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A classroom is a small community where students come together to learn, grow, and prepare themselves for the future. What do you see in your math classroom? In my classroom, I see engagement in problem-solving, pattern recognition in making connections, and students having fun learning math. Creating a culture that follows the four Cs—check-ins, collaboration, connections, and communication—in my math classroom helps my students appreciate being problem solvers and math leaders.
Getting students started with exploring a concept using check-ins and enabling teamwork eases them into learning with less anxiety. Developing creative and critical minds is essential for students to become successful leaders.
Making connections and finding multiple ways to solve a problem through reflection and feedback help my students know that there is no one way to solve a problem. This culture of effective communication through reflection and constructive feedback lays the foundation of trust, deepening the learning experiences and building a stronger community.
Using the 4 Cs to Build Math Leaders
1. Check-ins. Students use a check-in activity to help them comprehend what they know to bridge their understanding to what they need to know. I use a simple graphic organizer such as an emotion check to understand how my students are feeling and a KWL chart, which sorts what a student knows, wants to know, and has learned about a topic, to help build clarity about the learning process.
Check-ins can also look like starting class with a question and encouraging more productive questions to understand what the students currently know and understand and what they’re struggling with in order to diversify instruction. Through the check-ins, I instill a culture of curiosity and a safe place to encourage my young students to begin their learning journey.
2. Collaboration. Working in teams can enhance student learning and lead to better focus and engagement. Collaboration can occur through peer-to-peer coaching, cooperative learning activities, or working on group projects to enable problem-solving and develop a deeper understanding.
I use strategies such as think-pair-share, which encourages students to think first, then pair up, and share their steps. Sometimes my students are surprised to find out that there are multiple ways to solve a given problem.
I enjoy the discussions in my class and encourage my students to work together to have debates on the real-world applications of math. (This article shares some great strategies to get students talking in math class.) Debate may seem out of place in a math class, but it encourages my students to think outside the box.
For example, while working on my class’s concept of interest, I organized a debate between groups to talk about simple interest versus compound interest. Then, we discussed which one they should choose if they were a borrower versus a lender. It generated an engaging conversation on loans, banking, finance, and more.
3. Connections. There are different ways to make connections to learning, which can build a critical and creative mindset. Students can connect with prior knowledge to bridge a new conceptual understanding that increases engagement in education and helps students relate to the content.
I encourage students to connect the concept taught to real-life scenarios. The word algebra always creates anxiety in my students. Connecting algebra to real life makes the unknown known. For example, connecting linear equations to shopping is something that most of my students enjoy. On top of everything, when they connect a problem such as “If one shirt costs $7, then how much will three shirts cost?” they realize that they have been finding the unknown all their lives.
Helping my students connect with the math concepts taught in class makes math learning relevant, and they start leading the way in solving problems.
4. Communication. Communication is vital in a math classroom. Students can communicate during discussions through questioning, working on collaborative projects, sharing problem-solving strategies, and, most notably, reflecting on “What and how did I learn today?”
Discussing a concept helps students develop a deeper understanding, and using questions such as why and how allows my students to explore through different perspectives. It’s vital, for me as an educator, to understand how to generate effective questions to help my students learn and work together. I design several group projects to connect math to real life where my students work together to reveal the solution to the given problem.
For example, we would work on a project to bring out the entrepreneurs in us and design our futures by looking at investments, profits, and loans to learn about percentages, decimals, and interest. Some wanted to open a restaurant or manage a car showroom, while a few wanted to open their own bakery. This project ended with group presentations graded on a rubric based on effective communication.
Self-reflection is an excellent approach to communicating to yourself what you’ve learned, what you still need to work on, and what’s the best way for you to learn effectively. I also use journaling with PEMS, a tool that facilitates observation, to support my students’ emotional awareness.
Reflection through feedback and hours of contemplation can help a student know that there is no one way to solve a problem and thus help build a growth mindset. Using a simple framework can help boost this moment to think back and gear up for what’s to come.
The four Cs can help develop skills that our youth need to learn effectively and to feel confident in leading their learning.
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Many reports and research studies have documented the adolescent reading challenge — too many students are unable to learn and build new knowledge from the texts used in their subject matter classrooms. In addition to the challenges of general comprehension, reading in a subject area presents additional challenges that many students are unable to tackle on their own. For example, textbooks are dense with information — some important, some not so much. The chapters are long and packed with specialized vocabulary; assume background knowledge that students often don’t have; include various types charts, tables and graphics; and are poorly organized, covering too many topics piecemeal. They are not structured like any other authentic reading. Students who read these textbooks are already learning many other new concepts and data, as well as thinking and reasoning in ways that are important to the subject matter. And many of these students have not developed sophisticated comprehension skills for learning from text. So not only do they need to learn the content, they need to learn how to learn from complex subject-matter texts.
Although many content area teachers use a variety of texts in their classrooms, such as newspapers, articles, digital texts, and primary sources, textbooks remain the principal source of assigned reading in most content classrooms and in college.Textbook Reading Dilemmas
Over the past five years, we have worked with teachers in urban high school AP U.S. government and environmental science classes to develop strategies for helping students learn from textbooks. Through interviews and observations, we found that, although textbook reading is frequently assigned, many students don’t actually do it and, if they do, many don’t understand the most important content. Several things seem to contribute to this situation:
1. Many students tell us that they don’t read their textbooks because their teacher typically covers the important information during class. It’s easier and more efficient for them to just listen than to struggle through a typical 20-40 page textbook chapter. For others, the challenge of reading a typical textbook assignment is so overwhelming that they give up before they even begin.
2. Students who struggle with reading often don’t recognize that they don’t understand. We interviewed students who described reading homework as simple but couldn’t explain or synthesize what they’d read. They thought that because they could pronounce the words, they understood. These students often skim or skip over challenging sections, and they don’t monitor their understanding along the way.
3. As described above, content-area textbooks pose unique reading challenges for many students: density, structure, specialized vocabulary, background knowledge, or lack of coherence. Many students haven’t been taught or haven’t developed the skills and strategies needed to read this type of complex text.Strategies for Tackling Textbook Reading
Content teachers are in a unique and enormously powerful position to help students navigate these complex texts so that they can become useful sources for learning. These teachers deeply understand the most important information and concepts students need to learn, and they can identify the background knowledge and ways of thinking needed to make sense of the text. Below are several strategies we have developed with our partner content teachers to help students learn from the textbooks used in their classes.Identifying Purpose
Given the length, density, and broad-ranging topics found within textbook chapters, we suggest that subject matter teachers preview the material and strategically select sections that align with specific learning objectives. Then teachers should give students a specific purpose so that they know why they are reading and what they are supposed to learn. As novices in the subject area, students often can’t prioritize among all the information included in textbooks.Giving a Good Reading Homework Assignment
Following on the importance of setting a purpose for reading and identifying specific sections of texts to read, teachers can help students by taking time to give clear, focused homework assignments. Instead of telling students, “Read Chapter 12 for tomorrow,” teachers can include three parts to every homework assignment: the purpose for the reading, how students should approach the reading, and how students will use the information. For example:
If we were to look at our schools and communities through an ecological framework, we can say that educators are part of a learning ecology. In this ecology, I believe that our most precious natural resources are imagination and wonder. I also believe that the best way to cultivate imagination and wonder is through art.
A good educator introduces wonder by revealing the unexpected connection it has to our lives in an otherwise remote subject, or by showing the ordinary to be extraordinary. Wonder leaves us with a sense of fascination about mysteries yet unsolved or questions yet unanswered. It leaves us with renewed appreciation of the ordinary things before us.
The primary goal of art is to introduce wonder. Unlike other subjects, art strives to leave us with a sense of open-endedness and revelation. Art reveals patterns and connections that would otherwise remain unnoticed.
Wonder motivates everyone to learn and dig deeper. In a learning ecology that focuses on wonder, an artful approach can be introduced in any subject area, especially when lessons are framed by big questions that remain unanswered or even are unanswerable. Every subject is full of surprising connections and patterns that invoke meaning for us.
John Seely Brown introduced the idea of a “learning ecology” in his essay Growing Up Digital. In this essay, Brown uses the web as a platform to explore the ways that a community of learners creates — giving and taking in a way that enriches the learning environment. Brown shows us how web culture encourages users to share information for free with the expectation that they will be able to access free help and information when needed.
Brown’s learning ecology is driven by information as its most precious resource. Like in a natural ecology, this precious resource is cycled through the environment so that all organisms benefit.
Our job as educators is to make our primary resource – wonder – the essential learning incentive and outcome. This precious resource of wonder will feed our students, and in turn, our students will enrich their communities when they graduate with future public projects, businesses, cultural opportunities, and the exchange of ideas that in turn will foster wonder and curiosity for future generations. Our students and communities will pass on wonder in much the same way oxygen, water, and nutrients cycle through a well-balanced ecosystem.
How do we do this? Here are several ways to use art to cultivate imagination and wonder in a learning ecology.1. Develop Your Art Programs
Not only is it important for students to have the benefit of art education, teachers in other subject areas can also benefit from the way art introduces wonder into any subject area. Art is a way of thinking and not just doing. It involves changing perspectives (both literally and metaphorically) and reframing how we think, feel, and see a subject or an idea.2. Begin and End With the Big Questions
Once, when Albert Einstein was a child, his mother wished him goodnight and turned off the lights. Einstein wondered, “Where does the light go?” This is a question that any child or adult can wonder about, and although it takes genius and hard work to answer it, it is the type of question we should not be afraid to share with our students as a way to introduce wonder at any grade level.3. Model Curiosity for Your Students
As an art educator, I sometimes wonder at the way we perceive color and how it changes depending upon the surroundings and light. I share this sense of wonder with my students despite knowing that it might seem childish or make me appear unwise and unsophisticated. So what? What are the big questions you have about your subject area that might seem risky to share? What are the odd, strange, or mysterious aspects that still draw your attention despite years of experience in your subject area?4. Create Assessments That Reward Good Questions, Not Just Good Answers
What if we framed our exams as a series of answers and asked our students to ask questions? How do we take rote, clichéd statements such as, “Columbus discovered America in 1492,” and reveal them to be fraught with more misinformation than relevant information. Asking the right questions is the basis of good scholarship and query, and these questions are motivated by wonder.5. Develop Different Ways for Measuring Success
Success in our culture is modeled on the person with answers, but maybe we should look towards models and people who allow themselves to get lost, explore, and to readily say those three magic words: “I don’t know.”6. Find Solace in the Arts
Teaching our students to live with unanswered questions can be difficult, and many of us find a remedy for our suffering in music, literature, poetry, and cinema. Yet the remedy we find in the arts is not in the answers they provide, but it’s with the measure of solace that comes when we feel at peace with wonder and the unanswerable.
School counselors have a knack for being creative and finding new and innovative ways to support students’ social and emotional growth and well-being. Arts integration, the practice of integrating visual art, dance, drama, and music into academic content areas, can also be an impactful way for counselors to support students’ social skills, emotive connections, and creative expression in core curriculum, small-group, and individual settings.
While all of the following lessons and supportive strategies can be used interchangeably, they’re most supported in the medium listed below due to the level of engagement, students’ emotive reflection (especially in crisis), and their willingness to share private feelings.
Core Curriculum Lesson Benefits and Activities
Students can work on social skills in creative ways: Cooperation and communication are some of my favorite social and emotional (SEL) skills to support with the arts. When students have an opportunity to create, they become more invested in the process. This sometimes causes disagreements, emotional shutdowns, and frustrations because of their enthusiasm with the project they’re working on.
Observing the conflict in real time allows me to have authentic conversations on cooperation and communication with students, thus helping them with strategies to be more effective at cooperating and communicating with their peers.
Sometimes students need help with taking deep breaths, empathic listening, compromising, or cooperating. It’s an opportunity for growth because assisting students with these skills allows them to complete projects while learning about their communication and cooperation strengths.
It helps your relationships with teachers: Since using arts integration, I’ve found ways to use SEL and art standards to support some grade-level standards. Teachers are impressed when I do a whole-group lesson that not only focuses on my ASCA mindsets and behaviors and art but also reinforces a standard they’re working on.
In one fourth-grade lesson, teachers had just introduced the Revolutionary War, and students had a general understanding of the main historical figures involved. During a school counseling lesson, I shared three paintings depicting events that occurred during the war. Students selected one painting that they found interesting and completed a “see, think, wonder” written reflection about it.
Then I placed students into groups by the painting they selected. During this activity, students practiced active listening and perspective taking while discussing their thoughts and feelings about the painting. I monitored the groups and gave feedback during their conversations.
Teachers also use arts integration in math and science content areas. This can be done in school counseling as well, especially with collaborative science or math projects. However, I’ve found that social studies and English language arts (ELA) are the easiest content areas to connect to SEL and arts integration because there are more standards we can cover that focus on human characteristics such as empathy, kindness, perseverance, and resilience, as well as cooperative skills.
It allows you to be creative: It’s easy to get stuck in the story and worksheet lessons in school counseling. While there are many amazing SEL children’s books to choose from, using a worksheet to reinforce a concept isn’t exciting for anyone. I get to have fun, be creative, and think of ways to use visual arts, drama, dance, and music in my lessons.
Feelings and songs: Analyze the lyrics of songs by reading them to students, allow students to hear the instrumental version, and then allow them to listen to the version with words. During each listening segment, have students draw how they are feeling. They should draw a total of three times. After they’ve finished drawing, have students reflect and share how different parts of the song made them feel and how that impacted their drawings.
Music cooperation and science: Using palm pipes, have students create a song together by exploring palm pipes and figuring out how to use them. Once they realize that each palm pipe creates a different note, they can practice different songs (provided with the purchase of palm pipes). After they’ve practiced a few times, have them work together to create their own song and perform it for the class. Students love this lesson.
Small-Group Benefits and Activities
Insight: When students create something, especially with visual art, I’m able to gain insight into them that I may not have gotten playing a game or just talking. I may learn more about their feelings or social and personal interactions based on what they’ve created.
Creative freedom: With so much emphasis on standards and standardized testing, sometimes it’s fun to just be able to make something without expectations.
Fluid conversation: It’s much easier to have candid conversations while we’re engaging in creative expression either together or side-by-side. Students are generally more open to share their experiences and feelings while engaging in the creative process.
Self-portrait/self-awareness: Have students create a self-portrait of their past, present, and future selves, reflecting on regrets and accomplishments in their past, how they’re doing in the present, and goals and dreams for the future. Students can share their work with the group.
Feelings puzzle: Using a puzzle template (or blank wooden puzzle), cut out the pieces individually and distribute them to each member of the group until all of them are passed out. Allow students to draw the feeling of (insert feeling) on their piece(s) of the puzzle. Create the puzzle together once all students have finished their art.
Individual Benefits and Activities
Emotional regulation: Art is a helpful way to process feelings of anger, frustration, or sadness. Sometimes, children struggle with verbalizing or even understanding their emotions. Art can help them explore themselves.
Sharing vulnerabilities: Students who are afraid to share their fears or self-doubts verbally can use art to share private thoughts or feelings without having to verbally divulge them. This allows openness to happen gradually and helps students to feel more comfortable.
Processing trauma: With trauma, it’s often difficult for children to process any of their emotions at first. Making art allows them to navigate through the grief or anger process within their own space of comfort.
Molding clay: Sometimes students are not ready to share their feelings of grief. My relationship with them may be new, or they may not know how to process difficult feelings. Using clay or play dough is a way for students to process feelings of sorrow, sadness, and sometimes anger without having to talk. I usually keep it open-ended, allowing them to create symbols of their loved one, reflect on feelings, or sometimes just squish it. If they want to talk, I listen. If they want to sit in silence, I sit with them. I make decisions of support based on many factors: body language, verbal responses, tone, and facial expressions.
Paper toss: It’s important for children to release their anger, but the school setting isn’t always a realistic place to process extreme feelings. This is why I allow students to physically express anger in a safe space. For each thing that makes them angry, I have them draw it on a piece of paper (sometimes they have a lot of drawings). Once they finish their drawings, I let them crumple the paper up and throw it all over my room. It’s quite cathartic for them.
After they’ve finished and self-regulated a bit more, we talk about how to use that strategy in class: “No, you can’t throw paper all over the classroom, but you can draw something, crumple it up, and throw it away in the trash can.”
I also tell them that if they need some more angry time, they can come to my office to throw some paper.
As the competition amongst organizations has increased, adopting data-driven work culture has also become imperative for businesses.
However, often while integrating data science, organizations face the challenge of transforming digitally. This failure can be due to an absence of cultural adoption of data science within an organization, rather than a technical loophole. That’s why a planned strategical approach becomes necessary for building data-driven work culture.1. Leadership adopting Data Science:
For integrating AI or data science in any organizational set-up, the administration and the top management must be the first to accept that incorporating data is a necessity for improved business. An excellent example of leadership would readily amplify the involvement of employees towards accepting the new technology and acknowledging its presence, rather than viewing it as a threat. Once this leadership attains the comfort of propelling the institution with data science, management can guide its employees towards accepting the functionalities of data-science. By incorporating data-science, the top leaders can also monitor the market trials while launching the new product or services and will take evidence-based actions.2. Choosing the smarter metrics:
Often, the loophole in choosing smarter metrics could lead to the inability of organizations to adapt to a digital environment. By applying predictive accuracy, the organizations can be benefitted in planning out a strategy that would be better suited for understanding the competition process in an already competitive business world. By integrating data science in the current work culture, organizations would be able to organize and analyze the customer behaviors, up-gradation, and customer performance, while buying the products and services from the company. In this way, the organizations can examine the quality of services received by the customers, and which products or services are having more customer inclination and buy-out.3. Prioritizing Data Scientists-
It has often been observed that most of the time, the failure to integrate data-science amongst organizations is due to the gap between data analytics and business. Analytics is part of any organization which is looking towards transforming digitally; without the involvement of data scientists, this is unattainable. That’s why an approach must be built in aligning data analytics with businesses. This can be done by initially creating a highly porous boundary between the data scientists and businesses. With this approach, the organizations are rendered for instilling a rotational workforce that would alter as out of excellent staff and in-line roles, thus scaling up the proof of concept. Thus, integrating different functional areas with analytics would infuse domain knowledge and technical know-how amongst the organization.4. Fixing the basic data-access issues-
One of the often complained issues of business leaders, while moving towards digital transformation, is the inability to access the required amount of data. With only limited data available, the analyst faces difficulty in analyzing the data thoroughly. But this could be rectified by applying logjam. This means that organizations can grant universal access of data, to adjust one key measure, at a time, instead of slow-programs for organizing the data. This can also be achieved by constructing a standard data layer for anticipating the financial requirements, which would enable organizations to focus on the relevant needs.5. Quantifying Uncertainty:
Every new technology has a certain level of uncertainty, which is well acknowledged by organizations. However, addressing this uncertainty would not only help to make an improved decision but will also help in identifying the source of that uncertainty. By rigorously evaluating uncertainty, the organizations can have a deeper understanding of the data-driven models.6. Starting from small, going to bigger: 7. Data Science for Employees:
Data science is not only essential for understanding customer behavior but for enhancing data-driven organization work culture, the employees must be accepting the new technology. It is often observed that a lack of employee enthusiasm and expertise, becomes the reason for the data-driven transformation. So, to counter this thwart, the organizations are required to train their employees with the concepts of big data. This will not only make the employees more enthusiastic towards deploying their data-driven skills but also enable them to identify the gaps or the areas requiring urgent attention, without the involvement of leadership or experts.8. Offering Training Just in Time:
Offering training to employees before starting to transform the organizations digitally can enable them to gain an understanding of the functioning, methodology, and analysis required for data science. Thus, when the leaders plan out a strategy for organizational data-driven transformation, the employees can be more focused in delivering their inputs regarding the strategy, so that a finer deployment of data analytics can be possible.9. Trading Flexibility with consistency: 10. Making Analytical Choices:
Pardee School of Global Studies Redesigns Graduate Programs Changes consolidate degrees, offer new options in diplomacy, security
Ryan Wayne (GRS’18) started at the Pardee School of Global Studies in January and chose the new specialization in diplomacy, which he expects will make him more marketable once he graduates. Photo by Cydney Scott
Graduate students enrolling in the Frederick S. Pardee School of Global Studies in the fall will have three new degree programs to choose from.
“It’s a way of ensuring that no one leaves here without us being sure they are going to have both the breadth and the depth to fulfill what the strategic plan says we are going to do, which is to create the leaders of tomorrow,” says Adil Najam, dean of the Pardee School, and a College of Arts & Sciences professor of international relations and of earth and environment.
The school has redesigned and consolidated nine existing graduate programs to create the three degrees, while creating new in-depth specializations and options within those degrees:
• The flagship Master of Arts in International Affairs (MAIA) prepares students for a wide variety of careers over four semesters and offers specializations in diplomacy, international communication, global economic affairs, security studies, and religion and international affairs. “Before this, we didn’t have a degree that had ‘security’ in the name, we didn’t have a degree that had ‘diplomacy’ in it, but those were two of our biggest strengths,” Najam says.
• The Master of Arts in Global Policy (MGP) provides a grounding in core skills of global policy over three semesters while offering specializations in environmental policy, developmental policy, and international public health policy.
• The redesigned Master of Arts in International Relations (MAIR) is an early- to mid-career program for professionals with a few years of experience in the field. In most cases, the degree can be completed in two semesters, providing skills and knowledge students need to enhance their professional careers and impact.
The time seemed right to redesign the school’s graduate programs. “We looked at what we had and lots of things were excellent,” he says, “but now we had an opportunity to look at all of them again and say, how can we make them cohere. Let’s put a holistic strategy into this. And that’s what the graduate redesign is.”
Under the new degree programs, Pardee has designated four core courses that will be required of all graduate students: Fundamentals of International Relations, Quantitative Analysis for Global Affairs, Economics for Global Policy, and Negotiation and Diplomacy. (The first three were previously required in some degree tracks, but not others, and Quantitative Analysis is a restructured version of a previous course in research methods.)
“We went through and decided there were elements we thought people should have as core knowledge no matter which specialization they went down,” says Robert Loftis, a Pardee and CAS professor of the practice of international relations and Pardee director of graduate students.
The idea is not, for example, that students who take the quantitative analysis class are going to become “super statisticians,” says Loftis, a former US ambassador to Lesotho, but that in today’s world, all international relations students need to understand how to use and interpret data to support their policy recommendations and evaluate the claims of those they negotiate with.
The hope is that the required courses will also enhance a sense of community at Pardee, by allowing students to “get to know their cohort in these four classes, and they become part of your network during school, and more importantly, when you graduate,” Loftis says.
He points to two extracurricular events for graduate students that have already begun to enhance that sense of community: an off-site retreat, held at the beginning of the school year, and a trip to Washington, D.C., during spring break. On the Washington trip, “what we really focus on is giving them a chance to network,” he says. “Not, oh, can you give me a job, but, how do you break in, how do you market yourself, what are some different avenues? You can study it, but there’s something about talking to someone in person.”
The graduate students who entered Pardee in January were given the option of enrolling in the existing program or switching to the new one that formally begins in the fall.
One of them was Ryan Wayne (GRS’18), who graduated from California State University San Marcos with a degree in political science. “I initially applied to the Pardee School with the intention of focusing on the Middle East and North Africa, specializing in security studies,” Wayne says. “I was delighted to learn of the new specialization for diplomacy. It grants me the freedom to explore the issues that I am keen to, while offering me the ability to diversify my education, making me more marketable once I graduate.”
Another goal of the newly redesigned graduate programs is to raise the school’s profile. The Pardee School is currently an associate member of the Association of Professional Schools of International Affairs (APSIA), and Najam says the new degree programs should help Pardee attain full APSIA membership, which is considered the imprimatur of excellence.
Pardee is retaining a master’s degree in Latin American studies, a joint MA/MBA in conjunction with the Questrom School of Business, and a joint MA/JD with the School of Law.Explore Related Topics:
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