What if there was a better way to introduce math to young kids? For a parent, one of the first math concepts they teach their child is to count to 10. In this exercise, repetition is the name of the game: “Let’s count to 10!…Good! Now, let’s do it again!”

While rote learning of the first 10 numbers is important, it is not sufficient for a child to grasp the deeper meaning behind these numbers, and why they are important to their everyday lives.

Somewhere along the way, we lose an opportunity to take advantage of a critical component of early math development, because so many people are not aware of research on how the brain is wired for math.

Research on math development has long shown the importance of the Approximate Number System (ANS), a cognitive system responsible for estimating quantity without counting. For example, a child (or adult) can often answer questions such as, “Which plate has more grapes on it?” through estimation, without actually counting the grapes on the plate. For these types of judgments, people rely on their ANS.

The ANS is a preverbal system present in infancy and shared between animals and humans. Research shows that children who have a sharper ANS — e.g., those who can discern quantities that are closer together without counting— perform better on standardized math tests. This is surprising, given the apparent differences between estimating (which is inherently approximate) and the more precise, symbolic calculation skills evaluated in math tests, e.g., counting, addition, and subtraction. Nonetheless, the connection runs deep: studies on infants and young children show that ANS precision is a strong predictor of future math achievement, even years later.

Symbolic versus Approximate Math: Even before children can recognize numbers and do formal math (top row; “symbolic”), they are able to do approximate math (bottom row; “approximate”). By leveraging their Approximate Number System (ANS), or their intuitive sense of quantity, children are able to make quantity comparisons (bottom left) and perform approximate addition (bottom right). Two recent studies show that children who practice this imprecise math could potentially have a leg up in learning symbolic math when they start school.

Moreover, two recent papers have found evidence for a causal link, showing that ANS practice improves math performance in preschoolers. In one study from last year, researchers at Johns Hopkins University asked 40 five-year-olds to make a series of approximate comparisons between two sets of dots on a computer screen (“which side has more?”; see diagram), where the questions started easier and became harder. Control groups saw the same questions but in a different order. Amazingly, researchers found that children who played with the “treatment” version of the game for just five minutes demonstrated better math performance immediately afterwards (on tests of counting, number identification, addition, etc.), when compared to control groups.

In another recent study involving 103 low-income preschoolers in the Philadelphia area, researchers at the University of Pennsylvania studied the effects of a touchscreen ANS game on early math performance. Their game helped children to practice “approximate arithmetic” — that is, adding and subtracting quantities by estimating rather than counting (see diagram). Children in the treatment group, who played the game for a total of two hours over a two-to-three-week period, scored higher on a standardized math test than children in the control group, who played a picture memory game.

These studies indicate that ANS practice can help preschoolers develop their early math skills, in preparation for formal math education later on. Unfortunately, the ANS software used in the recent studies are research prototypes, and thus unavailable to parents and children who want to use them.

A New Kind of App for Learning Math

Given the importance of early STEM skills and the ubiquity of touchscreen devices amongst young children, my company, Cognitive ToyBox, saw an opportunity to develop an early math game based on this research, making ANS activities accessible to parents and children at home. We knew that simply rebuilding the games, as described in the research papers on ANS, would not provide a sufficiently engaging experience for young learners. In both of the studies, researchers sat alongside the child to encourage him or her to continue going, even if he or she got bored. In order to adapt the research to be appropriate for kids to use at home, our app would need to be engaging enough to stand-alone, without parent involvement (although it is always recommended).

Image from Cognitive ToyBox

With these guidelines in mind, we built Fuzzy Numbers: Pre-K Number Foundation, a fairytale-themed app with ANS practice activities. To adapt the research for home use, we reimagined the ANS practice concepts as a series of goal-oriented, engaging mini-games. For example, to practice approximating quantities, children attend Princess Poodle’s dinner party and serve her guests the plates with more food (rather than less). To practice approximating addition, children visit Potion School, where they help a student cat choose the cauldron with the same number of ingredients as the total sum in the teacher’s.

After developing the app, we reached out to the researchers, asking whether our app preserves the “magic sauce” that led to performance gains on math tests, and inquiring about possible collaborations.

Image from Cognitive ToyBox

So far, the response has been very positive. The researchers at University of Pennsylvania plan to use our app to run subsequent, longer-term studies, to better understand the relationship between ANS practice and math performance. Moreover, through remote app deployment, they can reach many more participants outside of the university’s geographic area. It’s a win-win: the researchers have better tools to conduct their studies, and we will be able to quantify the precise impact of our app on math achievement, beyond the existing science that supports ANS practice.

Apps that productize promising early childhood learning research could be transformative for a child’s early learning. Rather than using the “digital candy” that floods the market, children could have the opportunity to play evidence-based apps that foster interest in STEM and set the foundation for later academic success.

And, given the importance of STEM learning to a child’s life outcomes, that’s what counts.

Tammy Kwan is the co-founder and CEO of Cognitive ToyBox (CTB). The company partners with developmental psychologists to build evidence-based learning apps for children under 5. CTB has received support from the National Science Foundation, the Robin Hood Foundation, and 4.0 Schools. Tammy holds an MBA from NYU Stern and a BA in Psychology from Stanford University. Follow her on Twitter: @tammykwan. Follow Cognitive ToyBox on Twitter: @cognitivetoybox and Facebook https://www.facebook.com/cognitivetoybox/

Children today have access to more devices and platforms than ever before. And that means they have access to more entertainment software too. Over the past few years there have been a number of studies looking at video games and children, from how games affect the brain and motivation to learn. With the Digital Games and Family Life series, the Cooney Center has been digging into what parents of children ages 4-13 really think about their children’s game play.

A majority of the parents we surveyed (83%) put limits on the amount of time their children can play digital games, and 79% are aware of the titles of games their kids play (see this infographic for some popular titles). We also wondered what kind of effects that parents felt that the games have on their children’s attitudes and participation in family life. Half of our respondents (49%) said their children learn things that “may come in handy at school” or lead to interesting family discussions (42%). About one third of the respondents felt their children neglected homework or chores (35%) or were cranky (38%) because of their video game play.

We hope you enjoy this infographic. Check out the full series for more information about when and where children play digital games, popular game genres and titles, and more.

Download the full infographic as a PDF

Last summer, I had the pleasure of interning with the team behind the National STEM Video Game Challenge. While working with the Cooney Center, I helped create and publish online content to spread the word about the STEM Challenge, and I also had the opportunity to work with students in game design workshops. The technology available to kids today extends far beyond what was available ten years ago when I was in middle school. It was incredible to watch these middle and high school students work so intuitively with complex platforms—platforms that can serve as a gateway into STEM disciplines.

The STEM Challenge encourages youth to explore STEM disciplines such as coding and computer science by making those subjects accessible and engaging. Computer science has limitless applications, and if a student begins their journey into programming through something fun (like designing a video game) then other applications may feel more approachable.

Inspired by my time at the Cooney Center, I have taken classes in both computer science and game design at school this year. I am currently taking a game design class, and my team is creating a video game for mobile devices. Our team is multi-disciplinary—I am the design lead and make all the art and animation for the game. There are also four coders on our team, as well as a UX designer. Our game is called Slam-A-Lot, and it’s a medieval-themed platformer where you battle an opponent across a number of levels.

When creating our game, we faced a number of challenges from both a design and computer science perspective. Our game took six college seniors and a semester of intensive work to complete—giving me a renewed appreciation for the quality of games submitted by STEM Challenge participants. STEM Challenge games are remarkably polished, with creativity and effort evident behind each game.

In the fall I’ll return to Cornell to finish my master’s in Information Science and UX Design. I hope to expand on the game design principles I’ve learned so far, and to explore robot design and human-computer interaction. I definitely have the STEM Challenge to thank for sparking my interest in Information Science. After playing with some of the platforms in the STEM Challenge game design workshops, I went home after work and attempted to teach myself computer science fundamentals on Codecademy. There are many online resources available to those interested in computer science and game design, and I definitely recommend that you peruse them—even if you’re “too old” to qualify for the STEM Challenge. It’s never too late to learn!

Sloane Grinspoon was an intern at the Cooney Center last summer, working with the National STEM Video Game Challenge team. She graduated from Cornell University with a BA in Psychology, and is on track to finish an MA in Information Science and UX Design.

The “Endless” apps by Originator (Endless Alphabet, Endless Numbers, etc.) all follow a reliable and effective formula: genuinely funny antics + solid educational content = learning that sticks.  Most of their apps feature a lovable and irreverent cast of cute monsters who help to illustrate the definition of words, the meanings of sentences and the value of numbers through silly animations.  I was pleased to be able to interview Originator founder Rex Ishibashi in this most recent episode of the App Fairy to talk a little bit about their process.

Listen to our conversation to find out where much of Rex’s inspiration came from, be amazed by the small number of employees the company has (considering their large library of content), and hear stories of kids who learned to spell from using their apps.  Be sure to check out our episode extras for a free printable version of the alphabet letters.  You could print them onto sheets of magnets, cut them out and have a set of Endless Refrigerator Magnets that scatter as imaginary monsters run through them, just like in the app!

Carissa Christner works as a Youth Services Librarian in Madison, Wisconsin which she likes much better than her first job in high school, working at a theme park. She and her two young children love to test out new apps together, read books and go for walks in the woods. She blogs about her library adventures at librarymakers.blogspot.com. Check out the App Fairy website and follow along on Twitter at @appfairy.

As a children’s librarian at a small library, a significant part of my job is to find and purchase the best books, audiobooks, puzzles, apps, websites, devices, and even toys for kids and teens ages 0-18. I’m also tasked with making sure families can find them in the library. Some of these items will go on shelves for check out, some will be used in programs like storytime, the maker club or a long list of other programs held throughout the year, and others will be part of the library’s collection of digital resources. I am always looking for the best that will help my community’s kids learn and grow. It’s no small task, but I love it.

Winner of the 2017 Caldecott Medal

This year, my work reviewing and evaluating has taken on a new significance. I’m honored to serve on the Association for Library Service to Children’s 2018 Caldecott Award Committee, which each year recognizes the illustrator of the most distinguished picture book for 0-14-year-olds. I was also fortunate to spend the winter collaborating with KIDMAP on a checklist to evaluate digital media for kids. Each book I review for the Caldecott award, and ultimately the families at my library, is methodically evaluated using a rubric of sorts that draws on award criteria, research, and my experience working with children and teens. The digital media I review for sharing with families at the library undergoes the same scrutiny. As a media mentor, finding high quality media, in all of these formats, is an essential part of my work supporting the information, literacy, and media needs of my community’s families.

While the Caldecott has well-established criteria and the merits of individual picture books have been reviewed, discussed, and debated for many years, new media is well, new, and what makes high quality digital media is less defined. Often times what is determined to be high quality often reflects the needs of only some. The “best” do not always support a wide array of abilities, multiple home languages, and a variety of cultures. And while being glitch-free, entertaining, and age-appropriate is important, high quality also means being inclusive and rich in diversity.

What does diverse and inclusive digital media for children look like? With the KIDMAP Checklist we aimed to figure that out. The checklist is designed to help reviewers, educators, librarians, and caregivers find and create digital media that is high quality and relevant to families with a variety of experiences. As with paper books for kids, digital media should provide a mirror, window, and sliding glass door; allowing kids to see themselves reflected in the stories told and learn about worlds beyond their own.

Visit joinkidmap.org to view the checklist or click here to download a PDF.

The extensive checklist, made possible with the support of the Joan Ganz Cooney Center, includes sections addressing digital media’s content, art, audio, audience, purpose, functionality/navigation, support materials, and creative teams. The checklist can be used as a rubric or guide in both selecting digital media and designing it. Many elements of high quality traditional media can be applied to digital content and formats. Traditional media’s sometimes slow progress to broaden diversity and be inclusive does not need to be replicated however.

As with any rubric or evaluation tool, a specific app may not meet every criterion on the KIDMAP checklist and that is OK. Some elements may not apply to every type of media or title. The checklist is meant to be as all-encompassing as possible so that families, educators, designers, and decisions makers can consider inclusion and diversity alongside other elements of high quality digital media.  Each question draws attention to an aspect of digital media that impacts both kids’ ability to access the content and how positive the learning experience will be once they delve into it.

The checklist is now available as a download and we expect to update it. Please use the checklist as you evaluate, select, and create digital media for kids and feel free to send your comments and questions about the checklist to KIDMAP.

Note: As a librarian and media mentor, I am especially excited by the Association for Library Service to Children’s decision in 2016 to formally recognize high quality digital media for young children (Excellence for Early Learning Digital Media) and I look forward to seeing the product of their first year’s work!

The checklist was inspired by the work of many including Nova Scotia’s Bias Evaluation Instrument (Canada), Reading Diversity (from the Southern Poverty Law Center’s Teaching Tolerance), Joan Ganz Cooney Center’s The New Coviewing, Tap, Click, Read by Lisa Guernsey and Michael Levine, the Bias Screening Instrument for Interactive Media crafted by Warren Buckleitner (Children’s Technology Review) and Kevin Clark (Center for Digital Media, Innovation and Diversity), and Evaluating Apps and New Media for Young Children: A Rubric.

Thanks go out to Sandhya Nankani (Literary Safari), Amy Kraft (Monkey Bar Collective), J. Elizabeth Mills (University of Washington), Tamara Kaldor (TEC Center at Erikson Institute), Kevin Clark, Ph.D. (Center for Digital Media Innovation and Diversity, George Mason University), Chip Donohue, Ph.D. (TEC Center at Erikson Institute), Warren Buckleitner (Children’s Technology Review), Carissa Christner (Madison Public Library), and Daryl Grabarek (School Library Journal).

Claudia Haines leads storytimes, hosts Maker programs, and gets great media into the hands of kids and teens as the Youth Services Librarian and Media Mentor at the Homer Public Library (Alaska). She is a co-author of the Association for Library Service to Children’s white paper, Media  Mentorship in Libraries Serving Youth (2015). She trains other librarians as media mentors and serves on both local and national committees that support families and literacy. She blogs at www.nevershushed.com. @claudiahaines

Edited 10/26/17

The STEM Starts Early report talks about learning trajectories in early STEM. What are they? What difference do they make?

What Are Learning Trajectories?

Children follow natural developmental progressions in learning and development. As a simple example, they learn to crawl, then walk, then run, skip, and jump with increasing speed and dexterity. These are the levels in the development of movement. They follow natural developmental progressions in learning STEM content, too, learning ideas and skills in their own way. When teachers understand these developmental progressions for each major topic, and sequence activities based on them, they build learning environments that are particularly developmentally appropriate and effective.

Developmental progressions are at the core of STEM learning trajectories. Learning trajectories help us answer several questions. What should we teach? Where do we start? How do we know where to go next? How do we get there? Learning trajectories have three parts that address each of these questions:

1. A goal—STEM content,
2. A developmental progression—a path of levels of thinking along which children develop to reach that goal, and
3. A set of instructional activities and teaching strategies, matched to each of the levels of thinking in that path.

Let’s examine each of these three parts. To do so, we’ll use the case of mathematics, because more work with learning trajectories has been done with that subject, although educators are developing them for other STEM fields as well.

Goals: The Big Ideas of Mathematics

The first part of a learning trajectory is a mathematical goal­ including the big ideas of mathematics—clusters of concepts and skills that are mathematically central and coherent, consistent with children’s thinking, and generative of future learning. For example, one big idea is “counting can be used to find out how many in a collection.”

Development Progressions: The Paths of Learning

The second part of a learning trajectory consists of levels of thinking, each more sophisticated than the last, through which children develop on their way to achieving the mathematical goal. That is, the developmental progression describes a typical path children follow in developing an understanding and skill about that mathematical topic. Young children’s ideas and their interpretations of situations are uniquely different from those of adults. For this reason, good early childhood teachers are careful not to assume that children “see” situations, problems, or solutions the way adults do. Instead, they interpret what the child is doing and thinking and attempt to see the situation from the child’s point of view. Similarly, when they interact with the child, these teachers also consider the instructional activities and their own actions from the child’s point of view so they can help the child develop the next level of thinking. This makes early childhood teaching both demanding and rewarding.

The “Developmental Progression” column in Figure 1 describes three main levels of thinking in the counting learning trajectory (this is just a sample of levels—the full learning trajectory has more than 20, birth to 7 years!). Under each description is an example of children’s thinking and behavior for each level.

Instructional Activities: The Paths of Teaching

The third part of a learning trajectory consists of instructional activities and strategies linked to each of the levels of thinking in the developmental progression. These tasks are designed to help children learn the ideas and skills needed to achieve that level of thinking. That is, as teachers, we can use these tasks to promote children’s growth from the previous level to the target level. The second column in Figure 1 includes example instructional activities for counting.

In summary, learning trajectories describe the goals of learning, the thinking and learning processes of children at various levels, and the learning activities in which they might engage. See the pp. 21-22 of the STEM Starts Early report to see an example from measurement of length.

What Good Are Learning Trajectories?

We need learning trajectories in STEM. Too often, STEM teaching consists of pages 48-49 followed by 50-51 followed by…. Imagine a reading teacher whose 13-year-old students read at a 7-year-old level. Most certainly, the teacher would adjust curriculum knowing that texts and lessons appropriate for 13-year-olds would be fruitless for her students, leading to failure and frustration. However, in STEM, a teacher of an 8-year-old who doesn’t understand the learning trajectory for the topic at hand will not be able to adjust teaching to meet the needs of the child. This will also result in frustration and failure, including attempts to memorize material without understanding. Especially in STEM, where understanding is so critical, such rote learning is disastrous for children, especially those who have lacked opportunities to learn.

Usefulness to Teachers

Learning trajectories support high-quality teaching based on understanding both mathematics and students’ thinking and learning.  They help teachers use the power teaching strategy of formative assessment, the ongoing monitoring of student learning to inform and guide instruction. The three parts of learning trajectories answer the three basic questions of formative assessment.

Teachers who understand the goals—the big ideas of mathematics—are more effective. Teachers who know all three parts of learning trajectories can adapt their instructional activities to meet the needs of both the class and of individuals or groups of students who may be at different levels in the developmental progression. Those who observe their students for evidence of progressing ideas and thinking, and then iterate their activities based on that data, build effective learning environments

Usefulness for Professional Development

Professional development focused on developmental progressions results in increases not only in teachers’ professional knowledge but also in their students’ motivation and achievement. Used in preservice and inservice training, as well as learning communities, learning trajectories can facilitate developmentally appropriate teaching and learning for all students.

Usefulness for Policy

Surprising to many, learning trajectories have already been used in state and professional standards, including the NCTM’s Curriculum Focal Points and the Common Core State Standards—Mathematics.  They can help schools, districts, and states implement more connected, aligned, and coherent.

Final Words

Learning trajectories support high-quality education in many ways. Perhaps most important in early STEM, as they interact with children, teachers consider their actions from the children’s point of view. Nowhere is that more important than in early childhood. We believe that learning trajectories are the most powerful tool teachers can use to do this well. Thus, the benefit for the teacher is to have a well-formed and specific set of expectations about students’ ways of learning—a likely path that incorporates the big, worthwhile ideas.

Julie Sarama is Kennedy Endowed Chair in Innovative Learning Technologies and Professor at the University of Denver, Colorado, U.S.A. She has taught high school mathematics and computer science, gifted, and early mathematics. She directs six projects funded by the National Science Foundation and the Institute of Education Sciences and has authored over 65 refereed articles, five books, 53 chapters, and 50 computer programs, many with colleague Doug Clements. Her research interests include children’s development of mathematical concepts and competencies, implementation and scale-up of educational interventions, professional development models’ influence on student learning, and implementation and effects of software environments. http://portfolio.du.edu/jsarama

Douglas Clements, Kennedy Endowed Chair in Early Childhood Learning and Professor at the University of Denver, is a major scholar in the field of early childhood mathematics education, one with equal relevance to the academy, to the classroom, and to the educational policy arena.  At the national, level, his contributions have led to the development of new mathematics curricula, teaching approaches, teacher training initiatives, and models of “scaling up” interventions.  He has served on the U.S. President’s National Mathematics Advisory Panel, the Common Core State Standards committee of the National Governor’s Association and the Council of Chief State School Officers, the National Research Council’s Committee on Early Mathematics, the National Council of Teachers of Mathematics national curriculum and Principles and Standards committees, and is and co-author each of their reports. He has directed more than 35 funded projects. Additional information can be found at  http://du.academia.edu/DouglasClements, http://www.researchgate.net/profile/Douglas_Clements/, and http://portfolio.du.edu/dclemen9