A Few Problems, Many Solutions

At this point in the year, the iPads are pretty integrated into our class's curriculum and daily routines.  We have prioritized exploring what we call "creativity apps" as opposed to games and apps with a singular focus.  Meanwhile in math, our class has begun utilizing Exemplars problems and rubrics to further student problem solving, math thinking, and math communication (see Merry Melvin's previous post for more on assessment).  Each problem is rich with multiple questions, levels, and solutions, and our students are finding them appropriately challenging.  We gave them free range to decide how to present their work.

Here are some solutions from the one about predicting the number of Sweethearts in a box:

And the one about planning the sleeping arrangements for class camping trip:

And our most recent problem about carpeting a basement:

Each solution requires a written explanation and a visual representation.  Some students decide to use the iPad to prepare both.  Some students use different apps depending on what they are being asked and some have a favorite they choose consistently.  Some students create their graphs and diagrams using physical materials such as Base Ten blocks or  tiles or puff balls and then document or enhance them by importing a photo.  Some students are comfortable emailing us their work and some students prefer working offline and turning in physical products.  We remain open to all of their preferences and meet them in their comfort zone.

While it was no surprise that many students elected to use their iPads to prepare their final solutions we were fascinated by the range of apps children chose.  Through regular explorations and many months of projects, Drawing Box, AiWriter, Educreations, Explain Everything, Keynote, and Inspiration Maps have become familiar friends. Left to their own devices, students have to decide whether the iPad and our creativity apps are the "right tool for the job" and which tool will serve them best.

Of course we do have some students who insist that the iPad is the best tool for them and it's really not .  But after a few experiences of being distracted and not completing their work on time, they learn that lesson too and change tactics.  At the beginning of the year, we set a few goals for our 4th grade 1-1 iPad program and progress is visible on many fronts.  To me, these are examples of students taking charge of their learning and our classroom becoming a place that fosters and supports creativity, independence, differentiation, and meaningful assessment.

Slice It!

My family and I have recently discovered an app that we can’t stop playing! 

Slice It! (paid version) or Slice It Begins! (free version) by Com2Us is fantastic.  The point of the game is to slice various shapes into equal pieces.  In the beginning, the shapes are simple enough so the player can understand what to do in the game.  As the player progresses, the shapes and the slices become more challenging.  The directions are simple to understand and each page gives the player a “tip” at the bottom. When a shape is sliced, the player can get from 1-5 stars and the app encourages the player to try again to get 5 stars.  If the player fails to slice even pieces, the follow up page shows why the first try was incorrect.  When the player earns 5 stars on a shape, he or she earns a bonus “hint” to use in the future.  Hints can be used if the player is stuck and not sure how to proceed.

What We Like

·         Simple directions

·         Explains mistakes; encourages player to retry

·         Music can be turned off

·         Shows percentage of each piece sliced

·         Shows player that equal pieces can be different shapes

·         Challenging, yet not frustrating

What We’d Like to Change

·         Only keeps track of one player; would be nice if multiple players could track progress

·         Ability to move lines without having to “undo” (a drag and drop)

Mathemagica

A few weeks ago someone told me about Mathemagica by Remarkable.  My sons and I have since spent some time exploring this app at various levels.  In the introduction, the app says that it is for those who want to challenge themselves as well as those who need more practice as it is a genius tool that will adapt itself to your level of play.  While the app is a good idea overall, we have all found it to be very frustrating at times. 

Each player can customize their level of play by choosing specific skills or all the skills at a particular grade level.  We have all found that when all the skills are selected, the app does not randomize well.  The player will be given similar problems, sometimes even the exact same problem.  It doesn’t seem to matter if the player solves the problem correctly or not.  The player is not given a practice space to compute, all computations need to be held in the players’ mind.  While this is not necessarily a bad thing, it can be frustrating for the player that needs practice and repetition because they are not secure with a concept.  The worst part of this app is that it does not allow the player to make mistakes.  Once a mistake is made, the app shows the solution and then moves on.  This is not helpful.  In fact, this made both my sons want to stop playing.  There also seem to be time limits on some problems that are quite short.  If the player does not complete the problem in time, the solution is shown and play moves on.  There does not appear to be a way to turn this timing function off.  Again, this is not helpful to the player who needs to practice skills.  “Awards” are given at odd times. For example, when the player solves 25 problems correctly overall, the player receives a reward.  However, since this is overall, it could be after the player completes one problem in a session.  After the next problem, the player could get a reward for solving 10 questions in a category correctly overall.  These interruptions are very distracting.  Finally, there does not seem to be an end to a session.  The player can just keep going.  There is not a natural stopping point.  Overall, I feel that this app has potential, but there are multiple things that need to be fixed.  It is certainly not for someone who needs to practice skills.

What We Like

·         Player can choose specific skills to practice

·         Skills are grouped by grade level, however a player can choose from multiple grade levels

·         App can track up to three players’ progress

What We’d Like to Change

·         App does not randomize well; sometimes player has to solve exact same problem even if solved correctly in the past

·         App does not allow player to make mistakes; shows solution after one error; not helpful to players that need to practice skills

·         No space to compute; player has to hold computations in head

·         Time limits on solving problems

·         Awards are given at odd times; can be very distracting

Hungry Fish!

Motion Math Hungry Fish has made a big splash in kindergarten!

It's a simple concept - there is a hungry fish and he needs to be fed some bubbles that add up to, or are the same amount as, the number on hungry fish's belly.

Kindergarteners love this app! If you don't combine the bubbles (add the numbers) to equal the needed food number, the fish won't eat it and more bubbles will appear. If the fish doesn't get food, a hint will appear after some time. Eventually, without food, the fish dies and offers the student the chance to try again.

This is a Motion Math app so there are multiple levels and each level has varied degrees of difficulty. There are also some bells and whistles to make it fun - changing the color of the fish, creating new fish, and even caves and Mad Fish eating wrong answers!

This app fits nicely in our program - offering children a chance to explore numbers and an appealing way to practice addition.

I like this app "side by side" with:
* kindergarten addition using physical math manipulatives
* creative group thinking about a real world math application

What I might change... I would like to see the number sentence at the bottom of the screen each time I add bubbles together. Also, Hungry Fish only offers in-app upgrades which makes it difficult to manage bulk purchases in an education setting. (This is also true of Motion Math Zoom.)

Hooray for Motion Math apps

Motion Math Zoom
http://motionmathgames.com/motion-math-zoom/


This simple app is fast becoming one of my favorites in the classroom. It is a simple and intuitive number line that helps reinforce place value. The students need to move the number line in order to find the space for a particular number that floats down in a bubble. The number line is moved by sliding a finger. To get larger numbers, the student pinches or un-pinches their fingers. Larger numbers are represented by larger animals such as a rhino or dinosaur while smaller numbers are dogs or frogs.

This app has an even more advanced option as numbers can get as small as amoebas (thousandths) and can delve into negative numbers. I especially like the real representation of the animals in addition to the numbers.

My students have been working primarily with the first three levels. In addition to introducing this glimmer of an idea about place value, the students have really been reinforcing number ordering skills and number recognition.

As in all of our favorite apps, this one is self-correcting. It has really nice and appealing graphics and the sounds are not obnoxious or over praising. In addition, this app has scaffolding and support for students who are struggling. The app offers some "clues" if a particular puzzle is not solved in a certain amount of time.

This is a great app for use:
*partnered with learning / filling out / recognizing numbers on a hundreds chart...
*when you are teaching numbers that are greater than or less than...
*once you introduce numbers greater than 10...

A Challenge to App Designers - Where are the Essential Math Apps for Young Learners?

One of our Kindergarten teachers, Denise Coffin, and I have spent three intense days at the Leveraging Learning: the iPad in Primary Grades institute in Auburn, Maine. It has been a gathering of about 120 people from public and independent schools all asking the questions such as, "Are iPads the educational tools that will transform a student's experience by creating opportunities to customize learning?"   As educators, we are all in search of methods and tools that will help students access the curriculum in ways that extend their thinking and engage them more deeply in the concepts they are learning. Learning becomes engaging when students are given the chance to ask questions and are encouraged to discover the answers using materials, tools, and guidance from a teacher, or through collaborating with classmates. What are the teaching methods, combined with powerful learning tools, that will help all students soar, grow, and feel successful?  iPads offer an intuitive interface that we have seen students of many ages interact with creatively, confidently, and with engagement. In these early days, the apps designed for education are still in their early stages. There are new apps out every day, but few of them make the grade for constructivism, deepening of understanding, or richness of material. At the institute, we spent an evening with Ruben Puendetura discussing his iPad Flows. Ruben has deep roots in constructivist thinking and computers in education, going back to the early days of Seymour Papert and Alan Kay. He has reviewed over 800 apps in search of those that meet the qualities of engagement that deepens understanding. I will post about each of his flows in the near future. He has posted a pdf of his flows on the Institute Resources along with many other useful materials.  After his presentation, we approached him at lunch to ask about the absence of a math flow in his collection of apps for young learners. His response was that, at this point, there aren't apps out there for young math learners that fulfill our expectations. We looked together at his Math Flow for older students, which includes interactive graphing calculators, geometry, and higher math apps. Of all of these, the two that could be used with younger students are Touch Draw, which would allow us to create shapes, even virtual Cuisenaire rods, for students to explore and manipulate, Sketchpad Explorer, which offers geometry exploration and discovery similar to Geometer's Sketchpad, and WolframAlpha, a "computational knowledge engine".    What is missing? Where are the apps that help kids work through problem solving and logic questions in a real and engaging way? Where are the apps that make math thinking visible, that challenge children to question the underlying concepts of math? Where are the apps that introduce concepts in a way that students can interact with materials, repeat the experience, and customize their learning? Here is the challenge to app designers who would like to create worthwhile, potentially essential, math apps.    We reflected on the days when "The Logical Journey of the Zoombinis" was still able to run on our computers. This engaging activity presented kids with fun, but often tough, logic problems to solve in the context of a story about traveling Zoombinis. The closest program like that is available only on a computer that runs flash, called "The Lure of the Labyrinth". We are also waiting for programming experiences such as Scratch to move to the iPad. Evidently that app appeared, was taken down by Apple, and is in redesign at this time.
The Math Flow just doesn't exist yet for our younger learners. Educators are willing and eager to find a way to make this happen. There's never been a better time for creative app designers to connect with educators to explore new ways to deepen and broaden student understanding of math using the unique interface of the iPad.