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Close the Confusion Gap with Invention Activities

To help complex concepts sink in and nurture students’ natural curiosity, this professor offers activities before the lesson—and no time to forget.


Shu-Sha Angie Guan, PhD

Assistant Professor of Child and Adolescent Development, California State University, Northridge

PhD in Developmental Psychology, MA in Psychology, BA in Psychology

Culture, Technology, and Relationships Lab: CulTRe

If there is one thing Shu-Sha Angie Guan wants her students to know, it is that statistics tell a story. Often, an exciting story.

“Inferential [statistics] that we use in behavioral sciences really help to distinguish what is different and true in the world and what we’re observing. That’s why it is so key in research,” she explains. “I love that it helps organize the world.”

To bring students into a headspace where they might share her excitement for statistical storytelling, Guan first must ease the apprehensions that typically surround complicated mathematics. How she does so is its own interesting tale: her discovery of an inventive learning approach, to which she added a twist.

Challenge: Math phobia, amplified by complex calculations

Guan, an assistant professor at California State University, Northridge, teaches an accelerated version of Research Methods to child and adolescent development majors nearing college graduation. The course helps students understand research stats and math, so they can better grasp the compelling and sometimes surprising results of psychological research studies. This is equally useful for students who will ultimately work in a social and behavioral research setting and for those who go on to do therapy or counseling.

However, many of Guan’s students struggle with or even fear math. For example, Guan finds that a statistical concept known as a probability value, or p-value, can be especially challenging for students to comprehend. As she explains it in layman’s terms, the p-value tells you the likelihood of performing an experiment that yields an accidental result. The smaller the p-value, the less likely it is that you have arrived at your conclusions by chance. A larger p-value suggests your results may be random and, therefore, carry less statistical significance.

The math involved in arriving at a p-value is complex. There is no way around this, Guan admits.

Innovation: Activity first, lessons later

Guan did a lot of thinking about how to make the material less intimidating and more accessible. She struggled with this until she happened to run into a former colleague, K.P. Thai, who described the “invention activities” she was using in her own job as a developer of toys and games.

“She explained inventive education as an evidenced-based approach to learning, where you offer the activities before the lessons to give someone more control over how they learn and provide opportunities for deeper engagement,” says Guan. “I read up on it and was impressed by the results.”

Invention education has been used for more than 30 years to teach a variety of topics to learners of all ages, abilities, and education levels. Currently, hundreds of thousands of programs across the globe feature project-based learning and self-guided problem-solving to impart motivation, self-confidence, and free thinking alongside the foundations of a particular field of study. As its focus is student-centric, this approach works well for putting math, science, and other STEM subjects into personal context for students so they can see how the concepts can be applied in a very real way.

“We’re all born scientists!”

— Shu-Sha Angie Guan, PhD

Guan says she is drawn to this teaching technique because she views all her students as natural-born scientists and mathematicians who are capable of much more than simply regurgitating memorized material on a test. In Guan’s judgment, everyone is curious by nature and able to autonomously explore even the most complex topics. So it was a natural fit for her to adopt invention education methods to flip the script on traditional teaching.

Allowing students to lead themselves through the material, then bolstering what they have learned later (with the lecture and lab), helps the knowledge sink in deeper, says Guan.

“By promoting active-learning and self-discovery, students leverage their own unique perspectives and wells of knowledge and learn to apply them,” she explains. “This puts the student in the driver’s seat.”

Further, by leaving little time to pass between lecture and lab, students are able to engage in that practical application of theoretical knowledge while the material is still fresh in their minds.


“By promoting active learning and self-discovery, students leverage their own unique perspectives and wells of knowledge and learn to apply them. This puts the student in the driver’s seat.”

— Shu-Sha Angie Guan, PhD

Course: CADV 380 and CADV 381 Methods of Child and Adolescent Study (lecture and lab)

Frequency: A 2-hour, 45-minute lecture followed by a 2-hour, 45-minute lab, once a week for 16 weeks

Class size: 30

Course description: An accelerated course that combines a lecture and lab to introduce the scientific process of studying children and adolescents. Provides hands-on experiences for students to gain insight into some of the key issues facing researchers, including problems of measurement, observation and interpretation, generation and testable questions, development of coding systems, and establishment of reliability. With the support of the instructors, students work in small groups to plan and carry out their own research projects.

CADV 380 and CADV 381 Methods of Child and Adolescent Study

See materials

Lesson: Invention learning: Activity first, lecture later

By using invention activities, Guan’s students are completely immersed in statistics theory and application for an entire semester. This allows them to truly grasp what they have been taught and, more important, learn how they can apply the information to their future careers, whether they go on to do research or choose an “applied” career such as that of a counselor or a therapist.

The beauty of the invention learning approach, says Guan, is that it can be applied to virtually any topic, be it complex or simple.

For any educator who wants to try their hand at it, she suggests keeping the following tips in mind:

Explain the whys

At the semester’s start, help students understand why you are taking such a different approach to teaching. Explain the advantages of discovering at least some of the answers on their own and the importance of the lessons they will learn by trying multiple ways to arrive at a result. For example, given that her class is a research methods course, Guan presents the empirical research on invention activities to the class so that they understand the rationale behind the lesson.

Then assure them that, although you will give them the freedom to explore on their own, you will still be there to support them when necessary. In fact, providing that learning resource after the invention activity is crucial for maximizing the benefits of this approach, says Guan.

Start with lessons online

Each week throughout the semester, Guan assigns a series of online to-do’s that students must complete on their own or in groups. Each activity is designed to push students to try a variety of methods to solve a set of problems. These lessons call upon learning style, past experience, and innovation to arrive at the right responses. Although they cannot always get there on their own, Guan says that even incorrect techniques and solutions can be very enlightening.

Switching the order of things by assigning outside activities before classroom learning does not have to mean abandoning standard teaching principles, notes Guan. The goal is to take what your students have learned through their own exploration and help them make sense of it.

Add some hands-on activities

Many people consider math to be a dry subject, but Guan takes it as a personal challenge to bring it to life with relatable examples and intriguing explanations. If you can show your students what gets you excited about a topic, chances are many of them will come along for the ride, Guan says.

For example, before a lecture on statistical analysis, Guan does a p-value activity with students. She divides the class into groups and gives each group a bag of marbles. Most groups have a bag with two red marbles, two blue marbles, and two green marbles. One group has a bag that is “different.”

Guan tells them to draw marbles from the bags and replace them, recording the results, to figure out which one of the bags is “significantly” different from the others. (Winners get a prize, such as CSUN notebooks, bags, and other student store gear.)

“The pursuant discussion often highlights the ways that scientists make conclusions—either right or wrong—about ‘statistically significant’ differences between groups,” she says. This activity is followed by the lecture on p-values, as this learning resource after the activity is instrumental in promoting student learning, according to Guan.

Follow an activity with a session of lecture

On Fridays, the entire class meets up in the classroom for nearly three hours of lecture and discussion to go over the week’s assignments as a group and assess what they have learned. The lecture is followed by a short break, then students move into the lab for another nearly three-hour session. There, they take the calculations they have just reviewed and plug them into a statistical analysis software program. The program then runs computerized simulations and models based on the data. Lab work reinforces what students have learned on their own and in lecture, and it helps them understand how to apply statistical data to research and the real world.

Embrace mistakes

Failure is not the opposite of success: Quitting is! By trying and falling short again and again, students can learn a lot about how something works—and how it does not. Students often have a lot of anxiety about getting incorrect answers, Guan points out. Help them feel comfortable with arriving at the “wrong” place even if it happens repeatedly. This try-try-again approach also helps students grow beyond learning the subject matter by teaching them tenacity, resilience, and, yes, even a tiny bit of bravery when learning something new.

Hold frequent check-ins

Each week, before she gets the lecture rolling, Guan asks for a show of hands to see how confident the students are in their knowledge of the material. At first, many admit they are still wrestling with some of the concepts, but after nearly three hours of lecture time, another show of hands reveals that most students feel they understand the week’s lessons.

Besides these check-ins, Guan also schedules frequent evaluations throughout the duration of the course. According to Guan, obtaining formative assessments (rather than just summative assessments at the end of the course) from the class about how they are doing, and how you are doing as a teacher, “lets you know what to stop, start, or continue.” The evaluations vary in length and level, from a short quiz before and after every lecture to assess how much students have learned that day to a mid-semester evaluation that provides insights into what should be modified moving forward. Some of these formative assessments that track growth she learned from participating in faculty development opportunities at CSUN.

Be a role model

As a first-generation college student, Guan is the first to admit she did not always feel confident in math and science when she herself was a student. But by applying herself, she gradually became proficient and learned to love the more technical academic subjects. She feels this is a valuable lesson for her students, especially her female students who tend to have more math anxiety than their male peers.

By setting an example of growth, you show your class what is possible, Guan notes. She is proud to say that she has inspired several students to embark on a career path that they might not otherwise have chosen. You never know whose life you will change by blazing a trial for others to follow, she says.


Guan has been teaching this course for three years. Several years before that, as a graduate student, she also taught a version of it. She thinks the accelerated approach offers a significant advantage because it allows students to completely immerse themselves in a complex subject. They become so intimate with the statistical concepts she teaches that most of them sail through the class with flying colors. She has also empirically tested new approaches in her classroom and presented the results at local conferences to a wider audience.

She says the p-value lesson is of particular importance because it:

  • Teaches them how to interpret research, a useful skill for researchers and clinicians alike
  • Helps them tame math anxiety
  • Applies complex math and scientific concepts in a way that helps students understand what they observe around them
  • Imbues a sense of resolve and determination for learning a new subject

Student feedback

Guan’s course is a requirement for all students who graduate from the university with a child and adolescent development diploma. Still, she hears from both faculty and students that it is a popular and well-liked offering. Though it is rigorous, students appreciate the back-to-back nature of the introductory and applied courses, and they embrace the opportunity to try self-directed learning, secure in the fact that Guan and a supportive team of peer mentors will have their backs.

One of Guan’s most gratifying classroom experiences came when a peer mentor asked if she could try her hand at teaching the p-value lesson. Guan was delighted to see how well things went. Not only was the peer mentor able to run the class smoothly and explain all the concepts clearly and thoughtfully, some of her explanations helped Guan view the material in a different light.

“She had just learned the material the last semester, and she was able to frame and interpret things differently than I do,” says Guan. “Listening to her was a good reminder of what it is like to not know. What a terrific lesson.”

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