Pumphrey's Math

Patterns, everywhere


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How to Create Your Very Own Math Ed Search Engine

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Inspired by Robert Kaplinsky’s Problem-Based Learning Search Engine, I decided I wanted to create my own based on my favorite websites to check before starting every unit.

The process is very simple but at the end of it, you come out with a search engine that will only search websites that you decide are worth including.

Here is a step by step guide to creating your own.

1) Head to Google’s Custom Search Engine Site

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2) Click on ‘Add’ to create a new search engine

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3) Type in the websites that you want it to search

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4) Give your search engine a name and hit ‘create’

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And that’s it. From that point, you can bookmark the search engine, or embed the code into your website. Enjoy! Do share your URL in the comments.


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MathEd Out Event: Going Deeper

The MathEd Out Podcast

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MathEd Out Conference 3.0:
Going Deeper

Saturday February 6th 2016, 9am-12pm

Covenant Christian High School, Indianapolis, IN


CLICK HERE to register your free place

The first and second MathEd Out Events were so successful, we are doing it all again! Don’t miss out on your chance to meet with others who are passionate about being the best high/middle school math teachers they can be.

The morning will feature:
  • Time for delegates to share ideas and top resources with table discussions including:
    • Using rich tasks to deepen understanding
    • How to go deeper with simple ‘skill practice’
    • Discussions with course specific groups (Algebra 1/Geometry etc)
  • The popular ‘resource symposium’, sharing all the resources we love best

There are just 60 places for this event. Register soon to avoid disappointment!

CLICK HERE to register your free place

Share the facebook event, here

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Ep. 13 feat. Robert Kaplinski on Rich Lessons and Going Deeper in Mathematics

The MathEd Out Podcast

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Robert Kaplinsky has worked in education since 2003 as a classroom teacher, district math teacher specialist, and University of California Los Angeles (UCLA) instructor.  He graduated from UCLA with a Bachelors of Science in Mathematics / Applied Science (Computer Science) in 2000 and earned his Masters of Education in 2005.

He has presented and conducted professional development at across the United States and Canada.  His work has been published by Education Week (20122015) and the American Educational Research Association (AERA).  He has consulted for major publishers including Houghton Mifflin Harcourt and Pearson.  Robert is a member of the National Council of Teachers of Mathematics (NCTM), National Council of Supervisors of Mathematics (NCSM), California Mathematics Council (CMC), Orange County Math Council (OCMC), and Greater Los Angeles Mathematics Council (GLAMC).  He also co-founded the Southern California Math Teacher Specialist Network, a group that includes over 170 math teacher specialists from…

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Visual Patterns and Coding – Part 2 – Exponential and Inverse Relationships

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Once we have got to grips with the basics of using python to create ‘visual pattern calculators’, it is time to take our thinking to the next level. Up to now we have only been looking at linear relationships with a straight line graph.

The visual pattern above is a quadratic relationship as the pattern grows in a linear fashion in two directions (It’s useful to talk separately about the width vs. length and then bring them together). The nth term is either (n+1)^2 or n^2+2n+1. Can you see both in the picture?

Let’s pause for a second. In 6th grade, I can use visual patterns to introduce the idea that a quadratic has two linear factors! I had HS seniors that struggled with this idea. I love this!

Next comes the coding. Again, we use CodeSkulptor to ‘skulpt’ our function in three lines: Input, Function/Output, and the display output command. The difference in this is that for exponents we have to use **.Screen Shot 2015-12-07 at 11.28.42 AM.png

OR:

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Also, I get the students to Desmos to see if their prediction of the graph are correct. This brings up great discussions about why the graph is the shape it is in quadrants two and three.

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OR:

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I have also introduced the idea of an inverse function; using python to create a function that would enable us to answer the question: What step would contain 400 blocks? This forces the student to consider inverse operations and the fact that order matters. Here is the code (python reads from top to bottom so you can include this all in the one program):

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The benifit of this has been less about coding or nth term and more about introducing the composition of functions. It also enabled me to run some rich lessons on the topic of ‘Straight Line vs. Curvey Lines – Who Cares’ exploring linear vs. exponential relationships with finance and population growth.

The effects of this series will not be truly measured until these students take Algebra, next year. However, my hope is that this will have given them a solid foundation for many of the concepts that they will study in the coming years. We’ll see…


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Visual Patterns and Coding – Part 1 – Linear Relationships

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I have been running a ‘visual pattern’ every week with my 6th grade (pre-Algebra) classes. You can read more about this here.

To bridge the gap between pattern and function and following an online course I took with Rice University, I have started to introduce some basic coding. Python in particular. Even after one lesson of using coding and graphing, I have been able to have rich conversations about the differences between functions, input/outputs, the shape of a graph and the y-intercept. Here is the process I have taken them through:

Part 1: Have the students run through a basic (linear) visual pattern (from visualpatterns.org) using this sheet and reviewing using this slide:

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The nth term for this pattern is 4n+1.

Part 2: I now challenge them that we can create a calculator for this pattern using the Python coding language. I use the free python interface CodeSkulptor (from Rice University) to do this. I take them through step-by-step with some great conversations about functions and inputs/outputs.

The nice thing about CodeSkulptor is that when you hit the save button, it creates a brand new URL meaning that each student will have their own URL to post and share.

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They can then change the input and see clearly what happens to the output.

(Note: Lines with # are ignored by the interface)

Part 3: They then go to the Desmos Online Graphing Calculator and input the function y = 4x+1 to confirm or deny their prediction for the graph shape, from the start of the exercise. This is a great opportunity to talk about ‘step zero’ (as well as step -10 etc.) and why they graph is the shape that it is. I feel it is also important to stress the difference between 4n+1 as an nth term and y=4x+1 (which includes everything in between).

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Their homework is simply to follow the steps with a different (linear) visual pattern and to share their CodeSkulptor URL’s and Desmos screenshots on the class’ wiki page.

For student assistance I created this video:

Where Next?

There are two main places that I would like to take this:

  • Exponential functions
  • Inverse functions

I’m really excited about where this journey will take us. My hope is, that as these students start Algebra proper, next year, they will have a strong sense of functions graphs and their connections with patterns and geometry. Here goes…..

Have you done anything similar? I would love to hear your ideas/thoughts in the comments section, below.

 


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Why you should use Visualpatterns.org, every week

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I used to teach high school. I would often see students who struggled to see:

  • How to generalize patterns and extrapolate
  • The meaning and usefulness of a function
  • That the cartesian plane was just two number lines stuck together, useful for comparing two quantities changing at the same time
  • The difference between a linear relationship and an exponential relationship

Thanks to teacher and activity creating genius Fawn Nguyen, we have a way to address this problem. I now run a visual pattern activity at the start of my lessons, every Wednesday. Just a few weeks into the semester, I am already seeing the above gaps filled!

We have started mainly by mainly using linear patterns with constant differences. Now that this link is pretty strong I have started to introduce increasing differences and they are quickly getting the idea of a curved relationship on the graph. I have created this sheet to help organize the students thinking. I give them 4 minutes to think on the problem by themselves and 2 minutes to discuss their ideas. Then as a class we ask and discuss:

  • Can you describe in words, how this pattern is growing?
  • What do you notice about the numbers in the table?
  • What would be a really slow way of calculating the number of blocks/objects in step 43?
  • What would be a quicker way of calculating the number of blocks/objects in step 43?
  • Using this rule, what would step 1000 look like?
  • If I saw a step with [     ] blocks, which step would I be looking at?
  • If I were to graph steps against blocks/objects, what would the shape be? Why?
  • Ext: What would step 0, step -1 look like?

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I am quickly finding that, by accident, students are solving equations and building up a sense of the need for processes such as factoring, finding the inverse and finding the slope of a line. I have found I am able to coherently validate the need for calculus, 5 years before they take it. I believe this will really help my students when I run lessons such as Dan Meyer’s toothpick activity, later in the year. Sure this is just similar to the explicit/recursive rule section of particular algebra textbooks, spread over a year, but I think a regular discussion on this idea is crucial to making connections and getting the deep understanding needed for algebra and beyond.

I am excited to hear if it has made much of a difference, next year and into the future. I suspect it really will.


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Ep. 11 feat. Prof. Jo Boaler on Having a Growth Mindset for Learning

The MathEd Out Podcast

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Jo Boaler is an author/speaker, and is Professor of Mathematics Education at the Stanford Graduate School of Education. Boaler is involved in promoting mathematics education reform and equitable mathematics classrooms. She is the CEO and co-founder of Youcubed, a non-profit organization that provides mathematics education resources to parent and educators of K–12 students. She is the author of several books including, What’s Math Got To Do With It?(2009) and The Elephant in the Classroom (2010), both written for teachers and parents with the goal of improving mathematics education in both the US and UK. Her 1997/2002 book, Experiencing School Mathematics won the “Outstanding Book of the Year” award for education in Britain. Currently she is the Research Commentary Editor for the Journal for Research in Mathematics Education.

thJo Boaler Website

How to Learn Math: For Students

How to Learn Math: For Teachers and Parents

YouCubed

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Within 10 years, every math classroom will have one of these

It’s a cool trick, you think of something and then you can make it. But a visit to 3D printing company 3D Parts Manufacturing quickly convinced me that this could be a hugely powerful tool to help build understanding in mathematics.

Think about it:

  • After considering volume and surface area of 3d shapes, you could see your ideas come to life
  • After considering the coordinate plane, you could see your ideas come to life
  • After considering maximization and minimization problems, you could see your ideas come to life
  • After considering solids of revolution, you could see you ideas come to life

Using this well will be an art form. The temptation to be ‘hey, look how cool this project is because we used 3D printing’ will be strong. If used well, this could be an incredibly powerful tool to make more abstract ideas become more real. like an extreme version of Desmos, this visual, hold-in-your hand manifestation of mathematics will bring us ever closer to answering oh so common question, Why?

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Ep. 8 feat. Dr. James Grime

The MathEd Out Podcast

James is a mathematician with a personal passion for maths communication and the promotion of mathematics in schools and to the general public. He can be mostly found doing exactly that, either touring the world giving public talks, or on YouTube.

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After working in research in combinatorics and group theory, James joined the Millennium Mathematics Project from the University of Cambridge. On their behalf James ran The Enigma Project, with the aim to bring mathematics to life through the fascinating history and mathematics of codes and code breaking. Spys! Secrets! And secret messages!

James travelled extensively giving public talks and visiting schools, colleges, universities, festivals and other events, and reaching 12,000 people, of all ages, every year. Touring took James all over the UK, and the world, and involved talks for Google, Microsoft, RSA conference, Maths Inspiration, Maths in Action, BrainStem (Perimeter Institute Canada), and various science festivals. James’ aim is…

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Top Tech Tip – Rowmote Pro iPhone app ($4.99)

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I avoid my desk whenever possible during a class and like to be moving around or up at the board. This proves difficult when my computer and powerpoints are at the back of the room and I need to change between slides. Of course I can just buy a clicker (good ones fetch $50-70). However, I looked at the app store and found Rowmote Pro ($4.99), an app that not only works as a clicker but does pretty much everything your keyboard and mouse can do.

I’ve just finished a unit on spreadsheets and scatter plots and I was able to be at the board or walking around the room the whole time whilst working a functioning spreadsheet. It was awesome.

There aren’t many apps I can say this of (if any) but I now use Rowmote Pro in every lesson and it means I can be where I want to be at any point during the lesson.

What apps make your teaching life easier?