Eighth-grade Mathematics Teachers Research Articles

Talking about teachers: Would sampling weight adjustments allow for teacher-centric inferences in future TIMSS assessments?

The Trends in International Mathematics and Science Study (TIMSS) is an influential mathematics and science assessment administered at fourth and eighth grades in around 60 countries across the world. Under current practices, TIMSS does not support claims about teachers unless the inference is drawn as a student characteristic (“Half of the eighth graders in the country have mathematics teachers with Master’s degrees.”). With this in mind, this paper proposes and tests through a simulation study two methods that would allow for teacher-centric inferences (“More than half of the eighth-grade mathematics teachers have Master’s degrees.”) if links between sampled teachers and the unsampled yet eligible classes were known. The first method posits that with such links inverse-probability weights could be calculated, and the second method, the Multiplicity-Adjusted Indirect Sampling (MAIS) approach, posits that teacher estimates could be obtained by adjusting downward the classroom weights based on these links.

Assessing Eighth-Grade Mathematics Teachers and Textbook in Embodying Thinking Levels

Assessing Eighth-Grade Mathematics Teachers and Textbook in Embodying Thinking Levels

Creating Cultures of Participation to Promote Mathematical Discourse

IntroductionAs a former eighth grade mathematics teacher, I was aware of the impact discourse had in shaping students' thinking and thus often implemented strategies that supported these efforts. However, a reality became clear when pursuing these National Board Certification, which demanded a 15-minute unedited video of me facilitating a whole-class discussion. While recording the lesson, which centered on an introduction to irrational numbers, I thought students were engaged in lively discussion. However, analysis of the video-taped lesson revealed that I was doing almost all of the talking! The perceptions of my practice were not aligned with my actual practice. After this revelatory experience, I was curious to learn more about how other teachers perceived the use of discourse to support adolescents reasoning in mathematics and particularly how they created cultures of participation to support equitable discursive interactions with adolescent students from diverse backgrounds.Consistent with my own experience, equitable access to mathematically rich and meaningful learning experiences continues as a critical need in the classroom (Cobb 8c Hodge, 2011; National Middle School Association [NMSA], 2010). Rich learning experiences also are fundamental in supporting and developing students' mathematical reasoning and sense making (Chapin, O'Connor, 8c Canavan Anderson, 2003), which is of particular concern during the middle grades as the level of abstraction in mathematics increases greatly. As a means of openly engaging in understanding meaningful and rich mathematics, discourse offers one avenue for teachers to create equitable and mathematically rich learning environments and interactions; this article demonstrates why an emphasis on mathematical discourse should be a common practice within the middle level classroom (Bartolini Bussi, 1998).Discourse requires students to evaluate and interpret the perspectives, ideas, and mathematical arguments of others as well as construct valid arguments of their own. That is, students develop deeper understandings of mathematics when they engage in meaningful social interactions such as whole class discourse (Cobb, Yackel, W NCTM, 1991; Rigleman, 2010). The adoption of the Common Core State Standards in many states reinforces the importance of creating classrooms that focus on reasoning, deep conceptual understanding, and the communication of mathematics (Larson, 2012;NCTM, 2000). In addition, the teacher's efforts and attitudes in creating a caring and well-structured classroom environment with high expectations for all students are more likely to increase student engagement (Klem 8c Connell, 2004), which can lead to greater achievement (Smith, Rook, 8c Smith, 2007). Such classrooms exemplify cultures of participation. With that said, knowing that discourse can support student learning and creating the structures to help discourse come alive are not the same thing. Creating a classroom culture of participation is a necessary first step in implementing meaningful discourse and creating equitable learning experiences.What follows is a compilation of strategies and classroom structures from 13 middle level teachers from highly urban communities with tremendous cultural, linguistic, and ethnic diversity. …

Developing a Caring Ethic for Middle School Mathematics Classrooms

Angiline (first author) remembers her first day teaching middle school mathematics. She recalls feeling academically prepared, however, she was not ready for what was to come. She remembers being excited and enthusiastic about her first year of teaching, but she was not prepared emotionally for the 130 eighth graders she taught every day. They had so many needs. They wanted her to sign forms to go on field trips and to excuse their absences. They needed pencils, paper, and books. Mostly they wanted her attention, but Angiline had no idea how to meet the emotional needs of these young adolescents. A colleague gave Angiline a book about how to make the most of her mathematics class time. Out of desperation and exhaustion, she tried some of the suggestions to make the beginning of class a valuable time for her and her students. She began to start classes with a critical thinking exercise. Initially, Angiline did this warm-up activity to help keep the students busy while she managed administrative tasks such as taking roll, returning homework, and attending to announcements on the public address system. But as Angiline got better at designing these starting tasks, her students came to enjoy the challenging exercises, and a caring classroom community began to form. A call to care Like Angiline, teachers assigned to entry-level or low track math classes are entrusted with the students who need them the most. These students may be academically disengaged and, perhaps, do not see how education, especially mathematics, relates to their lives. Students in these classes have many labels, including at-risk, English language learners (ELL), and urban students. Students of color, especially African Americans and Latinos, are likely to be enrolled in these entry-level classes in higher proportions (Oakes, 1995). Mathematics educators are called to engage and educate every one of their students, including these disenfranchised students. Based on recommendations in the literature and their experiences in the classroom, the authors believe that for every student to be successful, teachers must foster a caring ethic (Ladson-Billings, 2006). The authors, Angiline and Al, are university teacher educators who share similar experiences building community in middle grades mathematics classrooms. In this article, they describe what a caring ethic looks like in a middle grades mathematics class, and they suggest specific practices drawn from their experiences that teachers can implement to make their classrooms more caring and engaging places. Caring community of learners As eighth grade mathematics teachers, the authors began the year building relationships with their students and encouraging communication to establish a caring ethic. In their mathematics classes, a caring community attitude was everything, and, as in any community, communication and relationships were paramount. Following Noddings (2002), an ethic of caring in the classroom has four key components. Teachers must model acting as caregivers and people who care for others in the classroom. Teachers and their students must engage in dialogue about caring as they seek to arrive at common understandings of the concept. Students must have opportunities to practice caring for other members of the classroom community. Finally, teachers must offer confirmation of the struggles and accomplishments of their students as they care for one another. Caldwell and Sholtis (2008) provided further insight into developing an ethic of care in the classroom. They identified five characteristics of student-oriented teachers who care for their students: 1. They treat all students with respect by using their names and model how to show respect for other students and other teachers. 2. Student-oriented teachers encourage positive discourse in the classroom, which they demonstrate by giving constructive written encouragement on assignments and frequent verbal praise (Caldwell, 1999). …

Teaching Math and Science

Local Systemic Change projects, funded by the National Science Foundation, were designed to help teachers of mathematics and science deepen their content knowledge and improve their instructional practices. Ms. Weiss and Ms. Pasley describe how these aims were accomplished through combination of intensive professional development and follow-up support when the teachers took their new knowledge and skills back to the classroom. ********** IN THE FALL of 2001, University of Delaware Professor Jon Manon observed mathematics lesson about factoring in an eighth-grade classroom of an urban middle school, a school which is home to what is often reputed to be one of the most challenging student populations in Delaware. Jenni Green (a pseudonym), the teacher he was observing, had been participant in an intensive summer institute, and Manon wanted to find out if any of the summer's workshop lessons had had an effect on her work. decided that I would look for 'residue' from the summer professional development across grades and units, writes Manon in case study published on LSC-net, an interactive website for the project leaders of the Local Systemic Change (LSC) initiative, funded by the National Science Foundation (NSF) since 1995. In particular, I was seeking evidence that our emphasis on the instructional model, the launch-investigate-summarize lesson cycle, was finding root in actual practice. (1) A LESSON IN FACTORING Jenni Green used to teach sixth grade. This year, was an eighth-grade mathematics teacher. According to Manon, she did have special concerns about particular students, e.g., one 14-year-old had baby and often stayed home to care for it. But when these kids were in school, Jenni was prepared to help them focus on learning mathematics. Manon's visit to her classroom came at what Jenni described as a very critical moment in the Mathematics in Context curriculum algebra unit, Building Formulas. (2) Manon continues: This was the lesson in which factoring was first introduced. We agreed that it was seminal concept, gatekeeper to success in more formal algebra course. As the name of the unit suggests, building situations were used to introduce algebraic representations. Section B, Basic Patterns, exploited the context of construction with bricks to introduce representation for rows of bricks involving Standing, S, and Lying, L, bricks. For example, the length of [a simple] pattern, made up of two Standing [bricks] and one Lying brick, might be represented symbolically as 2S + L. A such as this one might be repeated to produce longer string of bricks. And that new configuration might be represented as either three groups of two Standing and one Lying--3(2S + L)--or, dropping the reference to the pattern, as 6S + 3L. Before the students arrived, Jenni had described the approach planned to take to introduce her lesson. She decided to challenge her students to identify the basic pattern in longer string and then determine how many times that was repeated. As the first students entered the room, Jenni apparently made up her mind to try something different. Seated at the overhead projector, Jenni wrote 15S + 10L and asked, How can I figure out what the is in this case? Immediately, Ellen, diminutive girl in the front row, answered, Five ... it fits into [15] ... three times. For 10, it will be 2. Initially caught off guard by both the promptness and content of Ellen's response, Jenni recovered and asked, So the is repeated how many times? She drew 15 Standing and 10 Lying bricks on the overhead and, indicating in the drawing, said, I'll try to clarify Ellen's thinking ... for every three Standing, there are two Lying bricks ... pretty cool. I like that Ellen! Then, looking quite pleased and shifting her gaze from to the rest of the class, said, Ellen stole my thunder! …

The Thinking of Students: Have You Lost Your Marbles? Three Creative Problem-Solving Approaches

As an eighth-grade mathematics teacher, I have come to value the process of communicating about mathematics. I have learned that it is vital for students to explain and describe their work, not just simply submit their solutions. I use several methods to encourage my students to share their problem-solving processes, such as asking them to show their work on the board for the class, write essays, and answer a simple question like “How did you arrive at your answer?” Of these tasks, writing takes the most time and effort, but the results can be extraordinary. The formal essay requires students to organize their thoughts, prepare a logical sequence, and explicitly communicate the details of their work. This “thinking about thinking” translates to an improved problem-solving ability and greater conceptual understanding.

Collaborative action research on the learning and teaching of algebra: a story of one mathematics teacher's development

This paper presents the story of a mathematics teacher's transformation that resulted from her engagement in collaborative action research. The collaborative research, conducted by a university mathematics educator and an eighth-grade mathematics teacher (Marylin), centered on investigating the outcomes of implementing a ‘Hands-On Equations’ approach to teaching algebra. This algebraic study, which is briefly reported herein, serves as a vehicle for examining the questions, reflections, and changes brought forth by Marylin throughout the collaborative process. Thus, the project of investigating the teaching and learning of algebra can be viewed as the ‘sub-study’ within the broader study of the effects of collaborative action research on the mathematics teacher involved in the investigation. Within this paper, issues related to the broader study of collaborative action research in the mathematics classroom, that are connected to Marylin's transformation, are discussed. These issues include the characterization of and goals for collaborative action research as well as the challenges for collaborative action research in mathematics classrooms.

Blazing a Portfolio Trail—Without a Crystal Ball

Butterflies and excitement about the portfolio (inquiry) project. I'd like to have a crystal ball to see into the future, but then it wouldn't be a research project, would it! Marylin, eighth grade mathematics teacher and co-author, wrote these words in July. As we entered the 1994-95 school year, little did either of us realize how helpful a crystal ball might have been—or how much we would ultimately learn about portfolios, teaching and learning with adolescents, and trailblazing.