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Concrete to Abstract: Preparing Students for Formal Algebra
The document discusses strategies for teaching algebra effectively, highlighting the need for context and engagement in math education. It emphasizes the use of manipulatives, both physical and digital, to create meaningful learning experiences while encouraging students to explore and understand algebra concepts. Additionally, it promotes the importance of integrating standards for mathematical practice and offers insights into adaptive learning technologies like DreamBox Learning.
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Concrete to Abstract: Preparing Students for Formal Algebra
- 1. A Common Modelfor Elementary Classes Middle School Classes?
- 2. Elementary Class vs. Secondary Class
- 3. What is Algebra? Grant Wiggins, 2013 “Algebra, as we teach it, is a death march through endless disconnected technical tools and tips, out of context.” “Our student surveys consistently rank HS math as their least favorite course, by a wide margin – though 22% list it as their favorite. 46% don’t merely like it least: they hate it.”
- 4. Can Middle toHigh School Math become Accessible to All MSantyu stdudeentns sttasrt? struggling with math as they venture into Algebra and Calculus. But what will engage them?
- 5. Manipulatives in Math • Research supports the use of manipulatives • Students gain deep understanding by using manipulatives in their math learning. • Exploration comes to life. • Manipulatives are a means, not an end.
- 6. Concrete Manipulatives Whatdoes concrete mean? Sensory-Concrete Using materials to make sense of an idea Integrated-Concrete Built through learning (interconnected) Thinking like a mathematician, ideas are made integrated-concrete through meaning.
- 7. The Power ofDigital Manipulatives Digital materials can be just as meaningful as real objects! Concrete and Symbolic Link the concrete and symbolic with feedback and representations Cleaner No management of physical tools. More Flexible No restriction of physical objects, limits of size, scale, material. Thoughtful Assessment and Reporting Specific and fast communication to teacher and student Cleverly Restrictive Restrictions CAN be set for targeted learning
- 8. Rate of Change The long road through this “big idea” in Algebra
- 9. Checking Ourselves… Howare we avoiding the trap of “disconnected Algebra”? Are we forcing students through context-less practice? Or giving them tools to have rich conversations?
- 10. How do wecreate context and connections for Algebra? A Word Problem: An Introduction or a Conclusion? What is Context? Commonly these are used as one-off challenges to practice new skills or give context for learning a new skill.
- 11. What is Context? Models vs. Stories Look for the contexts that can be used through learning. Extend investigations over multiple lessons to explore many facets of a mathematical context. Does it have to be “real life” to be accessible?
- 12. What is Context? What does it take to be rigorous? Or perplexing? Are students challenged? Are they encouraged to be persistent and to try out their own strategies?
- 13. Critical Math Practicesusing Standards Using technology to align to the Standards of Mathematical Practice. Important to focus purposefully on the Standards for Mathematical Practice.
- 14. Quadratic Expressions Multiplicationwith Arrays & Landmarks in 4th grade Building squared bases Using the tool to create an array to represent the expression
- 15. Tips for DevelopingLessons Strategies for making engaging, connected experiences, either in the class, or on desktop. 1. Think big picture. 2. Use research. 3. Collaborate.
- 16. DreamBox Learning K-8Math Intelligent Adaptive Learning™ Engine • Millions of personalized learning paths • Tailored to a student’s unique needs Motivating Learning Environments • Student Directed, Empowering • Leverages Gaming Protocols Rigorous Mathematics Curriculum • Reporting Aligned to CCSS, Texas TEKS, Virginia SOL, Canada WNCP, & Canada Ontario Curriculum Reports • Standards for Mathematical Practice Seeing is believing! dreambox.com/request-a-demo
- 17. DreamBox Lessons &Virtual Manipulatives Intelligently adapt & individualize to: • Students’ own intuitive strategies • Kinds of mistakes • Efficiency of strategy • Scaffolding needed • Response time
- 18.
- 19. Strong Support forDifferentiation
- 20. FREE Interactive WhiteboardLessons DreamBox supports small group and whole class instructional resources. www.dreambox.com/teachertools
- 21. We value yourfeedback, compliments, suggestions, and complaints! Let us know how we’re doing: https://www.surveymonkey.com/s/MD8J6Z7 Also, join us for a 15 minute Tweet-Up Session immediately following this webinar: #edwebchat
Editor's Notes
- #6Â Research suggests to start with concrete manipulatives Manipulatives do not encompass the mathematical idea, however students gain deep understanding by using manipulatives in their math learning. Are a means, not an end.
- #8Â Digital materials can be just as meaningful as real objects. Manageable, clean manipulatives Flexibility Extensible Link the concrete and symbolic with feedback, can link multiple representations Build scaffolding Encourage problem solving and conjectures Focus and motivation
- #9Â Rate of Change: Answer_LevelFive Answer_LevelSix Answer_LevelNine Locate_LevelTwo
- #17 DreamBox Learning provides a new class of intelligent adaptive learning technology is the true game changer in education. Combines 3 essential elements 1) Rigorous K-8 Mathematics – DreamBox uses virtual manipulatives that enable students to build conceptual understanding and procedural fluency. Provided standards-based reporting. 2) Motivating Learning Environments that are age-appropriate and motives learners to persist and progress. 3) Powerful Intelligent Adaptive Learning engine providing millions of personalized, student-driven learning paths—each one—tailored to a student’s unique needs.