Mangahigh.com - Play maths, love maths Experimenting with the Mastery Flip.. In the fall of 2011, I piloted 1 class with the flip classroom. In January of 2012, I decided to roll it out with all four sections of 8th grade science and not only that (at this point, I must have lost my mind), I decided to try to the mastery flip technique. I am not going to lie, I spent most if not all of my Christmas break in 2011 assembling the pieces of trial run. Since my school district is not 1 to 1, I had to be creative and design a way that could work for my classroom. I was able to sign a laptop cart out for every Monday and Friday during the course of the unit. On the Friday, students chose how they wanted to demonstrate what they understood from the week. The mastery project was something students would continually come back to throughout the course of the unit and use it to extend their learning around a singular topic area that they would keep stretching and learning about. However, it wasn't all roses.
¿Le damos la vuelta al aula…? The Flipped Classroom Seguro que has leído en algún artículo, o en algún tweet, la expresión Flipped Classroom, que atendiendo a la traducción literal sería algo así como la clase del revés. Bueno, lo que nos faltaba …poner a los alumnos boca abajo y que en ese momento llegara el mismísimo Inspector Zito The Flipped Classroom es un modelo de trabajo en el aula con el que están experimentando algunos docentes. Si bajo la estructura tradicional el tiempo que estamos en el aula, especialmente en los niveles superiores de secundaria y en enseñanza superior, se dedica a explicar la materia y acercar al alumnado a las ideas fundamentales de cada unidad didáctica, mientras que las tareas se hacen en casa, bajo la estructura que propone la ‘clase del revés’, es precisamente al contrario: en casa los estudiantes acceden a los contenidos mientras que las tareas se desarrollan en el aula. Los docentes tienen más tiempo en el aula para trabajar con cada estudiante, conocer mejor sus necesidades y sus avances. 1. 2. 3. 4.
Music Math Harmony -- Math Fun Facts It is a remarkable(!) coincidence that 27/12 is very close to 3/2. Why? Harmony occurs in music when two pitches vibrate at frequencies in small integer ratios. For instance, the notes of middle C and high C sound good together (concordant) because the latter has TWICE the frequency of the former. Well, almost! In the 16th century the popular method for tuning a piano was to a just-toned scale. So, the equal-tempered scale (in common use today), popularized by Bach, sets out to "even out" the badness by making the frequency ratios the same between all 12 notes of the chromatic scale (the white and the black keys on a piano). So to divide the ratio 2:1 from high C to middle C into 12 equal parts, we need to make the ratios between successive note frequencies 21/12:1. What a harmonious coincidence! The Math Behind the Fact: It is possible that our octave might be divided into something other than 12 equal parts if the above coincidence were not true!
Engage All Levels of Education You want to use digital learning in your classroom, but how do you start? Today's educational climate puts an increasing emphasis on incorporating technology into student learning, including everyday projects, lessons, skill sets, and online assessments. Watch the recorded presentations, below, from your favorite flipping pioneers at ISTE 2013. Get Education Pricing Try TechSmith tools free for 30-days and save big with education pricing! Learn More >> Learn More about Flipping Use technology to flip your classroom and create the engaging learning environment you've always wanted. Learn More >> Dr. Graham Johnson, Okanagan Mission Secondary Steve Kelly, St. Lori Hochstetler, Northridge Middle School Rob Zdrojewski, Amherst Central Schools Kristin Daniels, Stillwater Area Public Schools Brian Bennett, TechSmith
Odd Numbers in Pascal's Triangle -- Math Fun Facts Pascal's Triangle has many surprising patterns and properties. For instance, we can ask: "how many odd numbers are in row N of Pascal's Triangle?" For rows 0, 1, ..., 20, we count: row N: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 odd #s: 1 2 2 4 2 4 4 8 2 4 04 08 04 08 08 16 02 04 04 08 04 It appears the answer is always a power of 2. THEOREM: The number of odd entries in row N of Pascal's Triangle is 2 raised to the number of 1's in the binary expansion of N. Presentation Suggestions: Prior to the class, have the students try to discover the pattern for themselves, either in HW or in group investigation. The Math Behind the Fact: Our proof makes use of the binomial theorem and modular arithmetic. (1+x)N = SUMk=0 to N (N CHOOSE k) xk. If we reduce the coefficients mod 2, then it's easy to show by induction on N that for N >= 0, (1+x)2^N = (1+x2^N) [mod 2]. Thus: (1+x)10 = (1+x)8 (1+x)2 = (1+x8)(1+x2) = 1 + x2 + x8 + x10 [mod 2]. (1+x)11 = (1+x8)(1+x2)(1+x1) [mod 2]
Flipped Classroom A New Learning Revolution There has been a growing buzz around a recently coined phrase " Flipped Classroom". This term starts to take root in education as more and more educators are discovering it. So what is this all about and what are its advantages in learning and teaching? Flipped Classroom is an inverted method of instruction where teaching and learning take place online outside of the class while homework is done in the classroom. Flipped Classroom shifts the learning responsibility and ownership from the teacher's hands into the students'. Flipped Classroom depends a lot on educational technology and web 2.0 tools such as podcasting and screencasting applications. "In most Flipped Classrooms, there is an active and intentional transfer of some of the information delivery to outside of the classroom with the goal of freeing up time to make better use of the face-to-face interaction in school. A direct and concrete example of Flipped Classroom concept is the popular Khan Academy.
Sums of Two Squares Ways -- Math Fun Facts In the Fun Fact Sums of Two Squares, we've seen which numbers can be written as the sum of two squares. For instance, 11 cannot, but 13 can (as 32+22). A related question, with a surprising answer, is: on average, how many ways can a number can be written as the sum of two squares? We should clarify what we mean by average. So if A(N) is the average of the numbers W(1), W(2), ..., W(N), then A(N) is the average number of ways the first N numbers can be written as the sum of two squares. A surprising fact is that this limit exists, and it is Pi! Presentation Suggestions: This might be presented after a discussion of lattice points in Pick's Theorem. The Math Behind the Fact: The proof is as neat as the result! Therefore, the sum of W(1) through W(N) counts the number of lattice points in the plane inside or on a circle of radius Sqrt(N) (except for the origin), and the average A(N) is this number of lattice points divided by N. How to Cite this Page: Su, Francis E., et al.
Using Flipped Learning in the College Classroom | Developmental Reading & Writing As the instructional specialist in the Learning Center at Robeson Community College, I was asked to develop a workshop for faculty. I chose to offer this professional development opportunity on Flipped Learning. I did so in part because I was using flipped lessons out of necessity in my own class. Most community colleges are leaning towards blending reading and writing classes into one class. Flipping a classroom is becoming increasingly popular in many academic arenas from primary school to university. By flipping the class, also called Flipped Learning, the instructor provides students with lesson content (lecture) before class and uses class time to practice concepts (do homework). If you’d like to know how Flipped Learning started, here is a good video from 60 minutes interviewing the originator of flipped learning and showing a flipped classroom in action. 60 minutes video on YouTube 13:27 minutes Advantages of Flipping a Lesson Resources How’s it Going?
A Random Math Fun Fact! From the Fun Fact files, here is a Random Fun Fact, at the Advanced level: The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the divisibility of the integers. (It is often covered in calculus courses and begins by assuming Sqrt[2]=x/y where x/y is in smallest terms, then concludes that both x and y are even, a contradiction. See the Hardy and Wright reference.) But the proof we're about to see (from the Landau reference) requires only an understanding of the ordering of the real numbers! Proof. So, suppose Sqrt[2]=x/y, that is, x2 = 2y2; then we show x1 = 2y - x, y1 = x - y works. x/y = (2y - x) / (x - y). So x1/y1 yields the same fraction as x/y. Secondly, it must be the case that 0 < y1 < y, because this is the same as y < x < 2y, which is equivalent to 1 < (x/y) < 2. Thus we have found an equivalent fraction with smaller denominator, giving the desired contradiction. (x/y) = (Ny - kx) / (x - ky)