emotional/behavioral disorders more often had peers with disabilities, often their same disability. Our results provide directions for future research regarding peer effects and understanding how schools group SWDs.

This exploratory study examines the relationship between preservice teachers’ performance on a teaching performance assessment for licensure in elementary mathematics and a measure of knowledge that, in studies of practicing teachers, was found to predict effective mathematics teaching. A sample of 89 preservice teachers completed the Performance Assessment for California Teachers (PACT) and the classroom video analysis (CVA) instrument. Correlation analyses found overall weak associations between measures for the whole group. For groups of high, medium, and low performers on PACT, average scores on the CVA measure and its subscales varied in the predicted direction. However, individuals within the PACT performing groups had a relatively broad range of scores on the CVA, and several preservice teachers who performed poorly on PACT had average or better than average performance on the CVA. Similarly, several of the PACT high performers scored below the whole group CVA average. In addition to suggesting areas for future research, the findings raise questions about assessing preservice teachers’ readiness to teach mathematics and the use of a single measure to make licensing decisions.

Enhancing all students’ academic performance continues to be a national priority, and although achievement gains have been made overtime, shortfalls in mathematics learning for students with disabi...

Low levels of patient numeracy are pervasive, yet patients are expected to use basic math skills to maintain health, avoid ill health, and make important health decisions. This article summarizes what we know about best practices when communicating numeracy-based information to patients. We offer advice to home health nurses faced with challenges of caring for patients with low numeracy and who are responsible for their health and safety that require quantitative reasoning. Comprehending statistical data is difficult and counterintuitive for many people (and experts), and we offer examples of widely misunderstood formats of quantitative information but clarify them in ways that will benefit the practicing home health nurse. We conclude that patients need help understanding and using numbers while nurses need help explaining them.

The present study investigated the effects of Primarily Math, an inservice elementary mathematics specialist program. Primarily Math sought to augment the mathematical knowledge for teaching of kin...

When a teacher educator is called on to teach a blind student in her class for aspiring teachers of elementary mathematics, she feels ill-prepared for the challenge. As she learns how to accommodate the student’s needs, she learns a lot about being a good teacher -- to not assume that a student will be able to show his or her learning the same way that other students do, to not underestimate what the student can do, and to trust that the student will do the work.

This study investigated developmental gender differences in mathematics achievement, using the child and adolescent portion (ages 6-19 years) of the Kaufman Test of Educational Achievement–Third Edition (KTEA-3). Participants were divided into two age categories: 6 to 11 and 12 to 19. Error categories within the Math Concepts & Applications and Math Computation subtests of the KTEA-3 were factor analyzed and revealed five error factors. Multiple ANOVA of the error factor scores showed that, across both age categories, female and male mean scores were not significantly different across four error factors: math calculation, geometric concepts, basic math concepts, and addition. They were significantly different on the complex math problems error factor, with males performing better at the p < .05 significance level for the 6 to 11 age group and at the p < .001 significance level for the 12 to 19 age group. Implications in light of gender stereotype threat are discussed.

This study utilized a mixed-methods approach to holistically examine single-sex and coeducational urban elementary mathematics classes through situated cognitive theory. Participants came from two urban low-income Midwestern elementary schools with a high representation of minority students ( n = 77 sixth graders, n = 4 teachers, n = 2 principals). Findings demonstrate that African American girls made more math achievement gains in single-sex classrooms; single-sex classrooms might mitigate math academic stereotypes for students and teachers; and that important contextual factors play a role in these outcomes. Testing these factors is a step toward delineating a theory of change for single-sex education in urban public schools.

Numerous studies have identified differences between males and females in academic performance across the areas of reading, writing, and mathematics. The current study examined whether or not gender differences exist when math curriculum–based measures (M-CBMs) are used to assess basic math computation skills in a sample of third- through eighth-grade students. Participants included 1,626 general and special education students from five schools in a rural southeastern school district. Two-way repeated measures ANOVAs were used to determine significance across genders at each grade level. Statistically significant differences in favor of females were found in Grades 5, 7, and 8. The discussion highlights applied and theoretical implications of these findings.

There has been a spike in negative comments about mathematics and standards since the implementation of the Common Core State Standards. Regardless of whether the comments are fueled by social media or traditional media, educators need to be armed with strategies for helping parents understand, navigate, and embrace the Common Core’s mathematics content and practices. In this article, the author outlines three strategies and accompanying action steps that can help school leaders and teachers to be proactive rather than reactive when addressing parent concerns about the Common Core math standards. While the examples in this article are embedded in elementary mathematics, the strategies and action steps apply to all K-12 settings.

Teacher nominations of students are commonly used in gifted and talented identification systems to supplement psychometric measures of reasoning ability. In this study, second grade teachers were requested to nominate approximately one fourth of their students as having high learning potential in the year prior to the students’ participation in a randomized control trial of an advanced mathematics curriculum intervention. Treatment students completed researcher-developed unit pretests and posttests intended to measure higher order conceptual mathematical problem solving. Results from multilevel analyses indicate that third grade treatment students who were nominated during second grade significantly outperformed their un-nominated peers on these posttest measures, after controlling for students’ composite reasoning scores and pretest scores. This finding supports the view that teachers perceive student qualities beyond cognitive factors that facilitate student success with atypically challenging mathematics content, reinforcing prior recommendations to include teacher nominations as one component of gifted and talented identification systems.

The purpose of this study is to provide evidence of reliability and validity of the Self-Efficacy for Teaching Mathematics Instrument (SETMI). Self-efficacy, as defined by Bandura, was the theoretical framework for the development of the instrument. The complex belief systems of mathematics teachers, as touted by Ernest provided insights into the elements of mathematics beliefs that could be relative to a teacher’s self-efficacy beliefs. The SETMI was developed in July 2010 and has undergone revisions to the original version through processes defined in this study. Evidence of reliability and validity were collected to determine whether the SETMI is an adequate instrument to measure self-efficacy of elementary mathematics teachers. Construct validity of the revised SETMI was tested using confirmatory factor analysis. Findings indicate that the SETMI is a valid and reliable measure of two aspects of self-efficacy: pedagogy in mathematics and teaching mathematics content.

As our knowledge about education continues to change, educators must refine and redefine their beliefs and teaching practices through professional development. In the peer coaching model of professional development, both participants have a chance to reflect on what they observe and on their own teaching practices. This reciprocal gain is one of the major benefits of peer coaching. This study examined the experiences of elementary mathematics teachers engaging in a peer coaching model of professional development. A Grade 1 and a Grade 3 teacher in Western Canada act as the participants in this case study and qualitative data were gathered from teacher interviews and observations of peer coaching sessions. Each teacher selected two dimensions from the Ten Dimensions framework for professional growth. This framework allows teachers to focus on the areas of teaching practices that generate higher levels of student achievement. The findings focus on three major areas, highlighting: (1) the fact that resources are needed to support the peer coaching process; (2) the challenges of peer coaching; and (3) the benefits of peer coaching. Overall, participants valued the peer coaching process and declared its collaborative nature as the greatest benefit.

The continuous inventions and evolutions in all information technology fields open new channels and opportunities to enhance teaching and educational methods. On one side, these may improve the abilities of educators to present information in interactive and media-enhanced formats relative to traditional methods. This may help students or learners through offering them the information in channels and methods that can be easier to understand, deal with and retrieve. On the other hand, offering those alternative methods of teaching can be helpful particularly for children, people with special needs, or students in rural areas where they can have virtual or remote instructors, especially for majors who have shortages. The purpose of this study is to investigate the impact of utilising multimedia technologies on enhancing, or not, the effectiveness of teaching students at early stages in Jordanian primary schools. To achieve this objective, a program has been developed to test the students' ability to understand basic mathematical knowledge and skills. Two groups were selected from a local school based on their own class distribution, where one group was taught the subject in basic math using a program developed for this purpose and the second class was taught the same subject using traditional methods of teaching (i.e. direct student-to-child instruction, board, etc.). Results showed that in such math skills at this age, using programs or multimedia-enhanced methods of teaching can be effective in getting students' attention, especially when cartoon characters are used. Results also showed that there is no significant difference in learning and knowledge skills and information absorption based on gender distribution, as a comparison of the results between little boys and girls showed no significant difference in their learning skills.

This study examines the ways prospective elementary teachers (PSTs) made connections to children’s mathematical thinking and children’s community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that asks PSTs to visit community settings and develop problem solving mathematics lessons that connect to mathematical practices in these settings (Community Mathematics Exploration Module). Using analytic induction, we identified three distinct levels of connections to children’s mathematical thinking and their community funds of knowledge evidenced in PSTs’ work (emergent, transitional, and meaningful). Findings describe how these connections reflected different points on a learning trajectory. This study has implications for understanding how PSTs begin to connect to children’s mathematical funds of knowledge in their teaching, a practice shown to be effective for teaching diverse groups of children.

In this exploratory study, teachers’ use of standards-based, discourse practices and their students’ mathematics learning in inclusive elementary mathematics classrooms were examined. Two beginning teachers (one third-grade teacher, one fourth-grade teacher) and six students identified with disabilities or as low performing in mathematics participated in this study (three students from each classroom). Six classroom observations of teachers took place over 4 months focusing on a subset of indicators associated with Walshaw and Anthony’s framework of mathematics classroom discourse practices. Follow-up interviews were also conducted. Curriculum-based and state-accountability measures were collected on the six target students in these settings. Different patterns of student performance emerged across the two classrooms in which teachers were observed using different types and degrees of standards-based discourse practices during mathematics lessons. Findings suggest indicators of effective mathematics teaching in inclusive general education classrooms to be validated by future research efforts.

The present review builds on earlier research that evaluated the curricular features of core math programs to improve the performances of students with or at risk for mathematics difficulties. In this review, three elementary math programs, at Grades 2 and 4, were evaluated for the presence of eight instructional principles. Math intervention studies have empirically validated these principles for promoting math proficiency of students struggling with mathematics. Data were collected via a researcher-developed scoring rubric. Findings indicate that adherence to the instructional principles varied markedly within and across programs. In addition, the results indicated that the current textbooks contain a general lack of explicit instruction and provide too few practice opportunities to teach material to mastery. Implications for future curricular reviews and enhancing core math instruction are discussed.

The reported exploratory study consisted primarily of classroom visits, videotaped sessions, and post-treatment interviews whereby second graders ( n = 12) worked on problems in planar geometry, individually and in triads, using physical and virtual manipulatives. The goal of the study was to: 1) characterize the nature of geometric thinking found within the interrelationships of social interactions and instructional artifacts; and 2) describe this nature of thinking in terms of instructional artifact transparency. Juxtaposing collective and individual views of mediated inquiry, we analyze interrelationships to reveal qualitatively different influences on geometric thinking for three conceptually related tasks using manipulatives. Our examination of interrelationships between social interactions and instructional artifacts leads to insights for designing and evaluating instructional technologies for early elementary mathematics, including emerging multi-touch, multi-user systems.

Homework represents one research-based instructional strategy linked to student achievement. However, challenges abound with its current practice. This paper presents the results of three 2-year longitudinal interventions of the Teachers Involve Parents in Schoolwork (TIPS) homework program in elementary mathematics, middle school language arts, and middle school science. Each weekly standards-related TIPS assignment included specific instructions for students to involve a family partner in a discussion, interview, experiment, or other interaction. Depending on subject and grade level, TIPS students returned between 72% and 91% of TIPS activities, and families signed between 55% and 83% of TIPS assignments. TIPS students and families responded significantly more positively than controls to questions about their emotions and attitudes about the homework experience, and TIPS families and students reported higher levels of family involvement in the TIPS subject. No differences emerged in the amount of time students spent on subject homework across the homework groups, but students using TIPS for 2 years earned significantly higher standardized test scores than did controls. The findings suggest that the benefits of TIPS intervention in terms of emotion and achievement outweigh its associated costs.

Starting from the assertion that traditional and reform mathematics pedagogy constitute two distinct figured worlds of teaching and learning, the authors explore the initiation of prospective teachers into the figured world of reform mathematics pedagogy. To become successful teachers in reform-oriented classrooms, prospective teachers must learn more than pedagogical tools and moves: They must understand what it is to participate in the figured world of reform pedagogy, develop models of identities for participants in this world, and negotiate new constructions of mathematics. In this article the authors present three episodes from an elementary mathematics teacher education class where positions of “teacher” and “child” were offered by instructors in activities designed to approximate practice in the reform figured world. Students negotiated new models of identity and conceptions of mathematics as they took up these positions in varying ways.

Background/Context Open-ended, or implicit, questioning has been described as central to reform teaching in mathematics. However, concerns about equity have caused some researchers to question whether this kind of teaching is productive for all children. Purpose This study explores the role that implicit and explicit questions played in encouraging mathematical thinking in an elementary mathematics class taught by a reform-oriented teacher. Setting The study took place in a third-grade classroom located in a small urban school. Participants Participants in the study were a European American teacher, a student teacher, and 19 third-grade students in an ethnically and socioeconomically diverse classroom. Research Design The study drew on ethnographic interpretive methods to collect data through a yearlong observation of 5 focal students in the third-grade classroom. Conversations during mathematics class were audio-recorded and transcribed. Data also included written field notes, student work, informal interviews with children, and formal interviews with the teacher. Analysis began with open coding of the transcripts and field notes and proceeded to more fine-grained coding and examination of other data. Data Collection and Analysis Analysis showed that implicit questions seemed to privilege some children, particularly those who shared the language and cultural practices of the teacher, whereas explicit questions allowed a wider variety of children to participate competently in the mathematics classroom.

Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching word problem (WP) story grammar on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or at risk for mathematics disabilities in two urban public elementary schools in the Midwest. An adapted multiple-probe-across-participants design was used to assess the functional relation between the intervention and students' problem-solving performance. The results indicated that conceptual model—based representation prompted by WP story grammar improved students' performance on arithmetic WP solving and promoted prealgebra concept and skill acquisition. The practical implications of integrating algebraic reasoning in elementary mathematics are discussed.

In this study, the author explores elementary mathematics instruction in the context of standards-based reform and special education policy. Based on observation of inclusive classrooms and interviews with 12 teachers, the author finds that instructional practice was only somewhat consistent with the policy messages to include students with disabilities under the standards umbrella and to individualize instruction. Moreover, the author suggests three ways in which teachers respond to converging policies: skimming the surface of both policies without engaging the ideological core of either, finding the common ground while remaining true to the spirit of both policies, and privileging one policy at the expense of the other.

Seventy-three Latino middle school students participated in a longitudinal study of the preschool antecedents of their mathematics achievement. Path analysis indicated that family resources (parents' educational level, occupation, and income) predicted home literacy activities, which predicted combined early Spanish literacy and English language proficiencies at kindergarten entry, which predicted elementary mathematics achievement, which in turn predicted middle school mathematics performance. These results and qualitative analyses with a subsample of 30 randomly selected families suggest that literacy and numeracy proficiency go hand in hand, and to close the Latino mathematics achievement gap a combined effort of preschool and early elementary literacy and numeracy interventions programs are needed to supplement efforts in middle and high school.

In mathematics, it is not just the how, the procedures for solving problems, that is important, but the why, the underlying concepts, Perla Myers explains. When teachers regain the childlike wonder that leads them to seek the why of math, they will be better able to help their students learn. ********** The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. --G. H. Hardy (1) EVERY parent knows well the most common question asked by a young child: "Why? Why? Why?" Answering such questions is one of the joys--and at the same time, one of the biggest challenges--of parenthood. How much detail should you include, without being dishonest or providing more information than a child wants or needs? When is it better to set up a situation in which a child can explore and discover his or her own answers? How can you answer in a way that encourages more questions and helps build a path toward lifelong curiosity and learning? Across the country, institutions of higher education offer a course in mathematics concepts for preservice elementary teachers. One goal of such a course is to help future teachers get back to that childlike stance of asking "Why? Why? Why?" Do they need to know the answers? Yes, but the questions themselves are just as important. Adults are generally less inclined to ask good questions than are children, and this is especially true in mathematics. So returning to the questioning mind of a child is an essential first step in preparing to become a mathematics teacher. Each teacher affects the attitudes of hundreds of children. Teachers can nurture or negate the innate curiosity young children bring with them into the elementary school classroom. Ultimately, teachers will help determine whether children see mathematics as a subject to be feared or revered. But in order to nurture curiosity among their young charges, teachers need to know that they should be asking questions, they need to know what questions to ask, and, above all, they need to want to ask the questions. Questions are crucial to understanding the depth of mathematics and getting a glimpse of its beauty. Depth is a measure of a subject's intensity and fullness. In mathematics, depth is not necessarily determined by the level of difficulty, for mathematics is more complex than complicated. Depth in mathematics is about the underlying connections between concepts, the generalization of ideas, the power of seemingly simple results, and the realization that mathematical facts make sense. For example, everything in elementary mathematics has a logical explanation. These connections and generalizations take our understanding of mathematics--and of the world around us--in new directions. To get a better sense of mathematical depth, let's begin with some questions about simple arithmetic--addition and multiplication. Many youngsters (and their teachers) place addition and multiplication in the same category. After all, multiplication is simply repeated addition, right? Many people argue that if you know how to add, you know how to multiply. But is that true? Let's assume that we have two, two-digit numbers that we intend to add together. How do we go about it? We all know that is it correct to add the units digits and then add the tens digits. Why should the algorithm for multiplication be any different? Why not multiply the units digits and then multiply the tens digits? What happens to those products? Should we add them? Multiply them? Are there other algorithms that might work? Why? And to return to our original question: Is multiplication really just repeated addition? Before you answer, what about [square root of 3] x [square root of 2]? (2) The ability to pursue such inquiry and the disposition to want to do so are particularly important qualities for teachers if they are to help their students come to understand mathematical concepts in any depth. …

HIGH SCHOOLS are under more scrutiny today than at any other time in recent memory. Employers and university faculty members lament that high school graduates do not have the knowledge, academic skills, and practical competencies to perform adequately in college or work environments. The senior year in particular is thought to be an educational wasteland. (1) Policy makers, including President Bush, say that at least two years of college are needed to function effectively in today's work force, a view affirmed by various advocacy groups. (2) But only 68 of every 100 ninth-graders graduate from high school on time, with about 40 of them enrolling immediately in postsecondary education. (3) Equally troubling, only 27 of the original group of ninth-graders persist to a second year of college. (4) Students drop out in part because they are not developing the skills they need to succeed in school--writing, spelling, basic math computation, and so forth. Even many of those who get to college are not well prepared. Threefifths of students in public two-year colleges and one-fourth of those in four-year colleges and universities require one or more years of MARTHA McCARTHY and GEORGE D. KUH are Chancellor's Professors at the School of Education, Indiana University, Bloomington. remedial coursework. (5) More than one-fourth of fouryear college students who have to take three or more remedial classes leave college after the first year. (6) Certainly we must ensure that students take the right courses in high school and perform well on college entrance and placement exams. Transcripts and standardized tests document whether students and schools "measure up," but they do not identify the student behaviors and school features that need to be changed in order to enhance achievement and improve test results. It is also necessary to determine whether students are developing the study skills that are the foundation for academic success after high school. This is where data on student engagement can be helpful. At first blush, the engagement premise appears simple, even self-evident. Under the right conditions, the more students do something, the more proficient they become. For example, the more students practice a skill, such as reading, writing, or problem solving, the more adept they become at the activity, especially when they get feedback about their performance. In addition to these important behavioral components, however, engagement has an affective dimension, involving such issues as whether students get along with their peers and how they feel about the school environment. Moreover, engagement also has a cognitive component, in that engaged students are more willing to spend time on complex tasks. (7) As Fred Newmann has observed, engagement is "the student's psychological investment in learning, comprehending, and mastering knowledge or skills." (8) And the benefits of student engagement are compelling. Students who devote more time and energy to various educationally purposeful activities in high school get better grades, are more satisfied, and are more likely to graduate and go on to college. (9) To what extent are high school students involved in the kinds of activities that will help them develop the habits of mind and the skills they will need later in life? The High School Survey of Student Engagement (HSSSE, pronounced "hessie") was developed to help answer this question and to guide high school improvement efforts. Building on the success of the National Survey of Student Engagement (NSSE) for college students, HSSSE collects data about students' activities and attitudes. In this article we report some key findings from the more than 170,000 students in grades 9 through 12 in 167 high schools across 28 states who completed HSSSE in 2004 and 2005. (10) Findings across the two years were generally comparable. We focus here on aspects of the high school experience that are directly related to preparing students for success in postsecondary education, occasionally drawing on results from HSSSE's sister surveys, NSSE (used with students attending four-year colleges) and CCSSE (Community College Survey of Student Engagement). …

ATHEMATICS textbooks are critical tools for student learning in American classrooms. Teachers use them daily to plan and deliver lessons, and students use them in class to explore and learn math ematics. When students bring the textbooks home for further study, parents can examine the books for a glimpse of their child's mathe matics classroom. Given textbooks' potential to support student learning, it is important to understand how they are developed. Who produces school mathematics textbooks? Who decides on their content and

In recent years, scholars have problematized terms used to describe instruction on teacher survey instruments. When scholars, observers, and teachers employ terms like discuss and investigate, they often mean to describe quite different events. This article problematizes another set of terms often found on survey instruments, those describing mathematical content. To do so, it examines terms such as geometry, number patterns, and ordering fractions for rates of agreement and disagreement between teachers and observers participating in a field pilot of an elementary mathematics daily log. Using interviews, written observations, and reflections on disagreements, this article also asks why disagreements occurred. Sources of disagreement included problems with instrument design, memory/perception, and, notably, differences in the way subject matter terms are used in different communities—university mathematicians, elementary teachers, and mathematics educators. Finally, implications of these sources of disagreement are explored.

No Child Left Behind mandates accountability data for school districts. This mandate has led to increased attention to instruction and academic remediation among educational researchers. The current study used schoolwide curriculum-based assessment (CBA) and curriculum-based measurement (CBM) data to plan and deliver mathematics instruction to examine if this would lead to improved student skill within one school year and improved group test scores between school years. The Screening to Enhance Equitable Educational Placement (STEEP) schoolwide problem-solving model was used in one elementary building, with CBM data used to track progress and CBA data used daily to track mastery at each skill level. Results suggested that children made significant progress within one school year, as measured by CBM, and the school significantly increased Stanford-9 mathematics scores after implementing the program. Potential implications for assessment and instructional practice are included.

The students in Ms. Thomas' classes are struggling with poverty, learning disabilities, behavioral disorders, transience, and home languages other than English. Ms. Thomas is struggling to understand how they are going to meet the same standards as students who don't face such difficulties. PRESIDENT Bush's No Child Left Behind (NCLB) Act, signed in January 2002, is the latest easy solution to education's woes. According to NCLB, all groups of students will be tested and will be required to meet the same standard. This means that schools must raise the achievement of the nation's historically lowest-achieving groups: students in special education programs, those from impoverished homes, minority students, and English-language learners. Susan Castillo, superintendent of Oregon's Department of Education, objected to NCLB, saying that the new requirements were unreasonable. In the end, the federal government rejected Castillo's plan to implement different standards for different student groups, and Oregon has had to fall in line. As a classroom teacher, I find that NCLB's requirements sound like an episode of "The Twilight Zone." Last year the students in my remedial math classes at Reynolds High School were years behind their peers. And as Oregon schools watched their funding evaporate, leading to fewer days in the school year and cuts in staff and programs, the chances that my math students would be snatched aboard the education train before it pulled any further out of the station were slim. I don't disagree with NCLB in theory: because every child is important, no child will be overlooked, and every child will meet the same standard. I would love to teach in this school and live in this world. But in reality the problems schools face are huge, and easy words on paper will not make them go away. NCLB requires teachers to be trained in their subject areas. Reynolds High School is perched at the windy mouth of the Columbia River Gorge. I've taught there for eight years, mostly English -- and math. My bachelor's degree is in English. My master's is in teaching English. I'm pursuing a second master's, in writing. I'm clearly a qualified English teacher. But math is another story. I took algebra and geometry in high school, and in college I earned three math credits through a correspondence course. That's it. In 1997, as a new teacher, I passed, on the second try, Oregon's test to certify teachers of basic math. It was an essay test. This makes me a math teacher, so when my assistant principal had two overflow sections of low-level math and no math teacher to teach them, he came to me. "I'd like to hire an experienced math teacher," my assistant principal explained. "Someone trained to teach low-level math." But there was no money to keep the teachers we had, and certainly none to hire more. (In the spring of 2003, we cut eight days from our school year.) No one was happy about it, but the job of teaching the low-level math sections was mine. Prep Math At Reynolds High School, "prep math" is our lowest math class, loaded with the kinds of kids that President Bush says should not be left behind. It's easy to say we're going to bring these kids up to par with their classmates. Doing it seems impossible. Most of our prep math students are freshmen, but others are older -- sophomores, juniors, seniors. These kids have minimal math skills. Many of them struggle to subtract two-digit numbers without a calculator. Ask one of them what four divided by four is, and you might get a blank stare. Ask what seven times nine is, and the student will look it up for you on the multiplication chart. These kids have no idea how fractions, decimals, and percentages are related. Mistakes like these are not uncommon: "This is stupid," the prep math students say. "When are we ever gonna use this, anyway?" I'm not sure I know the answer to that. I'm not sure I'm teaching them what they'll need to know. …

I remember how nervous I was when I accepted the position as the teacher for gifted students in our building. The task seemed overwhelming—meeting the needs of students who could think faster, harder, and smarter than any of our regular learners. What could I possibly do to impact the lives and learning for this new arrangement of students I was about to educate?

Testing of mathematical skills at a metropolitan newspaper provides a baseline assessment of numeracy in the newsroom. Drawing on social cognitive theory, the study also examines the interplay of mathematical competence and confidence of journalists. The results challenge the view that most journalists cannot handle elementary mathematics. Nonetheless, about one in six of news-editorial staff failed to answer the majority of math questions posed. Testing reveals high math anxiety even among strong math performers. The study also documents a gender gap in mathematics skills and confidence.

alcohol syndrome; he has been classified as having severe mental retardation. He does not speak, but uses some signs and pictures for verbal communication. • Megan is a 7-year-old girl with Down syndrome; she is classified as having moderate mental retardation. She has limited verbal ability and uses some pictures/symbols to communicate. Megan’s parents want her to learn academic skills, including basic math and reading, so that she will develop the skills needed to participate in general education. Both children are learning counting skills on ordered objects—snacks for their classroom. This article shows how we taught these children functional skills using real-life objects and settings (see box, “What Does the Literature Say?). Our experience indicates that to effectively teach children with severe disabilities how to count requires the use of both pointing and gesturing. In addition, we use pointing to teach children how to recognize items, such as milk containers, and the numbers that represent the total of containers. We use gestures as prompts to remind children of each step when counting. Using Real-Life Counting Experiences According to Westling and Fox (2000), using real materials in their natural context during teaching helps children learn how to carry out an activity as they will do in their daily lives and assists them in mastering the desired skill. In a natural environment, the skill learned can be practiced in school, at home, or in communities. To provide students with severe disabilities an opportunity to practice the skills that have been introduced in school, we considered a number of routine activities and decided to include these students in a snack delivery activity. The snack delivery enables students to walk out of their classroom and become involved in something that they like. Most important is that they can learn and practice counting skills in a functional and meaningful way. The following are the steps in our snack delivery activity.

Do advertising students really dislike math? Or is this question a manifestation of frustrated media planning course professors?Do women perceive they are poorer at math than men? Do students with better grades like math more? Are those interested in creative jobs more likely to be math averse than those wishing to pursue management-oriented advertising jobs?Or are these assumptions based on unfair stereotypes?There is scant research to address these questions, but the answers would be helpful to advertising educators, particularly to those who teach courses that include math.Surveys of advertising professionals clearly indicate that students who intend to work in the advertising business need to have math skills and understand statistics. A survey of advertising media directors, planners, buyers and executives (Lloyd, Slater & Robbs, 2000) revealed professionals believe students should have a mastery of basic math, percentages and index numbers. The study also indicated that professionals were concerned that newly hired advertising graduates lacked knowledge of media math.An earlier study (Martin & Lloyd, 1992) revealed that over half of media teachers surveyed used media planning software and were therefore spending less time teaching skills oriented material, such as media math. Crowley (1987) interviewed several agency media directors in an attempt to identify content for the advertising media planning course. The professionals in the study mentioned statistics as a need-to-know skill.There is clearly a need for advertising students to have math and statistics skills to work in the advertising profession; however, advertising professors sense an aversion among students to learning such skills. This paper will attempt to explore the unanswered questions about advertising students' level of anxiety toward math and statistics and determine differences, if any, among categories of students who claim to be math averse.Review of the LiteratureAttitudes Toward StatisticsThere is a substantial body of research dating back to the 1950s (i.e. Bendig & Hughes, 1954), probing students' attitudes towards math and statistics. Studies have documented both "math anxiety" and "statistics anxiety" (Roberts & Saxe, 1982; Adams & Holcomb, 1986) and define them generally as a fear that students have toward working with numbers and taking the statistics course (See Birenbaum & Eylath, 1994, for a historical review of statistics anxiety). Other studies have examined the variables related to negative attitudes toward math and statistics (Feinberg & Halperin, 1978; Roberts & Bilderback, 1980; Benson, 1989; Sutarso, 1992b; Schau, et al, 1995; Tremblay, Gardner & Heipel, 2000), though no studies can be found that specifically examine advertising majors' attitudes toward math and statistics.Numerous studies showed a high correlation between positive attitudes toward statistics and high course grades (Wise, 1985; Benson, 1989; Schau, et al, 1995). Anxiety was associated with lower achievement in statistics (Tremblay, Gardner, & Heipel, 2000).Sutarso (1992a) created an instrument that gauges students' attitudes toward statistics by measuring six underlying dimensions. Sutarso used a sample of education and business students in developing the instrument and found it to have strong reliability and validity. He also identified some variables that related to students' anxiety in learning statistics including student achievement, preknowledge of statistics, school, and current class level. Sutarso (1992b) found no relationship between statistics anxiety and other variables such as gender and ethnicity.Feinberg and Halperin (1978) identified several variables related to performance in introductory statistics including anxiety about math, mathematics achievement and previous math experience. Age, gender and academic major appeared to be unrelated to students' success or failure in statistics. …

April 1, 2002 Ms. Verity Keane Local University USA Hi Verity, Sorry I haven't been in touch for a while, but school is very hectic. In addition to my class in elementary mathematics methods, I am taking a course on teaching elementary physical education. I am really getting into shape now. Whew! But would you believe it's geometry again in math? We always hated geometry, didn't we? For me, it was just gymnastics in the mind. Talk about "no pain, no gain." I should be a geometrical Olympian by now, it hurts so much. Now we have a term paper to do on "Geometry Begins," so after this letter it may be a while before I write again. You know what these professors are like. A problem arose for me almost as soon as we started geometry. Don't forget, I had spent the whole of my mathematical life trying to remember things I didn't understand -- the sort of neurological equivalent of defying gravity. First off, the professor shook a colorful box and spilled out the contents onto the floor. That led to a bit of excitement. What would we be doing? Out came various blocks -- you know, sort of like the ones preschool children play with. (See Figure 1.) Kid's stuff. We nearly died. Then he said to a student named Kyra, "Pick up a shape, and tell me about it." "It's blue," she said. "I think it's a cylinder." "Good," he said. "Now," to another student, "you pick one up, and tell us how it's similar to or different from hers." "Mine's red," Paul said, "and it's more square than hers." "What would you call it?" "A box? A cube?" When it was my turn, I picked up one that was green. It sort of looked like a tent. (See Figure 2.) I had a feeling this wasn't about the colors, so I said, "Well, mine is 'pointier' than Paul's and Kyra's. But I don't know what it's called." I hated saying that, but it was true. Then get this: he didn't say what it was called. He didn't say! Instead, he displayed an overhead showing a lesson from a "reform- based" textbook. How about that? It was from a section on shape, and here is what it said: Give each student an attribute-block triangle, rectangle, square, and hexagon (or geometric shapes from plasterboard). Ask the students to examine each shape, touching the sides and corners. Have the students tell how many sides and corners each shape has. For the rectangle, square, and hexagon, have the students point out pairs of opposite sides. Taking an "attribute triangle" out of his pocket, he said, "This is part of a geometry kit used in elementary school classes," and he handed it to Juan. (See Figure 3.) "How many corners does it have?" he asked. Juan looked it over. "Three," he responded rather confidently. "I see," our professor said. "Tell me, Catherine, how many corners does yours have?" Verity, I was a bit unsettled by this whole scenario because I wasn't at all confident that I would get the answer right. I took quite a bit of time looking my shape over and touching each vertex. "Six," I answered somewhat hesitantly and with a bit of fear and trepidation. Isn't that silly? But math gets me like that. It just wasn't clear where all this was going. Anyway, he turns back to Juan and says, "Look at yours again. Why did you say 'three'?" Juan examined his block and then took mine as well. Then the most amazing thing happened. Juan got this quizzical look on his face. "You know, now that I've got both of them in my hands, they feel the same," he said. "They have the same number of edges, faces, and corners. And I know Catherine's shape is not a triangle because it's too long. But, in my mind, I saw this thinner one as a triangle -- even though it is nearly half an inch thick. These two shapes are the same!" They really were the same. I believe it hit all of us at once that the "attribute triangle" could not really be a triangle because the two shapes had identical properties. …

In this article, I address a major problem in the education of elementary teachers; namely, that teacher education programs constitute a relatively weak intervention (Ball, 1988; Borko et al., 1992; Evans, 1987; Speedy, Fensham, & Annise, 1989). Preservice teacher education in mathematics, for example, often has a limited effect on student teachers' willingness to learn and teach mathematics for relational understanding. Relational understanding, in Skemp's (1989) terms, is knowing both what to do and why (p. 2) and may be distinguished from instrumental understanding--the application of rules without reason. Initial surveys of student teachers entering the present undergraduate teacher education course demonstrate that most student teachers view the task of teaching mathematics instrumentally; they see mathematics as a set of rules not readily understood that must be memorized (Hill, 1994). The present mathematics methods program aims to achieve significant change in this attitude despite the daunting body of evidence indicating that such long-held attitudes are notoriously resilient (Ball, 1990). I investigated whether the mathematics methods program significantly facilitates preservice elementary teachers' willingness to learn and teach mathematics for relational understanding. The central aim of the methods program is to encourage student teachers to value this type of understanding. Only if student teachers value it will they want to teach in a way that facilitates children's relational understanding. The findings indicate that engaging in a continuous cycle of putting theory into practice by teaching children and reflecting on the results leads student teachers to value relational understanding. These findings are relevant to elementary teacher educators in mathematics and other discipline areas in which student teachers experience anxiety; they may also be relevant to educators in any discipline area in which conceptual change is a pertinent issue, for example, where student teachers must adopt teaching approaches different from those familiar to them from their schooling. The Mathematics Methods Program The mathematics methods program is a collaborative university-elementary school initiative and is designed to provide student teachers with the opportunity to form meaningful and effective connections among practice, theory, and reflection. Student teachers spend one day per week for 22 weeks in an elementary school where they attend a mathematics methods class taught by their university tutor. They also teach mathematics to small groups of children, under their tutor's supervision. After working with the children, student teachers and tutor regroup to discuss and reflect on their experiences of teaching. Student teachers then incorporate their new discoveries into their planning for the following week's session with the children. This weekly cycle of theory, action, and reflection continues throughout the academic year. According to psychodynamic theories of learning, the emotional component of learning, stemming from powerful emotional experiences, provokes significant attitudinal and behavioral change (Goldfried, 1979). The present mathematics methods program is based on the philosophy that productive change in learning and teaching practices will more likely flow from emotionally powerful experiences, part of the reality shock that Koetsier and Wubbels (1995) describe. In this approach, individuals consistently and repeatedly experience theory, practice, and reflection in an integrated way. If teachers are to practice effective methods, they must have the challenge and the opportunities to experiment with these methods (Lauriala & Syrjala, 1995). For meaningful and lasting change in attitudes and practices to occur, I believe that student teachers must experience the responses of children to their teaching and discuss and reflect on these experiences. …

The purpose of the present investigation was to develop curriculum-valid mathematics survey tests based on an analysis of district adopted basal mathematics curriculum material. We describe a taxonomy of curriculum analysis that was beneficial, in part, in item creation and test construction. Test items were selected to accurately represent the curriculum. The survey test was piloted with a group of 240 students each in Grades 3, 4, and 5 of six schools. A second, parallel test was developed and administered to the same group approximately six months later. Test results were reported to teachers as student and item information. Implications for future assessment research and practice involving students with learning difficulties are also discussed.

Dans cette etude, les AA. ont cherche a savoir de quelle facon l'approche de l'enseignement des mathematiques chez de futurs enseignants de cette discipline peut etre modifiee par une reflexion sur leur conceptions du metier et une collaboration entre collegues

Ms. Verity Keane Local University U.S.A. Hi ,Verity- Sorry I haven't been in touch for a while, but school is very hectic. In addition to the class in elementary mathematics methods, I am also taking a course on teaching elementary music. Have you ever played a record-er? Trust me when I tell you that you'd rather not hear me playing one. Even my dog goes into the other room when I do. That's why I am so thankful for math; it is so much easier. Well, at least that's what I used to think. We "did multiplication" in class today, and you will never guess what happened! First, let me say that I do know how to multiply. Well, at least I have the mechanics of it down straight, that sort of thing. My educational experience in this area was "the multiplication facts" - also affectionately called the "times tables" - all done by rote memorization over lots and lots of time, until they were sufficiently drilled into our heads. We could practically recite them in our sleep. But in class today, boy, did I get a shock! And we have an assignment to do on it, so there may be another delay before I write again. Our professor was smart. He didn't say very much. He just quoted some research by Thomas O'Brien and Shirley Casey, who had looked at children's understanding of multiplication.1 Evidently, when these children were asked if they "knew" 6 x 3, they all responded "18." But when asked to set 6 x 3 in a real-life context, they couldn't do it. Well, about 74% couldn't. So our professor tested it out on us. Here we are in a college-level mathematics methods class for future educators, with our average age being about 29+, and he asks if we know 6 x 3. Can you believe it? Of course we know - it's 18! I have to tell you, we were a bit put off. Then, instead of telling us the answer, he had us get into our cooperative groups and come up with a situation for 6 x 3 =18. That was fun. My partner and I had a bit of a heated debate over what to do, but we settled on six students with three Twinkies each. You know, six lots of three. It was obvious, really, and didn't take us long, so we had a little chat. But here's the kicker. After all that, our professor never asked us what we had decided. Honest, he never asked! Instead, he had us look up the meaning of "multiplication" in our dictionaries that we had brought with us. For heaven's sake, Verity, we all knew it was "six lots of three." No dissent. It is not something you vote on. Mathematics is mathematics is mathematics - all over the world! Why waste time looking it up? So we all looked up multiplication in the dictionary, and wow! You should try it. What a shock! Well, actually at first it didn't help much, as the Living Webster Encyclopedic Dictionary defined multiplication as "the act or process of multiplying; the state of being multiplied; the operation by which any given number or quantity may be added to itself any number of times." Not very clear, don't you agree? Then we found Webster's II New Riverside Dictionary, which said multiplication was "repeated addition in which one number indicates how many times another is to be added to itself." Not a great help either. We wondered which number or quantity is to be added to itself. But Verity, read this one from Webster's 3rd Edition College Dictionary, and read it carefully. It totally blew us away: "Multiplication: the process of finding the number or quantity (product) obtained by repeated additions of a specified number or quantity (multiplicand) a specified number of times (multiplier); symbolized in various ways (ex. 3 x 4 = 12 or 3 [middle dot] 4 = 12, which means 3 + 3 + 3 + 3 = 12, to add the number three together four times)" (my emphasis). We also had a handout about Euclid. You remember him, the mathematician from around 350 BCE - the one who wrote the Book of Elements? Seems an article in the Arithmetic Teacher in 1966 had quoted Euclid as having defined multiplication like this: "One number is said to multiply another when the number multiplied is so often added to itself, as there are units in the number, and another number is produced. …

Students with learning problems (i.e., students with learning disabilities or emotional disabilities and those considered at-risk for school failure) are not making acceptable math progress in the nation's schools. Fortunately, instructional practices exist that help these students achieve in math. Ten instructional components that have research support for promoting math achievement are presented. A math curriculum, the Strategic Math Series, which incorporates the research-based teaching practices, is described. Next, the results from field-testing the Strategic Math Series with 22 teachers are presented. The field-test results indicate that 109 students with learning problems were able to (a) acquire computational skills across facts, (b) solve word problems with and without extraneous information, (c) create word problems involving facts, (d) apply a mnemonic strategy to difficult problems, (e) increase their rate of computation, and (f) generalize math skills across examiners, settings, and tasks. Finally, issues in math instruction are discussed, and the need to include best practices within instructional materials is highlighted.

This study was designed to determine if the advantage of Chinese children over American children in basic numerical skills is related to differences in the strategies used to solve elementary mathematics problems or to the speed of executing the underlying processes. To achieve this goal, first-grade children from China and the United States were administered a pencil-and-paper numerical ability measure and solved a series of computer-presented addition problems. For the computer task, strategies and solution times used in problem solving were recorded on a trial-by-trial basis. The Chinese children showed a 3-to-1 performance advantage on the ability measure. Chinese and American children used the same types of strategies to solve the addition problems, but the Chinese children were well ahead of their American counterparts in terms of the developmental maturity of the strategy mix. The Chinese children also showed a speed-of-processing advantage for retrieval-based, but not counting-based, processes. The strategic and speed-of-processing differences appeared to mediate the advantage of the Chinese children on the ability measure. Implications for the acquisition of more complex mathematical skills and concepts are discussed.

Policymakers and researchers have for many years advocated disparate approaches to ensuring teachers deliver high-quality instruction, including requiring that teachers complete specific training requirements, possess a minimum level of content knowledge, and use curriculum materials and professional development resources available from schools and districts. In this paper, we investigate the extent to which these factors, which we conceptualize as resources for teaching, predict instructional quality in upper elementary mathematics classrooms. Results show that teachers’ mathematical knowledge and their district context explained a moderate share of the variation in mathematics-specific teaching dimensions; other factors, such as teacher experience, preparation, non-instructional work hours, and measures of the school environment, explained very little variation in any dimension.