Expand Your Toolkit: Teacher Strategies for Deeper Math Learning
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The road to conceptual understanding in mathematics is difficult. Through this journey, our students are required to demonstrate this understanding at every step. With the integration of technology in the classroom, blended learning can support student growth and understanding in math. Of course, preparing students to model math concepts is problematic if teachers are struggling with the concepts themselves. Blended classrooms can provide support for both the learner and teacher. Want to learn how? In this webinar, Courtney Foreman showed you how to expand your teaching toolkit by exploring new strategies and techniques for introducing traditionally difficult mathematics concepts to your students. Explore tools to promote the following in your blended classroom: How to implement tasks that promote reasoning and problem-solving How to use and connect mathematical representations How to build procedural fluency from conceptual understanding
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Expand Your Toolkit: Teacher Strategies for Deeper Math Learning
- 1. Expand Your Toolkit: Teacher Strategies for Deeper Math Learning Courtney Foreman, Professional Development Specialist
- 2. Implement tasks that promote reasoning and problem-solving Use and connect mathematical representations Build procedural fluency from conceptual understanding 2 Strategies for Deeper Math Learning
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- 5. Deeper Learning Competencies 5 defined by The Hewlett Foundation
- 8. Integration of Technology in the Classroom Supporting your students in problem solving and critical thinking is essential to building a classroom that focuses on Deeper Learning. Strategy: Empower Students to Design Their Own Solutions * pose question to the whole class * gather formative assessment information * openly conduct justifications 8
- 9. Let’s Try ! 9 As you work on your own, consider: What mathematical ideas and strategies are you using? How might a student approach this problem?
- 10. 10 Strategy: Empower Students to Design Solutions Supporting your students in problem solving and critical thinking Formative Assessment Pathways 1. ACTIVATE students as resources for one another 2. ENGINEER classroom discussions and questions 3. PROVIDE feedback to move learners forward Student Task: Work with your table groups to create a poster Make sure your poster clearly illustrates your group’s thinking. Please be prepared to discuss your group’s poster and thinking with the entire group.
- 12. Task that promotes “doing” mathematics 12 For more info, see the characteristics of mathematical tasks at “Levels of Cognitive Demand” from Smith and Stein https://www.youcubed.org/grade/low-floor-high-ceiling/ Visit for archived low floor high ceiling tasks by grade level
- 13. Anticipating student responses 13 Anticipated likely solution paths and student misconceptions: Prepared questions to: Support students with misconceptions Advance student thinking Produce “student work” in advance containing errors and solution paths
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- 16. One Key Shift from Answer Finders to Doers of Mathematics Doing Mathematics 16 Finding the Answer
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- 18. 18 Strategy: Use Prior Knowledge to Tackle Unfamiliar Tasks Use concrete mathematical representations Make Connections Deepen Understanding “Floating Capacity”
- 19. Self-Directed Learning: students set goals, monitor progress, and reflect on their own strengths and areas of improvement. Strategy: Put Each Student in the Driver's Seat 19
- 20. 20 Reflection: What captured my attention? What is important for me tomorrow? Next week? Next school year? If I had to pick a word or phrase from today what would it be?
- 21. Questions?
- 22. DreamBox Teacher Tools for Deeper Learning • Interactive white-board teacher lessons K-8 • English and Spanish • www.dreambox.com/teachertools
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- 24. DreamBox Learning® K–8 Math Available in English & Spanish
- 25. DreamBox Lessons & Virtual Manipulatives Intelligently adapt & individualize to: • Students’ own intuitive strategies • Kinds of mistakes • Efficiency of strategy • Scaffolding needed • Response time
- 26. Insight Dashboards Tailored insights for every participant of the learning experience.
- 27. ISTE is right around the corner… Catch us at @DreamBox_Learn Seeing is believing! www.DreamBox.com/request-a-demo
- 28. We value your feedback! Let us know how we’re doing: https://www.surveymonkey.com/r/BXMMK59
Editor's Notes
- Imagine walking into your classroom, school, or district and knowing with confidence that every student is getting exactly what they need to develop the learning strategies, critical thinking skills, and reasoning abilities needed to develop a deep understanding of math.
- What is deeper learning? In classrooms where deeper learning is the focus, you find students who are motivated and challenged—who look forward to their next assignment. They apply what they have learned in one subject area to newly encountered situations in another. They can see how their classwork relates to real life. They are gaining an indispensable set of knowledge, skills, and beliefs, including: Deeper learning is simply what highly effective educators have always provided: the delivery of rich core content to students in innovative ways that allow them to learn and then apply what they have learned. Rigorous core content is at the heart of the learning process; true deeper learning is developing competencies that enable graduating high school students to be college and career ready and then make maximum use of their knowledge in life and work. The basic concepts of deeper learning are not new to education; indeed, they are routine educational practice for many accomplished individual teachers and educators and some high-performing schools. These successful practices are now being confirmed by increasing bodies of evidence underscoring the necessity for deeper learning as an integral part of the education process. Deeper learning prepares students to
- When students are developing knowledge, skills, and academic mindsets simultaneously, they learn more efficiently. They acquire and retain more academic knowledge when they are engaged, believe their studies are important, and are able to apply what they are learning in complex and meaningful ways. Trends in the economy mean that the fastest-growing jobs are those that require problem solving and critical thinking, while those that require only routine manual skills will be in decline. A 2012 report by the National Research Council concluded that deeper learning competencies—the ability to apply knowledge to new situations—are associated with better life and work outcomes.
- Help students uncover knowledge Instead of teaching scripted curriculum defined by a textbook, consider putting your teaching skills and expertise to better use during the instructional planning phase by designing Essential Questions to drive the learning. Eliminate the front of the classroom To fully engage students in the learning process; the focus of instruction must shift from the teacher in front of the classroom to the actively engaged student. The teacher’s role must shift from one who delivers content to one who facilitates learning, or serves as a guide on the side. This type of classroom is a busy, noisy and productive place Encourage collaboration Promote real world learning experiences and help students develop 21st century skills by encouraging collaboration. Let them discuss, present ideas, consider points of view and make decisions in order to increase their stakes in their own learning. Informally assess students Make good use of the time you spend with students every day as a facilitator of learning by taking advantage of opportunities for informal assessment, and then pull together groups for re-teaching and challenge. In addition to observations and conversations in class, an online learning platform can provide students with 24/7 access to digital tools to connect with teachers and classmates for guidance and feedback.
- In addition to personalized skill building, tools and schools that promote deeper learning, a third set of emerging benefits of technology is the freedom to learn anything: anywhere, anytime. Improved access to quality content and great teachers is making a difference with Blended Learning Blended learning—the method of using multiple media and methods to teach—has been around for decades. Only recently, however, has it come to mean combining face-to-face learning with technology-based learning. Blended learning has evolved significantly in the last 20 years, and with increasing pressure on schools to ensure that all students achieve higher standards of learning with fewer resources, it has never been more important. Online and face-to-face interaction is a powerful combination that makes the most of every moment for both student and instructor. Blended learning can help ensure that every elementary school student receives the education—and specifically the foundational math understanding—to succeed both now and in the future in increasingly competitive domestic and international environments. -
- pose the question to the whole class rather than tackle it alone by asking students to research, gather information, and collectively draw conclusions. These inquiries culminated in engaging, fun, and creative responses.
- Chat box place your “smaller array” to start off with? What is the big idea behind your strategies?
- Take to your grade level instructional meetings. Scaffold the efficiency of strategies
- “low floor high ceiling” Imagine a room. The way in is unproblematic - a few small steps and you're in. Once inside there are lots of possibilities for activity, many of them unproblematic too, others more challenging. In fact the only limit on your choice of activity is the space in the room, and the height to which you can rise. A mathematical activity is one which pretty well everyone in the group can begin, and then work on at their own level of engagement, but which has lots of possibilities for the participants to do much more challenging mathematics.
- Favorite – prework , to take a question and have all teachers answer and discuss
- The iceberg diagram illustrates the importance of effort spent on the conceptual development of mathematical concepts. Students spend time inventing and using pre-formal and informal strategies as they stimulate prior knowledge, make connections, deepen their understanding, and develop the “floating capacity” necessary for them to use and apply formal notations and strategies. If students are asked to grapple with, represent, and justify their own thinking and reasoning, they develop a deeper understanding of the concepts and become better problem-solvers.
- Focus on the one sentence -
- CONNECT TO IDEAS YOU KNOW
- Activate Relationship between Vertical documents Math PLC’s
- Learning to Self-Monitor Providing my students with the tools to correctly monitor their outlined goals was an important part of their self-directed and Deeper Learning experience. Self-monitoring academic progress goes deeper than simply knowing scores on quizzes and assignments. Students must be responsible for linking back to their established goals and use evidence from their assignments, assessments, and class work to form valuable insights. To help bookmark their successes, my students used a math journal to make graphs about their individualized progress based on the class's overall learning targets and their own personalized goals. Taking Time to Reflect Finally, I believe students' self-reflection, which is greatly undervalued, is the most impactful piece of the Deeper Learning process. I provided time for this activity by shutting down the classroom so that my students could produce a plan of action by thinking about their goals or life skills, and then asking questions
- DreamBox Learning provides a new class of intelligent adaptive learning technology the true game changer in education. Combines 3 essential elements Think differently about math. DreamBox Learning creates transformative learning experiences because it ... Adapts differently Our innovative DreamBox platform goes beyond what a student gets right and wrong, and captures every decision a student makes as they solve a math problem. Using this formative data, DreamBox adjusts within and between lessons to the student’s level of readiness. Millions of individualized learning paths are delivered, each one with support and scaffolds tailored to each students’ unique needs. Delivers deeper learning Offering depth and rigor required by the standards in Grades K–8, DreamBox students build core foundational skills as they develop the conceptual understanding required to be successful in higher learning. Engages students every step of the way Our game-like environment is motivating and engaging. In every DreamBox lesson, students actively engage with manipulatives that connect students to math in ways that paper and pencil never could, by exploring—making connections and sense of math. We’re passionate that every child should have access to a learning experience that motivates them persist, progress, and achieve success for a lifelong confidence in math and in life.
- Identify learning trends, gaps, and growth The Insight Dashboards bring your data into focus so you can get the answers needed to drive instructional decisions. Know at a glance if students are mastering the standards, where learning gaps exist, and where you need to focus your intervention efforts. Role-based views provide data across a grade, class, school, or entire district so you get a complete picture of student progress and proficiency.