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Uncategorized

Redos and Retakes – #sbgchat on twitter

These days, all of the “cool kids” in twitter chats are checking in at 9PM on Wednesday evenings, where #sbgchat (standards-based grading chat) is growing quite an audience.  After just a few weeks, I am hooked into the discussions, and look forward to more challenging discussion from hosts Tom Murray and Darin Jolly.  This past week, the hot topic was redos and retakes.  Before the chat, I enjoyed videos by Rick Wormeli, whose ideas pumped me up to learn more, not unlike a football coach motivating his athletes.

Rick Wormeli on “Redos, Retakes and Do Overs”:  part 1 and part 2

This week’s chat featured some fantastic discussion about redo’s and retakes, with the following questions:

  1. Should students be given the opportunity to redo formative assignments, why or why not?  How about summative assignments?
  2. How should a redo or retake be altered from the first opportunity?
  3. What steps should occur prior to the retake of an assessment for the student and the teacher?
  4. How should the number of redos factor into a student’s grade?

If you have never participated in a Twitter chat, be prepared for information overload.  But the wonderful thing is that you will always find someone to share your ideas with, and you can always go back to the archives to pick up on pieces you missed.  You can check out the chat archive and review the ideas, and perhaps make some new Twitter contacts.

THINK ABOUT YOUR OWN EXPERIENCES

My advice to anyone considering redos in their classroom is to do some reading, think about your goals, and discuss your ideas with colleagues.  Perhaps you will find teachers in your own building who already have begun a system for retakes, which you could attach yourself to.  Or create a PLC in your building to think about how a system of redos or retakes would work.

One of the best resources for gettting started is the November, 2011 issue of Educational Leadership, which focused on effective grading practices.  You will need to be an ASCD member to access the article.  If you aren’t, contact your administrator and hopefully they can help you with access.  Rick Wormeli’s article on “Redos and Retakes Done Right” contain many of the same ideas seen in the videos, and a great starting point for thinking about your own classroom philosophies.

HOW TO DO IT: here are resources on retakes and redos from teachers who have implemented them in your classrooms.  Hope you find something you can use!

A Principal’s Reflections – blog by Eric Sheninger, with a how-to guide from one of his building’s math teachers.  Includes a contract for retakes, and a classroom policy to share with parents.

Dan Meyer’s thoughts on assessment – personalizing assessment and keeping track of skill progress in math class.  What I really enjoy about Dan’s thoughts here is the amount of responsibility students begin to accept for their own progress, and in making good choices.

Cybraryman’s List – a comprehensive list of grading practices.  From articles providing rationales for differing grading procedures, to classroom look-in, there is something for you to think about here.

The Solon District in Iowa has a implementation guide for Stanards-Based Grading.  Check out the sections on student re-takes, and how students initiate them.

Dan Longhurst – On his blog, Dan shares his experiences with Standards-Based grading and his classroom experiences with embedding redos into assessment on newer material.  Dan is a physics teacher, and his ideas are easily transferrable to math classrooms.

Categories
Technology

“Wow” Moments with Wolfram|Alpha

The Siemens STEM Academy offers great resources for teachers, from lesson plans, to blog posts from teachers, to fantastic free webinars.  Full disclosure: I have written for the STEM Academy blog, and been a part of the Academy summer program…but I am but a small fish in a cool ocean of resources!

This week, the Academy hosted a free webinar featuring a demonstration of the dynamic knowledge provided by Wolfram|Alpha.  Having used Wolfram Demonstrations before in my classroom, I was looking forward to learning more about this search tool.  Crystal Fantry provided an hour-long overview of this exciting resource, and ideas for classroom uses.  It’s amazing how many “wow” moments I have these days with the new tech tools our students can have in their hands, but this one goes beyond that.  Knowing that students have access to resources like this should cause us all to think about our roles as math teachers / facilitators….this is a game-changer!

So, just what is Wolfram|Alpha?  The site is simple, just enter what you want to search for, and off you go…but this tool is so much more than that.  The “about” from their website provides some insight:

Wolfram|Alpha introduces a fundamentally new way to get knowledge and answers—not by searching the web, but by doing dynamic computations based on a vast collection of built-in data, algorithms, and methods.

So, what the heck does that mean exactly?  Let’s learn by diving in.  And while you can use Wolfram|Alpha for far more than math, this is a math blog so let’s focus in on some math….

Try this: “y=2x +3”.  Let’s start with something simple…what does Wolfram|Alpha give us?

WA1

Fun stuff.  A nice graph, the domain, and alternate form.

How about this: “3x+5=2x-9”

Also nice, a plot of the the functions.  And the equations’s solution..but what’s this…a “step-by-step solution”?  If you are logged in (free accounts) you can step through the solution:

WA2

So, what happens now when you give that worksheet of equations to solve for homework?

There are a lot of other neat computations to explore, try some of these as starters:

  • “y=(x+2)(x-3)”
  • “inverse y=x^2+3x+1”
  • “sin(x)+cos(x)=1”
  • “Integrate x^2 dx from 0 to 5”

WA3But Wolfram|Alpha goes beyond quick lists and computation.  How about “Pascal’s Triangle mod 5”. Or “triangle sides 3, 6, 8”, or try the elusive 17-gon, and see the many facts to check out.

A TOOL FOR RESEARCH AND GENERALIZATION

I have only scratached the surface of the many features, and there are also lots of nooks, crannies and links for you to explore.  I’m eager to use this tool with students as a means to research new ideas, and make some sense of their characteristics.  For example, let’s think about domain and range, as I ranted about in a previous post.  I like that Wolfram|Alpha expresses domains using set notation, and this is a great opportunity to have students research new functions.  Most of what we do in Algebra 1 deals with linear functions, so we get a lot of “all real numbers” domains.  Expose your students to non-linear functions, once they know how to make their x,y tables.  Try these:

  • y = 5 / x
  • y = rt (x-2)
  • y = 1 / (x^2 – 9 )
  • y = 2^x
  • y = x^2 – 4

And what to do with these new functions?  Let’s place them into categories, share our findings, and communicate our ideas.  Give each group 2 or 3 new functions to look at and share their findings on www.padlet.com.  This site, formerly called WallWisher, allows everyone to contribute their ideasd and move them around the canvas.  Here’s a sample of my function domain wall, click the link to contribute your own, play around the wall, and double-click in any empty space on the canvas to contribute.  Or sign up for a free account and create your own wall.

Padlet

Thanks to Kyle Schutt (@ktschutt) and the gang at Discovery Education for providing these great webinars.  Be sure to check out the Siemen’s STEM Academy blog for more great resources, blog posts, and archived webinars.

Categories
Middle School Technology

Probability Openers – Separating the Possible from the Plausible

A recent problem I reviewed from the Mathematics Assessment Project (MAP) caused me to refelct upon the coverage of probability in our classrooms.  The website provides sample tasks and assessment tools for schools and districts as they adjust curriculums to match the Common Core.  In the standards, probability begins to take center stage in grade 7:

Investigate chance processes and develop, use, and evaluate probability models.

Probability is treated like the ugly step-sister in many math courses: ignored, shoved to the side.  Look at standardized testing results, including AP Statistics, and you will find that probability standards often produce weak results.  The isolated fashion with which we treat probability is certainly not helping.  Let’s develop strategies to not only re-think probability, but to encourage communication of ideas and develop understanding.

I have taught probability at many levels: as an 8th grade teacher, as an AP Statistics teacher (and reader) and as the author of a Prob/Stat course delivered to 9th grade students.  This year, I taught my first college course in Statistics, where the problems with probability persist.  The picture below is from my college Stat 1 class, which you can also see on the great site Math Mistakes, by Mike Pershan.  Visit and provide your input:

Conditional

Here are two activities I hope you can use in your classrooms to help fight the probability battle.

“WHICH IS MORE LIKELY” OPENER:

The Core Standards provide a framework for our students base knowledge of probability:

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Before we can start diving into formulas and fractions with probability, we need students to understand, and be able to express, whether an event is likely or not likely.  For simple events, like flipping a coin or drawing a card, this can be an easy discussion, but what happens when we start talking about complex events, like flipping multiple coins, tossing 2 dice, or choosing a random car from a parking lot?  Download my Probability Opener, which asks students to assess events and compare their probabilities.  Answers are provided.  The events start off innocently enough, but soon meander into more complex tasks, where students are asked to identify the more likely outcome:

You roll the dice and move your piece in the game of Monopoly…

A:  You end up on Boardwalk

B:  You end up in Jail

This is also a great activity if you have a classroom clicker system, or for Poll Everywhere if cell phones are allowed.

SPINNER BINGO

This activity is an adaptation of a Spinner Bingo problem from the Mathematics Assessment Project site I mentioned at the top of the post.  Visit the MAP site for not only the task, but a rubric and samples of student work.

The problem presents a scenario where students are asked to assess a spinner game, and bingo cards created for the game.  Read the files given on your own, but here is a quick summary:

  • 3×3 bingo cards are filled out, using non-repeating numbers from 1-16.
  • Two spinners with 8 equal spaces numbered 1-8, are spun, and the sum computed.
  • Players mark off their bingo cards if the sum appears on their card.

This is a nice scenario, so let’s adapt it and use it as our unit opener.  Having students play a game, and develop and justify a strategy, is a great way to get started.  Here is a lesson guide I have written to help you get started.  Also, the site Unpractical Math provides a virtual spinner applet you can use.  It’s often easier to just dive in and play, so here is a brief video demo of the game and how you can play it in your classroom:

Please let me know if you use either of these activities, and would appreciate your feedback. Thanks.