Math 2.0: Teaching Math in a Technical World

1. Fostering Conceptual Understanding Through Reading-Math ConnectionsAntony T. SmithRobin AngottiUniversity of Washington Bothell

2. Math 2.0: Teaching Math in a Technical World 3 Identified Aspects of Math Instruction • Content: Algebra as a gatekeeper for access to higher education (Rand, 2002), functions, data and graphical analysis, and mathematical modeling • Pedagogy: Student motivation and alienation to standard instructional practices (National Research Council, NRC, 2003) • Technology: Unfulfilled promise of technology integration in mathematics education (Cuban, 2001)

3. Essential Question • How does technology change the way we teach and learn math? • But what does this have to do with the reading/math connection???????

4. Context and Demographics • Rural Eastern Washington

5. Context and Demographics Rural Eastern Washington • Geographic Separation • School Size • Multiple Subject Areas • Inequitable Resources • Large population of students of low socio-economic status • Large population of migrant families

6. English Language Learners • Challenges • Without vocabulary and language skills to participate fully in traditional math curricula • Disproportionately high numbers not meeting proficiency standards • Goal • To foster mathematics related communication and language development of ELL students

7. Reading-Math Connection Question: • In what ways may students’ understanding of mathematical concepts be enhanced by teacher instruction and student use of cognitive reading strategies targeted to help students make sense of complex mathematical texts?

8. Content-Area Literacy • Recognize language as a medium of teaching and learning mathematics (Rubenstein, 2007) • Focus on assisting students in acquiring skills necessary to negotiate content-area texts (Draper, Smith, Hall, & Hiebert, 2005) • Utilize reading and writing as ways to facilitate deeper understanding of concepts (Fisher & Ivey, 2005) • Avoid the assumption students understand just because they can read the words (Routman, 2003)

9. Activity: Thinking Through an Algebra Lesson • Cognitive Strategy: Asking questions while reading and trying to answer them • Mode of Instruction: Think-aloud

11. Cognitive Strategy Instruction • Cognitive strategies are constructive interactions with texts both written and digital in which good readers and writers continuously create meaning (Pressley, 2006) • “What is needed is an emphasis on particular strategies that are closely aligned with the way historians or scientists or mathematicians read and the manner in which students should approach texts in order to foster conceptual understanding of content-related materials” (Shanahan & Shanahan, 2008, p. 13)

12. Cognitive Strategy Instruction Strategies • Monitoring comprehension while reading • Noticing text structure features and patterns (including vocabulary) • Asking questions while reading and trying to answer them Modes of Instruction • Think-aloud • Whole group lessons • Small group guided practice • Small group and individual application

13. Cognitive Strategy Instruction and Vocabulary How do students learn new words? • Connections between new and known • Word repetition in meaningful contexts • Opportunities for deeper processing of word meaning • Active use of newly learned words • Explicit instruction on word-learning strategies Vocabulary strategies and activities to consider • Read alouds • Word cards • Word wall dictionary • Vocabulary journals • Vocabulary self-collection • Dictionary use

14. Reading-Math Connections: Emerging Themes • Instruction • Thinking aloud is a powerful means of introducing mathematics texts, ideas, and vocabulary to students and of helping students deepen their understanding of mathematical concepts • Strategies • Drawing attention to features of nonfiction text helps students become aware of and utilize these features to better understand mathematical concepts in mathematics textbooks • The strategy of asking questions while reading and trying to answer them helps foster cognitive thinking among students, so that confusions are noted and connections to existing knowledge are made

15. Reading-Math Connections: Emerging Themes • Vocabulary • Mathematics vocabulary is important and distinct, needing to be explicitly taught and applied throughout a lesson or unit • Using existing knowledge of students, teachers need to identify key mathematics vocabulary in a lesson or unit and work with students to make sense of these terms in relation to math concepts

16. Reading-Math Connections: Vocabulary Virtual Word Wall: Numerator

17. Reading-Math Connections: Vocabulary Virtual Word Wall: Fraction

18. Reading-Math Connections: Questions How might teachers effectively address the tension between content coverage and knowledge depth? In what ways might teachers focus on conceptual understanding of math concepts within the constraints of time, curriculum, standards, and testing? What are some assessments teachers might use to assess students’ use of cognitive reading strategies to understand math concepts? Antony Smith: ansmith@uwb.edu Robin Angotti: rrider@uwb.edu