As secondary math teachers, we're often frustrated by the lack of true number sense in our students. Solid research at the elementary level shows how to help all students become mathematically proficient by redefining what it means to compute with number sense. Pam Harris has spent the past ten years scrutinizing the research and using the resulting reform materials with teachers and students, seeing what works and what doesn't work, always with an eye to success in higher math. This book brings these insights to the secondary world, with an emphasis on one powerful goal: building numeracy.--Page [4] of cover
Building Powerful Numeracy for Middle and High School Students brought the world of research on numeracy at the elementary level to the secondary level, helping teachers build numeracy in their students and showing how that work supports students in understanding higher math. Now, Pam Harris continues her work by offering lessons and activities that promote her strategies for teaching as much mathematics as possible with as little memorization as possible. Two types of activities for building numeracy are included in this workbook: Student Workouts include reproducible worksheets that students can work on independently or in pairs, followed by robust class discussion to promote understanding of the ideas. Teacher Directed Activities are whole-class mini-lessons designed to help students construct numerical relationships as they work with the teacher. While the student workouts provide starting points for students to build important numerical relationships and choose effective strategies, the teacher directed activities provide opportunities for discussing, comparing, modeling, verbalizing strategies, finding and describing patterns, and making generalizations. Together they help develop the mathematical habits of mind that students need for higher math.
A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.
Classroom intervention strategies to build confidence and competenceBuilding Numeracy has been designed to assist all teachers, at all levels, to develop expertise and confidence in diagnosing student difficulties.This book uses evidence-based, peer-reviewed intervention strategies that help teachers to:understand how mathematical concepts and processes are constructed and connectedovercome mathematical misconceptions and inappropriate ways of thinkingplan and implement appropriate intervention programs to build students' competence and confidence.In addition to the numeration, addition, subtraction, multiplication, division and fractions screening tests from the first edition of Building Numeracy, this second edition also includes an early number screening interview and problem solving tests.Building Numeracy is an Oxford Teacher Reference title.The Oxford Teacher Reference series supports educators with high-quality professional resources to help deliver the best educational outcomes in primary and secondary mathematics. Led by research and written by experts in the field, this suite of stand-alone teacher reference titles offers comprehensive support across all areas of mathematics.Oxford Teacher Reference titles are fully aligned with the Australian Curriculum: Mathematics and are supported by complimentary digital resources available online through Oxford Owl.
Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts.
Includes teaching scenarios modeling the crossover of literacy and math strategies, and provides techniques to strengthen students' grasp of foundational concepts and advance their skills in reasoning and problem solving.
The key to good primary teaching of numeracy and mathematics is confidence in mathematical knowledge and its relevance to the real world. In particular, effective implementation of the National Numeracy Strategy requires student teachers, primary teachers and mathematics coordinators to realize the place of mathematics across the range of National Curriculum subjects. This book explores mathematics as a set of tools for thinking about, designing, evaluating and changing the world of the child through the broader curriculum, rather than focusing on skills and concept building exclusively in the 'mathematical world.' Practical activities are included to stimulate readers to apply these ideas with confidence both within and beyond the mathematics lesson.
Talking math with your child is simple and even entertaining with this better approach to shapes! Written by a celebrated math educator, this innovative inquiry encourages critical thinking and sparks memorable mathematical conversations. Children and their parents answer the same question about each set of four shapes: "Which one doesn't belong?" There's no one right answer--the important thing is to have a reason why. Kids might describe the shapes as squished, smooshed, dented, or even goofy. But when they justify their thinking, they're talking math! Winner of the Mathical Book Prize for books that inspire children to see math all around them. "This is one shape book that will both challenge readers' thinking and encourage them to think outside the box."--Kirkus Reviews, STARRED review
Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.
Do your students need more practice to develop number sense and reasoning? Are you looking to engage your students with activities that are uncomplicated, worthwhile, and doable? Have you had success with number talks but do your students crave more variety? Have you ever thought, "What can I do differently?" Swap out traditional warmup practices and captivate your elementary students with these new, innovative, and ready-to-go routines! Trusted elementary math expert John J. SanGiovanni details 20 classroom-proven practice routines to help you ignite student engagement, reinforce learning, and prepare students for the lesson ahead. Each quick and lively activity spurs mathematics discussion and provides a structure for talking about numbers, number concepts, and number sense. Designed to jump-start mathematics reasoning in any elementary classroom, the routines are: Rich with content-specific examples and extensions Modifiable to work with math content at any K-5 grade level Compatible with any textbook or core mathematics curriculum Practical, easy-to-implement, and flexible for use as a warm-up or other activity Accompanied by online slides and video demonstrations, the easy 5–10 minute routines become your go-to materials for a year’s work of daily plug-and-play short-burst reasoning and fluency instruction that reinforces learning and instills mathematics confidence in students. Students’ brains are most ready to learn in the first few minutes of math class. Give math practice routines a makeover in your classroom with these 20 meaningful and energizing warmups for learning crucial mathematics skills and concepts, and make every minute count.
