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### Josh Fisherowner

General Discussion - *The Learning Scientists are a group of US education academics that aim to increase evidence-based practice in schools. In the second installment of a series of blogs for TES USA, an assistant professor makes the case for testing and lists five key benefits of getting students to recall information.*

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### Josh Fisherowner

Measurement - A very common way of teaching students the reasoning behind the formula for the area of a non-rectangular parallelogram is to demonstrate how to take apart such a parallelogram and turn it into a rectangle. Some U.S. states' ...

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Paul Hartzer

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Squares, in turn, are a special kind of rectangle, but all rectangles can be broken into squares.

My personal crusade is on units, and that's why squares matter. In geometry, there are four basic kinds of units: Rotation, length, area, and volume. Squares and cubes are uniquely flexible in fully packing spaces with regular shapes, so it makes sense to use them (regular hexagons and triangles can also tessellate a plane, of course, but the cube is the only regular polyhedron that can tessellate space [http://mathworld.wolfram.com/Space-FillingPolyhedron.html]).

We break the number line into integers as units, area into unit squares, and space into unit cubes. I think that's a nice parallelism. Rectangles are, in turn, composed of squares.

My personal crusade is on units, and that's why squares matter. In geometry, there are four basic kinds of units: Rotation, length, area, and volume. Squares and cubes are uniquely flexible in fully packing spaces with regular shapes, so it makes sense to use them (regular hexagons and triangles can also tessellate a plane, of course, but the cube is the only regular polyhedron that can tessellate space [http://mathworld.wolfram.com/Space-FillingPolyhedron.html]).

We break the number line into integers as units, area into unit squares, and space into unit cubes. I think that's a nice parallelism. Rectangles are, in turn, composed of squares.

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### Yashika Gupta

General Discussion -What is graph of a biquadratic equation with no real roots?

For example- graph of x^2+1

For example- graph of x^2+1

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### Josh Fisherowner

Teachers' Lounge - 1) About your own teaching
a) What is your favorite aspect of teaching?
This is very basic: I like it when students come to understand a concept
that they didn't understand before and particularly if that fires their
interest so that they ask lots of follow-up questions.

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### Daniel Kaufmann

General Discussion -If a robot can do it, should it be part of your summative assessment?

Graph y=2x+1 (through formative assessments I should already know if a kid can do this)

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The y-intercept of y=2x+1 has shifted 2 units up. What is the new equation? How is it similar to the original? How is it different than the original?

Graph y=2x+1 (through formative assessments I should already know if a kid can do this)

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The y-intercept of y=2x+1 has shifted 2 units up. What is the new equation? How is it similar to the original? How is it different than the original?

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### LEARN EASILY

Algebra / Pre-Calc / Trig -LEARN EASILY how to solve examples on product rule of derivatives.

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### Josh Fisherowner

Algebra / Pre-Calc / Trig - The beginning of a really, really good series introducing linear algebra, by

+Norman Wildberger.

+Norman Wildberger.

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Aner Ben-Artzi

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Wildberger has a lot of great content, including a playlist for primary school curriculum.

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### About this community

Welcome to the Mathematics Education (K-12) Community on Google+!
This is a forum for all stakeholders--teachers, students, mathematicians, researchers, and laypersons. The only requirement is that you have an interest in mathematics education.

### Josh Fisherowner

Teachers' Lounge - Zoe and I often play games where one of us makes a figure with some objects (stones, chips, snap-cubes, etc.) and the other one has to make an identical figure. Today, for this purpose, we were us…

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This is related to a problem I have in teaching geometry at the high school level. Students have trouble understanding that horizontal and vertical line segments can be the "diagonal" in a shape. Kites in particular create problems, since they're usually drawn with the diagonals being vertical and horizontal and the sides being drawn, um, diagonally.

Geometry is using the original meaning of the word ("connecting corners"), but hey, language changes.

Geometry is using the original meaning of the word ("connecting corners"), but hey, language changes.

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### Josh Fisherowner

*Book Club* - Over the past few months, Nick Rose and I have been working together on a new book which sets out what, in our admittedly biased opinion, every teacher ought to know from the field of psychology. Luckily, Nick is a psychology teacher and has post-graduate degrees in psychology, so at least one of us knows what

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### Josh Fisherowner

Teachers' Lounge - *The idea is that when a student gives an incomplete or wrong answer, the teacher replies with a question that provides just enough hint, reminder, or new information to allow the student to try again and get the answer correct.*

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### Math With Kousou

Technology -I have a whole blog dedicated to integrating technology into my math classroom (1:1 with chromebooks).. I create a successful blended learning environment by creating tutorial videos on youtube. Students can watch tutorial videos and from there, instruction is instantly differentiated. Students can go back, pause examples, take as long as they need to watch example or move on when they are ready. This has helped me tremendously because I can have more 1 on 1 time with students who need it. I'm much more available to help more students.

Youtube: https://www.youtube.com/channel/UCD_2iZv8TP_8IgH3OqdaUhg

Youtube: https://www.youtube.com/channel/UCD_2iZv8TP_8IgH3OqdaUhg

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### Joyentanuj Das

General Discussion -Notebooks of S. Ramanujan

The original manuscripts of the Notebooks of S. Ramanujan at the University of Madras are given below

The original manuscripts of the Notebooks of S. Ramanujan at the University of Madras are given below

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### Conchi

Technology -Hello Math teachers of the community! Smartick, the company I work for, is launching its private Beta this week. We are looking for teachers of kids ages 4-14 who would like to try our adaptive math learning platform for free and give us some feedback. Our method consists of 15 minute daily sessions and 94% of the students improve their logic and math skills. Feel free to send me an email at conchi.ruiz@smartickmethod.com with your questions or for more information. You may also sign up for FREE here:

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### Josh Fisherowner

Research - As Learning Scientists, we clearly support testing (or retrieval practice
) as a means of promoting student learning. We have included blogs about
the value of standardized testing, the pushback from parents and teachers,
and even systemic issues discussed in a documentary in standardized
testing. For a summary of our thoughts on some benefits of standardized
testing, we recommend that you read through our Boston Globe piece.
However,...

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### Josh Fisherowner

Teachers' Lounge - by +David Didau.

“The chief trick to making good mistakes is not to hide them – especially not from yourself.” – Daniel Dennett. I’ve been rereading the philosopher, Daniel Dennett’s wonderfully erudite manual for making and improving on mistakes, Intuition Pumps. The first – and maybe most important – of his seven tools for thinking is that we should

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### Mauro Micó Ebro

Teachers' Lounge -**Multiply with Max**

**What's new? Configure and take the exam.**

https://play.google.com/store/apps/details?id=com.mmicoe.elementaryschoolmultiply.android

Good luck!

Welcome to your elementary school games for kids!

Multiplication is an important subject for success in elementary school.

This multiplication game is a great resource for children in Kindergarten, 1st Grade (first grade), 2nd Grade (second grade), 3rd Grade (third grade), 4th Grade (fourth grade), and 5th Grade (fifth grade).

“Multiply with Max” helps kids practice multiplication in a fun and rewarding way. Ideal for primary education.

Playing with puppy Max in a fun way and learn maths. Drag the numbers to complete the multiplication.

The puppy will indicate you if it is properly calculated. This game has been created to provide practice for children who are beginning to understand the concepts of multiplying numbers.

This game is part of the best school learning free apps.

►You can configure your exam.

►You can take advice the multiplication tables. The times tables have been added to provide practise for children who are beginning to understand the concepts of multiplying numbers. This is an excellent resource to improve their multiplication table skills.

►Perfect for schooler’s kids.

►Recommended for tablet.

Enjoy learning !

Help --

The multiplication that you must calculate and the empty squares that you must fill in with numbers to successfully complete the transaction appear at the top of the screen. Numbers 0 through 9, which you must move with your finger, appear at the bottom of the screen. To calculate the result, drag the numbers at the bottom of the screen to the corresponding empty cell of the multiplication. If you make a mistake in calculating the result, you can move the numbers from one cell to another of the multiplication, or return them to the bottom by only moving and dropping them off the cells. Puppy Max will tell you automatically if you have correctly calculated the result once you have completed all the boxes of the multiplication. Get a bone for Max every time you correctly calculate the multiplication, otherwise you will get a negative point. You can play with different types of multiplication.

Have fun !

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