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.