1.19: Classroom Centered Practices in Mathematics

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Culturally Responsive Teaching

motivational framework for culturally responsive teaching which can support learning. The framework is made up of four essential motivational conditions, which Ginsberg has found to act “individually and in concert to enhance students’ intrinsic motivation to learn.” The conditions are:

Establishing Inclusion—the teacher creates a learning environment in which students and teachers feel respected by and connected to one another.
Developing a Positive Attitude—the teacher creates a favorable disposition among students toward learning through personal cultural relevance and student choice.
Enhancing Meaning—the teacher creates engaging and challenging learning experiences.
Engendering Competence—the teacher creates a shared understanding that students have effectively and authentically learned something they value.

Ginsberg, M. B. (2015). Excited to learn: motivation and culturally responsive teaching. Thousand Oaks, CA: Corwin Press.
Ladson-Billings, G. (1994). The Dreamkeepers: Successful teaching for African-American students. San Francisco: Jossey-Bass.
Pewewardy, C. (1994). Culturally responsive pedagogy in action: An American Indian magnet school. In E. R. Hollings, J.E. King, & W. C. Hayman (Eds.), Teaching diverse populations: Formulating a knowledge base (pp. 77–92). Albany, NY: State University of New York.

Teacher and Student Relationships

Developing a Growth Mindset

Boaler, J. (2015). Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. John Wiley & Sons.
Dweck, C. (2008). Mindsets and Math/Science Achievement. Prepared for the Carnegie Corporation of New York-Institute for Advanced Study Commission on Mathematics and Science Education.
Motivating Students to Grow their Minds. Copyright © 2008–2012. Retrieved from Mindset Works.

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Support, Structure and Scaffolding

$math icon$ Educators should provide structure and support for students by intentionally teaching how to participate in these types of math conversations. Students benefit from learning how to question, reason, make connections, solve problems, and communicate solutions effectively (Echevarria, Vogt, & Short, 2009).

variety of scaffolds that foster students’ participation supports students both in organizing their thinking and making sense of the mathematics. Examples include:

Sentence frames, which provide tools to support mathematical conversations.
Teacher modeling and think-alouds.
Word walls and posters displaying commonly used terms, operations, and math processes.
Graphic organizers, which provide visual representations of mathematical information.
Artifacts and Manipulatives upon which to build shared meaning and support sensemaking.
Structured peer interactions, to communicate ideas and clarify understanding (Echevarria, Vogt, & Short, 2009; Zwiers et. al., 2017).

Adoniou, M., & Qing, Y. (2014). Language, Mathematics and English language learners. Australian Mathematics Teacher, 70(3), pp. 3-13.
Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics (CCSSM). Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. Council of Chief State School Officers. (2012).
Framework for English Language Proficiency Development Standards corresponding to the Common Core State Standards and the Next Generation Science Standards. Washington, DC: CCSSO.
Echevarria, J., Vogt, M. E., & Short, D. (2009). The SIOP Model for Teaching Mathematics to English Learners. Boston: Pearson Allyn & Bacon.
Ernst-Slavit, G., & Slavit, D. (2015). Mathematically Speaking. Language Magazine.
Hill, J., & Miller, K. (2013). Classroom Instruction That Works with English Language Learners, 2nd Edition. Denver, Colorado: Association for Supervision and Curriculum Development.
Pierce, M. E., & Fontaine, M. (2009). Designing Vocabulary Instruction in Mathematics. The Reading Teacher, 63(3), pp. 239-243.
Roberts, N. S., & Truxaw, M. P. (2013). For ELLs: Vocabulary beyond the definitions. Mathematics Teacher, 107(1), pp. 28-34.
Slavit, D., & Ernst-Slavit, G. (2007). Teaching Mathematics and English to English Language Learners Simultaneously. Middle School Journal, 39(2), pp. 4-11.
Background and Philosophy
Wagganer, E. L. (2015). Creating Math Talk Communities. Teaching Children Mathematics, 22(4), pp. 248-254.
Walqui, A. (2009). Improving Student Achievement in Mathematics by Addressing the Needs of English Language Learners. NCSM: Leadership in Mathematics Education, No. 6.
Zwiers, J., Dieckmann, J., Rutherford-Quach, S., Daro, V., Skarin, R., Weiss, S., & Malamut, J. (2017). Principles for the Design of Mathematics Curricula: Promoting Language and Content Development.

Cross-Curricular Teaching Practices

Mathematical Representations and Manipulatives (CRA)

begin with developing a conceptual understanding of mathematical ideas. This can be accomplished through the use of concrete and representational models before moving to abstract representations. When planning instruction, teachers should consider how to sequence the learning to support moving from concrete representations to the symbolic and abstract. Visual representations of the mathematics are critical in laying a strong foundation of mathematical ideas. Students need experience using concrete manipulatives and then moving to representational models to solidify the use of imagery in problem solving before moving to abstract symbols. The connections students make throughout these stages are essential and should be an intentional
design of any lesson.

The first stage is the concrete stage in which students experience math by physically manipulating various objects. The second stage engages students in using representational models to solve math. During this stage, students represent concrete objects as pictures or drawings. Using abstract symbols is the third stage.
Instructional practices should support students moving from the concrete and representational stages to using numbers and symbols to model and solve math problems. Students need opportunities to develop mathematical thinking at each stage and to make connections between the stages to develop the ability to move flexibly among the different representations.

Mathematically Productive Instructional Routines

Productive Instructional Routines (MPIRs) are high leverage instructional routines that focus on student ideas as central to the learning, make student thinking visible, and provide opportunities for mathematical discourse thereby allowing opportunities for students to make sense of mathematics in their own way. Consistently engaging students in these routines can change student’s dispositions about mathematics, support shifts in instructional practice, and deepen mathematical content knowledge and a growth mindset for both students and teachers.

They are routine. MPIRs are brief and used frequently. Students and teachers engage in these activities often enough that the routine itself is learned and can be engaged in quickly and meaningfully. The predictable structure creates a safe time and space for students to take risks and explore and share their ideas.

They are instructional. While classrooms also rely on routines designed to manage student behavior, transitions, and supplies, MPIRs are routines that focus on student learning. MPIRs provide an opportunity for students to share their mathematical ideas and make connections and deepen their understanding of math concepts as they listen and respond to other students. Routines also provide an opportunity for the teacher to formatively assess students.

They are mathematically productive. Prompts for each MPIR are carefully chosen to opportunities for students to enact the Standards for Mathematical Practice. Student discussions highlight central mathematical ideas. Students gain important insights and develop positive dispositions about engaging in mathematics through their participation in MPIRs.

Number Talks

Number Talks are an example of a mathematically productive instructional routine that can support the development of a classroom culture in which students feel encouraged to share their thinking, and teachers become skilled at listening to their students’ thinking. This short mental mathematics routine can be used daily with any curricular materials to promote number fluency as well as develop conceptual understanding of numbers and operations.

flexible and conceptual nature of mathematics (Boaler, 2015).

Number Talks help students become confident mathematical thinkers more effectively than any single instructional practice we have ever used.… With Number Talks, students start to believe in themselves mathematically. They become more willing to persevere when solving complex problems. They become more confident when they realize that they have ideas worth listening to. And when students feel this way, the culture of a class can be transformed.

Number Talks Webinars for OSPI, Watch a recorded one hour webinar.

a 15-minute video about Number Talks that gives a full description of the practice and shares examples to help schools get started with Number Talks in every classroom.

Boaler, J. (2015). Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. John Wiley & Sons.
Hiebert, J., & Morris, A. K. (2012). Teaching, rather than teachers, as a path toward improving classroom instruction. Journal of Teacher Education, 63(2), 92–102.
Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. (2010). Using designed instructional activities to enable novices to manage ambitious mathematics teaching. In Instructional explanations in the disciplines (pp. 129–141). Springer US.
Humphreys, C., & Parker, R. (2015). Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4–10. Stenhouse Publishers