Posted on August 8, 2022October 11, 2023 by

August 8, 2022 8:00 am

Creating Collaborative Math Classrooms

Dr. Bill McCallum, co-founder and CEO of Illustrative Mathematics, discusses how the theme of collaboration runs through the program’s design, creating dynamic learning environments for today’s students.

Collaboration is a core value at Illustrative Mathematics. Creating a high quality instructional system — with curriculum and professional learning — is complex work. The demands of mathematical coherence and pedagogical appropriateness often pull in different directions; you can have a curriculum that is mathematically correct but not engaging for students, and you can have a curriculum that students enjoy but where they are not learning grade-level mathematics. We think IM K–12 Math has achieved the perfect balance between coherence and engagement, and we got there by having mathematics experts and educators working together, reviewing and critiquing each other’s work, and coming to a consensus around tough questions.

Collaboration in writing the curriculum and professional learning

A good example of the balance between mathematical and pedagogical priorities is the tuna casserole activity in Lesson 2.6 of Grade 6 in IM 6–8 Math. Recipe contexts are good for learning about equivalent ratios because the ratios between various quantities in the recipe have a real world meaning (the flavor of the recipe) and because recipes are often scaled or cooked in containers of different sizes. The tuna casserole example provides a rich arithmetic context, particularly with fractional quantities, thus affording important skill building as students work with the ratios in the recipe. Furthermore, the extension activity, Are You Ready For More?, depends crucially on the fact that the vessel is rectangular, and gives students an opportunity to reinforce and use prior knowledge about area and volume. This is an example of the sort of collaborative thought that went into all the IM lessons.

Another sort of blending of expertise occurs when we try to put research about pedagogy into practice. Research recommends a problem-based approach to instruction where students have a chance to work on problems for themselves and the teacher synthesizes learning afterwards. But the practical experience of the teachers involved in writing our curriculum reminded us that you have to make the problem-based instructional model explicit and learnable. This led us to develop a carefully curated set of instructional routines, which help teachers and students manage problem-based instruction without getting bogged down in logistics, and which teachers can learn over time as they become more familiar with the curriculum.

“Because students are sharing their thinking, students using less efficient strategies will see other students using more efficient ones and learn from them. It also works the other way around. Students using more efficient strategies deepen their understanding as they explain those strategies.”

Dr. Bill McCallum

Collaboration in the IM classroom

The principle of diverse teams collaborating extends to what goes in a classroom using IM. Many of the activities are designed so that students can use a range of strategies to solve them. Because students are sharing their thinking, students using less efficient strategies will see other students using more efficient ones and learn from them. It also works the other way around. Students using more efficient strategies deepen their understanding as the explain those strategies.

The Mathematical Language Routines in IM K–12 use collaboration to help all learners, including English learners, produce mathematical language to enable rich discussion of mathematical ideas. For example, in the Information Gap students work in pairs where each student has different parts of the mathematical problem and they ask each other questions to collaboratively solve the problem. The structure of the routine is designed so that students must formulate specific mathematical questions in order to get the information they need.

The collaborative learning embedded in the IM instructional model is particularly important in supporting culturally responsive pedagogy. Collaboration comes naturally to many cultures that are often marginalized in the classroom. Giving students an opportunity to share what they bring to the classroom builds their sense of belonging and self-efficacy.

Collaboration with partners

Another way in which we live out our value of collaboration is in working through IM Certified distribution partners such as Imagine Learning. Again, each partner brings something different to the collaboration. IM brings its expertise in curriculum and professional learning, whereas Imagine Learning brings a digital platform that makes teachers’ lives easier and supports student engagement with additional features such as Student Spotlight Videos.

The future

The next phase of IM’s journey involves collaborating with schools and districts around implementation support. We plan to build an implementation support ecosystem around our curriculum and professional learning that provides schools with a coherent suite of products and services that all work together to help teachers bring about our vision of a world where all learners know, use, and enjoy mathematics. Stay tuned for more exciting news about these plans over the next few months!

About the Author — Dr. Bill McCallum

Bill McCallum, co-founder of Illustrative Mathematics, is a University Distinguished Professor Emeritus of Mathematics at the University of Arizona. He has worked both in mathematics research, in the areas of number theory and arithmetical algebraic geometry, and in mathematics education, writing textbooks and advising researchers and policy makers. He is a founding member of the Harvard Calculus Consortium and lead author of its college algebra and multivariable calculus texts. In 2009–2010 he was one of the lead writers for the Common Core State Standards in Mathematics. He holds a Ph. D. in Mathematics from Harvard University and a B.Sc. from the University of New South Wales.

Posted on June 9, 2022October 11, 2023 by

June 9, 2022 8:00 am

THINK Points Add Up to Make Change

Imagine Math’s THINK points program allows students to earn rewards for themselves, their class, and charities by completing lessons.

What motivates you to work harder? I knew I was getting closer to middle age when I realized the harder I worked, the better I’d sleep — motivation level 10: unlocked. Sometimes motivation comes in the form of little bonuses (ahem, dessert), sometimes it’s a healthy sense of competition, and sometimes the prospect of a warm, fuzzy, ‘do-gooder’ feeling is what gets us to tackle a challenge.

It turns out that kids and adults aren’t that far apart in this respect; Imagine Math has demonstrated as much with its THINK points program. This innovative motivation system inspires students to learn by helping develop problem-solving skills, perseverance, and confidence. As students work through their Imagine Math lessons, they earn THINK points. THINK points are awarded for completing lessons, with additional points awarded for performing well. Students can use their points to design and accessorize their Imagine Math avatar, contribute to classroom goals (pizza party, anyone?), or donate money to students in need.

Earn, See, Spend

The points students earn by working through lessons are applied to their total number of points after they have completed the entire lesson, which helps keep them motivated to finish the full lesson before spending their points.

They can view their points on their home screen and the Class Leaders dashboard. Students can see the number of THINK points they’ve earned in the current lesson, the total of the points they’ve earned this year, and the number of points available to spend at the moment (grand total minus points already spent).

867 Average THINK Points Donated Per Student

The points leaderboard shows a hierarchy of who has earned the most THINK points that week and who has completed the most lessons. It updates every 15 to 30 minutes and resets every Saturday evening, only displaying the number of points each student has earned for the current week. It’s designed to continually motivate students and give each student a fair chance to be at the top for that hour, day, or week.

As a reward and part of what makes Imagine Math so engaging, students get to choose how they’ll spend their hard-earned THINK points. Some like to build out their avatars, expressing themselves with different skins, features, and accessories. Others are motivated to contribute to the teacher-established classroom goal, and an inspiring number of students opt to transfer their points into monetary gifts to charity. The charity calendar changes month to month, exposing students to a variety of opportunities to make a difference in their world.

“I wanted to be the No. 1 on the leaderboard in the state of Texas, so I had to do a lot of lessons – and that’s how I racked up the points. It makes me very proud that I can be of some help to the people in need.”

Yash Anand

Imagine Math student, Vista Hills Elementary

THINKing of Others

Imagine Learning is proud to report that 2021–2022’s students donated to 29 beneficiary charities, choosing to transform their math achievements into an impressive $83,060 for worthy causes! (Cue Whitney Houston because we, too, believe ‘the children are the future.’) It’s an incredible testament to their characters and their efforts to advance their learning, and as a bonus, it gives teachers a morale boost.

Tracy Gonzalez, a 4th-grade math teacher at W.C. Andrews Elementary in the Gregory-Portland ISD, says, “it makes me so happy, and I’m so proud of my students when they enjoy donating their THINK points to charities! They are helping towards a great cause every time they do so!”

The American Red Cross Tornado Relief Fund was one of the partner charities this year. Vista Hills Elementary student Yash Anand was the top donor in the nation, earning a remarkable 1.6 million THINK points to contribute to the fund.

“I wanted to be the No. 1 on the leaderboard in the state of Texas, so I had to do a lot of lessons – and that’s how I racked up the points,” said Anand. “It makes me very proud that I can be of some help to the people in need.”

Find What Drives Them

Students should be celebrated for working hard, whether they’re in it for the avatar, the parties, the competition, or the good karma. Their motivation can be as personal as the learning path they’re on, just as long as they also have a meaningful exploration of (and growth in!) mathematical understanding.

About the Author — Kallie Markle

Kallie Markle lives in Northern California with her family of humans, house plants, and dogs. The humans take up the least amount of space. Before joining the education world, she wrote her way through national parks, concerts, tourism, and brewing.

Posted on June 30, 2021October 13, 2023 by

June 30, 2021 8:00 am

Engaging Families in Math Learning

Family members are important partners in student learning, but how do we best to engage them in the learning process? Imagine Learning undertook a two-year-long research study, and these are the results.

Educators know that parents and family members are important partners in student learning, but some may not be aware of how best to engage family members in the learning process.

To help answer this question, Imagine Learning undertook a two-year-long research study, specifically around middle-years mathematics learning with a focus on third-grade students and their families.

At the outset of this study, Imagine Learning positioned family engagement in math learning as a design challenge, not a social problem. Imagine Learning did not want to perpetuate the idea that family engagement with low-income, Black, and Latino families is a social problem, meaning the problem resides within families and needs to be solved. Instead, the work was framed with an asset-based lens, which acknowledges that family members want to and do support their children in learning mathematics.

To partner and collaborate with family members to increase student academic achievement, it is essential for educators to support families and, most importantly, know how to recognize, honor, and acknowledge all efforts made by family members throughout the learning process. This is particularly important with low-income, Black, and Latino families, whose efforts supporting their students have commonly been unacknowledged or leveraged in mathematics.

By redefining family engagement and partnership as a design challenge, a pivotal change happens, in which family members — specifically those from low-income, Black, and Latino families — are properly seen and recognized as a child’s greatest asset in the learning process.

Our recent white paper describes the lessons learned from this study, which educators everywhere can use to further engage families as collaborators and partners in all learning, but particularly in math learning.

Here, we’ll share the research study’s five key lessons — “Lessons to Design By” — that may help other educators develop or further enhance approaches for increasing family engagement in mathematics, building stronger community relations, and accelerating academic achievement for students.

parent congratulates child with a high-five

Key Lessons and Takeaways for Engaging Family Members as Partners and Collaborators

As a result of this study, Imagine Learning determined five key lessons related to the importance of communication, establishing trusting relationships between schools and families, and inviting families to be partners in supporting their child’s learning. These lessons should all be considered when working to engage families as partners and collaborators in learning.

Lesson 1: The Importance of Invitations to Families. Family members do not always feel that teachers and schools welcome their involvement as educational partners, and this can be a particular issue for low-income families and families of color, even though they reported wanting to be engaged in their child’s math learning. Helping families feel welcome and as equal partners in their child’s learning is an important contextual factor that needs to be considered.

Lesson 2: The Importance of Family–Teacher Trust. Family members trust teachers as the primary source of information regarding their child’s learning. For families to engage with online supports or other resources, messaging about their value and importance needs to come from the teacher. This trust goes both ways, so building relationships of trust in which family members can share concerns is an essential precondition to a successful design. Research finds that low-income families of color and families of varying linguistic backgrounds are often underrepresented in school-level decision-making and family involvement activities. This speaks to differing needs, values, and levels of trust rather than families’ lack of interest or unwillingness to get involved.

Lesson 3: The Importance of Family–Teacher Collaboration. In general, teachers are frequently only in touch with families when discipline issues arise. Hence, there is value in establishing collaborative relationships and proactively communicating with positive and learning-related news early and often. Families value invitations to discuss their child’s learning as an equal to educators. Family members demonstrated that they sometimes do not feel like equals in decision-making relative to their child’s education, which supports the notion of empowering parents as partners in supporting learning. Not all parents know where to look for help, and some may not come to the school for assistance when they are not sure how to help their child.

Lesson 4: Honoring Family Experience Over Theoretical Models. To fully engage in community work with restricted resources, challenges with poverty, public trust, and language barriers requires significant energy, attention, and nuance. This is particularly true in math, as this is a subject in which parents and families tend to have less confidence in their content knowledge and skills, and are therefore more reluctant to get involved in their child’s learning at home.

Lesson 5: Community-Based Work with Families is Resource-Intensive. Implementing this project was resource-intensive work and given that, Imagine Learning concluded that there is a need to identify additional strategies that are more cost-effective in building math efficacy. We know that there is a need to develop community-specific, family-responsive designs, and one potential solution could be to provide coaching and support to families at the community level instead of individual schools.

Imagine Learning continually seeks design solutions to support the relationship between teachers, families, children, and mathematics content, as we recognize that family members are the greatest asset in children’s learning and development. Learn more in our white paper about this research study and the effects COVID-19 also had on the body of work.

Posted on June 19, 2019October 12, 2023 by

June 19, 2019 8:02 am

Growth, Grit, and Gaming: Video Games in Education

How game-based learning engages students, improves academic outcomes, and helps to build grit and a growth mindset along the way.

Recent studies show over 90% of American children play video games. Ask a parent their opinion of children and “gaming” and you’re likely to get a response about the amount of time kids are wasting. Additionally, many educators express concern about the negative impact of gaming, but some researchers are working to change these perceptions, especially around the idea of gaming and education.

“Children tend to be more engaged in learning when we incorporate gaming into lessons,” expressed Patrick Efird, a curriculum game designer at educational technology provider Imagine Learning.

And Efird would know. A self-declared video game aficionado, Efird taught middle school for five years. “I incorporated video games into the classroom whenever possible,” he explained. “My students loved the gaming components of their learning and I believe it helped them dig deeper into the material, retain what was being taught, and develop a belief that they could learn if they worked hard at something.”

Growth Mindset and Gaming

Efird isn’t alone in his beliefs. Scholar Carol Dweck found that video games can play an important role in supporting growth mindset, or the belief that an ability to learn is not fixed but can grow with effort.

In Dweck’s research, students who played a video game with rewards for productive struggle stuck with the game longer, were more engaged, and used more strategies than students who received traditional “level completion” rewards.

Video game experts believe video games can support growth mindset in a variety of ways.

Leveling up. Students are feel a sense of accomplishment when they reach goals, and are motivated to endlessly engage in video games as they advance, learn, and achieve in the program.
Learning from mistakes. Games are a safe place for students to make mistakes, learn, and ultimately succeed over time.
Visualize growth and progress. Games utilize features such as maps, treasure hunts, and statistics to show a player where they have the potential to progress. Visualizing where a player can go motivates them to continue trying.
Experiencing growth. Students experience growth as they have opportunities to evolve, take on new abilities, or earn add-ons when they stick with their task in the game.
External rewards. Students who persist at tasks receive rewards for trying, motivating them to keep striving.
Real-life growth. Apps with game-like elements, such as Fitbit or Happify, transfer growth to real life by tracking progress towards physical, emotional, and cognitive goals that benefit users.

Grit and Gaming

Video games can also help students develop “grit,” or the passion and perseverance to work towards long-term goals as described by Angela Duckworth, PhD. Some argue that video games develop grit as players “follow the rules, acquire and practice skills, and apply those skills to achieve specific goals.”

Duckworth posits that “students may need help from supportive others to become comfortable with facing, accepting, and learning from failure.” Video games can play the role of the “supportive other” by incorporating positive messaging.

Efird suggests that positioning messages in educational video games that “praise effort despite outcomes, show evidence of growth, and acknowledge players for tasks accomplished or improvements made” can support students to persist in pursuing tasks. Additionally, live-supports—such as online, certified teachers available to students using digital instructional programs—can provide needed support while fostering perseverance and determination.

“Game-based learning engages students, and research indicates strong correlations between student engagement and student achievement across all levels of instruction and subject areas.”

Sherri Walker

Imagine Learning

Engaged Students Achieve

Ultimately, educators want to know students are learning and achieving.

Game-based learning engages students, and research indicates strong correlations between student engagement and student achievement across all levels of instruction and subject areas.

Studies have also shown that when students are engaged in their learning, they are more focused, more motivated, and have more meaningful learning experiences. Educators agree, ranking “student engagement and motivation” as the highest driver of achievement, good attendance, good grades, positive behavior, high school graduation, and readiness for postsecondary education.

In the end, utilizing video games in education can be a powerful tool for teachers to engage students and help them learn and achieve. “I believe we can use video games in classrooms to help students learn that they can accomplish whatever they put their energy into,” shares Efird. “I know as a kid, I would’ve been even more engaged in what I was learning in the classroom if games were utilized. I’m pretty sure there are other students out there today who are just like me.”

Engage More Students

Give gaming in education a try with Imagine Math Facts, where students gain automaticity with basic addition, subtraction, multiplication, and division.

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