Beyond teacher egocentrism: design thinking As teachers we understandably believe that it is the ‘teaching’ that causes learning. But this is too egocentric a formulation. As I said in my previous post, the learner’s attempts to learn causes all learning. From this viewpoint, the teacher is merely one resource for learning, no different from a book, a peer, an experience, or an experimental result. Put in terms of a phrase that many now use, in and out of education, such a viewpoint reflects design thinking. I know this sounds a bit unromantic. The learning is the center of our world, not the teaching. What all good designs have in common. What are those conditions, in a nutshell? The key ideas here are self-sustaining, challenging and productive work, where learners themselves become and feel more competent in transferring their learning with ever-increasing autonomy. In other words, it is a poor design for learning that puts all the burden of teaching and processing on the teacher. Group-worthy tasks – Like this: Like Loading...
Articles For Educators - Lesson Plans and Activities Overview | LMR - Development Site Learning Mathematics through Representations (LMR) is a research-based curriculum unit for the teaching and learning of integers and fractions in the elementary grades, using the number line as the principal representational context. The curriculum builds on two core ideas: mathematical representations are fundamental to mathematical communication and learning, and curriculum units should be designed as well-orchestrated lesson sequences that support insight and understanding of representational forms. The members of the LMR staff bring expertise in developmental and educational research, curriculum development, pre-service education and professional development, and elementary classroom teaching. The LMR team is led by Geoffrey B. Use the menus above to explore the following links: Research & Dev: Provides background information and the design principles, which guided the development of the LMR curriculum.Curriculum: Offers various ways of exploring and downloading the LMR curriculum.
Multiplication Games Get ready to play some fun and interactive multiplication games! On this page we have a variety of games that kids will enjoy while building strong math skills. Whether students are learning the good old boring times-tables or even multiplying fractions or integers; we have some fun games for them on our website. Are you tired of boring multiplication drills? Try playing these fun games instead! Multiply Numbers Ending in Zeroes (New) Earn points by multiplying numbers ending in zeroes to discover the hidden treasure. Multiplication Game In this fast-paced car racing game, 2nd and 3rd grade students will practice multiplying one-digit numbers. Basketball Multiplication Game Kids will have a lot of fun playing this interactive basketball game, but they will also practice multiplying one-digit whole numbers. Multiplication as Repeated Addition In this math racing game 3rd grade students will learn to view multiplication problems as repeated addition problems. Properties of Multiplication
* Math Struggles 401: Instructional timing and confusion | Teachezwell Blog Brain-based research gives us a clearer picture of the optimal times for learning new content. According to Sousa in his book, How The Brain Learns Mathematics, there are two “best” times for learning: at the beginning of a lesson and and the end. Using a 40 minute lesson as a model, he explains that the brain’s capacity to download and retain new information declines in the middle of that lesson. This model of learning also makes plain sense. Kids’ brains (like that of adults) have a limited capacity to maintain attention and absorb and apply new information. After a “high” point of acquiring information and a relative period of reduced retention, there is another maximum learning opportunity in the last portion of the lesson (these times are approximate, of course). How does this affect special needs kids who are struggling in math? As Sousa points out, “unlearning and relearning that process correctly is very difficult…. There is hope. Like this: Like Loading... Related In "Math"
Johnnie's Math Page - The Best Math for Kids and their Teachers -Hundreds of Interactive Math Tools, Math Activities, and Math Games Johnnie's Math Page is the site to find fun math for kids, math games, and even a little math homework help. Interactive math activities from across the web have been organized by topic to make math learning enjoyable and interesting. These activities have been chosen to represent the range of math learned from kindergarten to middle school. I have put together resources for middle school math. In the middle school math section you will find fantastic models for all kinds of algebra- from linear equations to quadratics. For parents and teachers, you will find math lessons and free math worksheets as well as links to other math teaching resources. For those who like a challenge, you will find free math games in the math puzzles section. Contact Johnnie
A veteran teacher turned coach shadows 2 students for 2 days – a sobering lesson learned The following account comes from a veteran HS teacher who just became a Coach in her building. Because her experience is so vivid and sobering I have kept her identity anonymous. But nothing she describes is any different than my own experience in sitting in HS classes for long periods of time. I have made a terrible mistake. I waited fourteen years to do something that I should have done my first year of teaching: shadow a student for a day. This is the first year I am working in a school but not teaching my own classes; I am the High School Learning Coach, a new position for the school this year. As part of getting my feet wet, my principal suggested I “be” a student for two days: I was to shadow and complete all the work of a 10th grade student on one day and to do the same for a 12th grade student on another day. My class schedules for the day(Note: we have a block schedule; not all classes meet each day): The schedule that day for the 10th grade student: 7:45 – 9:15: Geometry Wow.
Scientists Discover 15th Convex Pentagon Able To Tile A Plane Consider the ceramic on the floor beneath you. Those squares or rectangles tile the plane. That's a mathematical term, and finding a new shape that covers a flat surface using only exact copies of that one shape without overlapping or leaving any gaps is a mathematical challenge. All triangles can tile the plane, all quadrangles, too. Welcome back to the program. JULIE REHMEYER: It's my pleasure, Robert, happy to talk to you. SIEGEL: How big a deal this is? REHMEYER: It's exciting. SIEGEL: Who found this new pentagon? REHMEYER: Three mathematicians at the University of Washington - Casey Mann, Jennifer McLoud and David Von Derau. SIEGEL: And there have been many searches for these geometric shapes over the decades? REHMEYER: There have. SIEGEL: I'm looking at a representation of a plane that's been filled with this particular pentagon with identical copies of it, and it's odd to describe. REHMEYER: That's a great description. REHMEYER: That's right. SIEGEL: I'm thinking ahead to hexagons.
Research shows how children can enjoy and succeed in math, Stanford expert says Stanford Report, December 17, 2015 Stanford Professor Jo Boaler says that research findings show how all students can learn to enjoy math and achieve at high levels without suffering from fear or failure. By Clifton B. Parker Aaron Kehoe Education Professor Jo Boaler (center) observes the work of her students in the Stanford Teacher Education Program. For many students, math class is the subject of nightmares. "All children are different in their mathematical thinking, strengths and interests," said Jo Boaler, a professor of mathematics education at Stanford Graduate School of Education. Boaler has studied how students learn math, to identify why so many students end up hating or fearing math, and, too often, underachieve. In her new book, Mathematical Mindsets, Boaler describes how society has traditionally valued one type of math learner – one who can memorize well and calculate fast – as opposed to others who have the same potential but may be deeper, slower and more creative.
Weapons of maths destruction: are calculators killing our ability to work it out in our head? Since the 1980s we have had access to calculators of various types. Today, we can include computers and smartphones – which are attached to our hip 24/7. So does this ubiquitous access to calculators affect our ability to do maths in our heads like we used to? Thirty years ago calculators promised immense opportunity – opportunity, alas, that brought considerable controversy. The sceptics predicted students would not be able to compute even simple calculations mentally or on paper. Multiplication, basic facts, knowledge would disappear. The controversy has not dissipated over time. Research conducted in response to this found little difference in performance tests whether students used calculators or not. Researchers recommended moving the conversation on. Using calculators to extend maths Teachers had high hopes that calculators would be used in enhancing and extending the learning of mathematics. Multiplication tables are no longer limited to 12 x 12.
The Math Forum at NCTM The Problems of the Week Program The Math Forum offers an integrated program based on our award-winning Problems of the Week. The program has three components: Problems of the Week (PoWs) and Write Math: PoWs by Standard, including teacher support materials.Problem Solving and Communication Activity Series, focused on strategic competence and writing fluency.Professional Development for effective implementation, formative assessment, and building mathematical knowledge for teaching. Do the problems with your students, use the Activity Series to develop student confidence and higher order thinking skills, and collaborate with leading experts and fellow teachers through our professional development programs. Problems of the Week Problems of the Week (PoWs) are inventive, engaging challenges designed to get your students thinking, talking, and doing mathematics. Each Current PoW (and many problems in the Problems Library) comes with supplemental materials, including: Professional Development
By opposing tracking well-meaning educators are hurting disadvantaged kids Twenty years of classroom instruction experience has taught me that classes with diverse academic abilities present one of the most difficult teaching challenges. Typically, one is forced to focus on only a sub-group of students, usually the second quartile. As a consequence the lower and higher quartiles are not properly served. At the university level, we minimize this problem by offering different levels: remedial math versus math for engineers, probability for the Masters program versus probability for PhD students, co-ed intramural sports versus the varsity basketball team, intro to World Music versus a spot in the orchestra, etc. Unfortunately, there has been a trend recently to move away from tracking and several school districts now forbid it. [t]he number of Hispanic students [in the advanced track increased] by 130 percent and the number of black students by 80 percent. (Click to enlarge).
The need to catalyze change in high school mathematics - kappanonline.org The high school mathematics curriculum needs to be reformed to encourage all students to understand the math that underlies the fabric of society. High school mathematics is not working for far too many students in the United States. Although the National Assessment of Educational Progress (NAEP) has shown significant and long-term positive trends in mathematics learning at the elementary and middle levels, high school NAEP scores have remained essentially flat for decades (National Center for Education Statistics, 2015, 2016). In addition, the Program for International Student Assessment shows that U.S. high school students trail their international peers in mathematical literacy, defined as the “capacity to formulate, employ, and interpret mathematics in a variety of contexts . . . to describe, explain, and predict phenomena” (Organization for Economic Cooperation and Development, 2016, p. 28). Why learn mathematics? The need for equal access Improving instruction Next steps References St.
The High School Mathematics Curriculum—What Can We Learn from History? Over the years, the journals of the National Council of Teachers of Mathematics (NCTM) have published numerous articles on the history of mathematics and its use in teaching. These journals have included Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Mathematics Teacher, each of which was published through May 2019. In January 2020, these three journals were replaced by NCTM's new practitioner journal, Mathematics Teacher: Learning & Teaching PK–12 (MTLT). Thanks to the efforts of Convergence founding co-editor Frank Swetz, NCTM has allowed Convergence to republish (in pdf format) up to two articles from Mathematics Teacher annually since 2015. One of the editors’ picks for 2022 is an article by Robert Reys and Barbara Reys, in which they reviewed several of the major programs for reform in American mathematics education that appeared between 1894 and 2010: The authors recently reflected on what they learned while preparing this article: About the Authors