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.
The Flipped Classroom Model: A Full Picture Due to Khan Academy’s popularity, the idea of the flipped classroom has gained press and credibility within education circles. Briefly, the Flipped Classroom as described by Jonathan Martin is: Flip your instruction so that students watch and listen to your lectures… for homework, and then use your precious class-time for what previously, often, was done in homework: tackling difficult problems, working in groups, researching, collaborating, crafting and creating. Classrooms become laboratories or studios, and yet content delivery is preserved. Flip your instruction so that students watch and listen to your lectures… for homework, and then use your precious class-time for what previously, often, was done in homework: tackling difficult problems, working in groups, researching, collaborating, crafting and creating. A compiled resource page of the Flipped Classroom (with videos and links) can be found at The Flipped Classroom Model Summary
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!
Math_Johnson: My wife's first #flipclass... L'interdisciplinarité: un enjeu réaliste? | Mon cahier d'écolier Le débat Dépasser le débat Parmi les points d’achoppement de la la réforme du collège, l’on trouve cette fameuse interdisciplinarité sur laquelle s’opposent en gros – encore une fois – les “Républicains” (pas ceux de Nicolas) et les “Pédagogues”. Pour les seconds, souvent issus du mouvement socio-constructiviste, l’apprentissage est synonyme d’appropriation des connaissances par les élèves. Depuis des décennies, ces deux groupes se heurtent, s’invectivent, s’accusent des pires maux (nivellement par le bas, élitisme,…) et s’enlisent dans un débat peu constructif, mais très médiatique. L’interdisciplinarité: kezako? L’interdisciplinarité n’est pas une lubie de notre Ministre de l’Éducation Nationale qui se serait dit un beau matin: “et si j’inventais un truc moderne pour embêter les profs”. L’interdisciplinarité a trois objectifs: Mais pour cela, certaines conditions sont à réunir: le projet doit être soigneusement préparé et planifié. L’interdisciplinarité: est-ce que cela va marcher?
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]
Edcamp Leadership: Flipping the Faculty Meeting | Apace of Change Edcamp Leadership marked my entrance into the world of Edcamps this month, both as an attendee and an organizer. I have known most of the key players in the Edcamp Foundation for many years through traveling in the same educational circles in social media, so knowing the kinds of educators they are, it really didn’t surprise me that a) I had a blast, and b) so many attendees enjoyed it as well. I suppose the true measure of how effective it was or was not will be determined by which of the many ideas discussed actually get implemented and lead to some improvement in the attendee’s schools. In the meantime, however, what I want to record here are my thoughts on the organizational process, the session I ran that morning, and some general overall takeaways from the day. Although I specifically asked about obstacles to flipping faculty meetings, most participants only brought them up along with ideas for how to get around them.
Math inversées - Introduction 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.