Posted on April 12, 2024April 30, 2024 by Imagine Learning Corporate

April 12, 2024 10:38 am

Open Any Door with Critical Thinking

Workplaces are changing fast. Jobs with “routine” work have decreased and there’s a much bigger emphasis on soft skills like the 4Cs. In part one of our four-part series, discover how critical thinking unlocks future pathways for students and how STEM in particular fosters it.

Ever thought that studying STEM (science, technology, engineering, and mathematics) is only useful for students considering careers in science or tech? If so, then you wouldn’t be alone — but it’s time to change that perspective.

The truth is, workplaces are changing fast, and some traditional skills are becoming less relevant today. Growing digitalization of roles, AI technologies, and new communication methods demand a totally different set of skills fit for the modern workplace (Thornhill Miller et al., 2023).

This is where STEM subjects come into play. By studying STEM at schools, students pick up the soft skills that are exactly what employers look for today. Not only do these soft skills make the transition from education to the workplace smoother, they also open the door to any career — whether that’s a STEM-related role or not. These soft skills are commonly referred to as 21st-century skills, or the 4Cs: critical thinking, collaboration, communication, and creativity.

“The world is incredibly complex. It’s like a giant jigsaw puzzle, and I use those fundamental [STEM] skills to find all of the puzzle pieces and put them together in a way that makes sense to me.”

Noby Leong

Chemist

Critical Thinking: The First C Unveiled

What do we mean by critical thinking? And why does it take center stage? Critical thinking is about analyzing and evaluating information to make sound conclusions. It’s more than solving math problems or conducting experiments — it’s about challenging assumptions and seeing beyond the obvious to become an active, engaged problem solver.

In the classroom, this might look like students debating the best approach to solving a problem or designing multiple hypotheses to test an experiment. Ultimately, it’s a skill that prepares students for overcoming real-world challenges in any field.

From STEM Classrooms to Any Career

So how does mastering Pythagoras’ theorem or challenging scientific approaches benefit students who don’t want to pursue STEM? The answer lies in the universal transferability of the critical thinking involved. Whether it’s strategizing a marketing campaign, improving customer service protocols, or writing compelling narratives, critical thinking is woven into the fabric of every career you can imagine.

The message is clear: critical thinking is more than an academic skill. It unlocks potential across all disciplines and all future pathways for students.

In the next installment of our series on the 4Cs of STEM, we’ll explore the power of collaboration and how it shapes the leaders of tomorrow.

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Posted on November 22, 2022October 11, 2023 by

November 22, 2022 8:00 am

The Four Cs of STEM in Computer Science

Celebrate Computer Science Education Week and the international Hour of Code by exploring the four Cs of STEM. Students can learn about real-world applications of the four Cs in computer science from Chicago to Mars and roll up their sleeves for their own practice with Imagine Robotify, a fun online quiz, or an adventurous robot named Axel.

Digital tools, automation, network security, and AI are shaping our future. Recognizing the increased demand for digital literacy in the workforce, more than 500 CEOs recently petitioned education leaders to prioritize computer science instruction in K–12 schools. The U.S Department of Education followed that by launching the YOU Belong in STEM initiative to enhance science, technology, engineering, and math (STEM) education for all students.

Computer Science Education Week, December 5th–11th, is the perfect time to get involved! A great way for educators at any grade level to explore STEM (which includes computer science!) is to teach its essential skills. Four of the most important abilities in STEM are critical thinking, creativity, collaboration, and communication, also known as the four Cs. These skills are necessary for 21^st-century college and career readiness, in STEM and beyond:

Critical thinking involves analyzing systems, assessing evidence, integrating prior knowledge to make connections to new situations, and the ability to interpret information.
Creativity is necessary to come up with new ideas. The ability to “think outside the box” when challenged, improve ideas, work within constraints, and learn from failure are all components of iterative design, which require creativity!
Collaboration means working in groups, sharing responsibility, and making decisions and compromises.
Communication is critical in our global world. It’s the ability to express ideas, understand their meaning, and demonstrate concepts to different audiences.

The four Cs in the real world

Computer Science Education Week presents a great opportunity to learn with your students about how the four Cs are applied in the real world. Here are three examples.

1. Trashbot

Urban Rivers creates solutions to transform urban waterways, including a volunteer-controlled robot called Trashbot that cleans the Chicago River. The creators of Trashbot used critical thinking to recognize the complex system in which Trashbot would operate while also ensuring the safety of wildlife, civilians, and infrastructure.

The team realized the robot would need to be controlled because an automated robot could pose a risk to wildlife habitats. However, financial and personnel constraints made having a manual operator 24/7 impossible.

Urban Rivers tapped into their creativity and learned from previous failures to find a solution: volunteers could control Trashbot throughout the day to clean the river safely. Next, they collaborated with volunteers to make the solution possible, using media communications to teach them how to operate the equipment. Now, Trashbot is run by community volunteers who can clean up the Chicago River regularly.

Watch this video to learn more with your students.

2. UTM Project

An unmanned aircraft system (UAS) consists of drones or satellites, and the potential uses are limitless! NASA’s UAS Traffic Management (UTM) project aims to find ways for low-altitude drones to operate in large numbers, enabling businesses like Amazon to offer drone delivery services.

The UTM team uses critical thinking skills to identify problems before they arise, such as how extreme weather could affect a drone or what happens if it is lost. The UTM project also researches how future technology would be managed. Drone technology could reduce traffic, fight wildfires, and perform dangerous tasks.

The project is complex, with many interested partners in corporations and governments. The UTM team knows collaboration and communication are the keys to the project’s success, allowing them to include the needs and challenges of different groups in the research and share that research with the public.

NASA’s UTM website provides up-to-date information and updates about the project.

3. Mars Rover

The Perseverance Mars Rover roams the red landscape of Mars with the help of NASA’s scientists. On one mission, the team was challenged to drive Perseverance as far as possible. However, the rover would be self-driving, so the team needed it to drive effectively while avoiding obstacles.

The amount of possible paths to take on Mars is endless, but some paths are better than others. That’s why critical thinking is crucial to the mission: it’s used to assess the situation, make connections, and interpret data. Critical thinking also helps the team learn from previous Mars missions and determine new solutions.

Using creativity, they can overcome obstacles and imagine new ways to program the rover. The team coding Perseverance also understands how to collaborate. By working with teams across NASA and using clear and thorough communication, they can share and interpret data to put the rover on the right path.

Empowering the next generation

The significance of the four Cs of STEM is apparent across these three real-world examples. Critical thinking, creativity, collaboration, and communication are key to any mission. From cleaning up a river to exploring space, computer scientists use the four Cs daily.

What about the future STEM professionals in your classroom? Students can start their own journeys to Mars and practice the four Cs by celebrating Computer Science Education Week and participating in its international Hour of Code.

Hour of Code

Hour of Code is – you guessed it – a one-hour introduction to computer science, using activities to show that anybody can learn the basics. If your school doesn’t already have a coding program, a few fun options to spark engagement and pique students’ interest could include:

Testing their computer science brain power with a themed quiz on Kahoot
Coloring Axel the robot’s many adventures with downloadable coloring pages
A special Hour of Code Imagine Robotify project. If you’re using Imagine Robotify, head to the projects tab on your menu to find an Axel drawing project in either Python or Blockly. Students can learn to create programs to draw common shapes on a coordinate plane.

Whether you celebrate Computer Science Week and Hour of Code with robots and crayons or by exploring essential skills, you’ll create more STEM possibilities for your students’ futures.

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 March 15, 2022October 12, 2023 by

March 15, 2022 8:00 am

Empowering Girls to See Themselves in STEM

When the goal is to encourage more girls to pursue an interest in science, technology, math, and engineering, words and representation matter.

If asked to name a famous female scientist, who comes to mind? For many of us, it is likely Marie Curie, who is the most well-known for a reason. She developed the theory of radioactivity and was the first female scientist to win a Nobel Prize, among other achievements.

Thanks in part to the critically acclaimed movie, Hidden Figures, you also may have thought of Katherine Johnson, the Black mathematician whose work helped the first manned spaceflight land on the moon.

Both Curie and Johnson paved the way for future women in STEM fields.

While we should absolutely celebrate these remarkable women, we also need to reflect not just on why most of us are able to name only one or two, but also on the impact of the lack of female scientist household names.

On a basic level, we can assume there are fewer women in STEM careers because, as a group, they do not see themselves represented in those fields. This becomes a feedback loop — girls grow up not seeing women in STEM, they don’t pursue STEM careers, and the cycle continues.

three students learning about science in the classroom

Words matter.

Catherine Cahn, founder of Twig Science and President of Core Curriculum at Imagine Learning, recently remarked on the power of language to both empower and exclude women and gender-diverse individuals. If a company is looking to hire a new CFO and they say in a meeting, “Where are we going to find him?”, that one tiny pronoun tells everyone exactly who they picture (and don’t picture) in the position.

It is like when you mention your new (female) doctor by title and are asked, “did you like him?”

These words contribute to the “persistent, subconscious images of male mathematicians and scientists that start at the earliest ages, [which] may be one explanation why girls enter STEM fields… at dramatically lower rates than boys.”

Teachers are in a unique position to disrupt this subconscious bias by being deliberate about language choices in the classroom. In order to make sure girls feel welcome in the sciences, we should also reflect upon how we represent scientists and mathematicians.

Representation matters.

Here are three ways we can better represent girls and women in STEM:

1. This month (and every month), share information about prominent women in STEM

Share biographical information about women in the sciences in your classroom, on social media, and with the kids in your life. Tell them about Curie and Johnson, of course! But also tell them about Jane C. Wright, who contributed to chemotherapy developments; Tu YouYou, who saved millions of lives with her malaria treatment; Françoise Barré-Sinoussi, who discovered HIV; Lydia Villa-Komaroff, who helped find a key molecule in Alzheimer’s diagnosis and treatment; Mae C. Jemison, the first Black American woman to travel to space; and many more.

2. Connect with women working in STEM fields

They may not be as well-known as Marie Curie and Katherine Johnson, but the women in your community working in STEM fields are just as extraordinary – and possibly even more inspiring. We know that “girls who see women working in STEM careers are more likely to consider a career in science, technology, engineering or math.” Whether you have a friend working as a computer scientist, a cousin studying biology, or you make a connection at a local Society of Women Engineers event, being able to talk to a “real” woman in a STEM field could influence a young girl’s future choices.

3. Ensure that girls see themselves in the curriculum

If we want girls to picture themselves in STEM careers, we should start with the curriculum. That’s why Imagine Math PreK–2’s cast of characters is designed so that every student can see themselves reflected in the program. These characters narrate and demonstrate concepts to students in an engaging virtual environment created to look like the diverse world in which we live.

Ruby likes to play dress-up and wants to be an engineer when she grows up. As the main character in the Imagine Learning cast, she was intentionally designed to change the narrative about who excels in STEM careers.

Older Imagine Math students can design and customize their own avatars, so they can quite literally see themselves in their math program.

The more we normalize the image of females in STEM careers, the more young girls will picture themselves following in their footsteps. And just think, in a few years, we can add this generation’s names to a much longer list of famous female scientist household names.

About the Author — Ally Jones

Ally Jones is a California credentialed educator who specialized in teaching English language learners at the secondary level. Outside of education, she is passionate about fitness, literature, and taking care of the planet for her son’s generation.

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.