In AP Physics (and many other science studies) the journey to find an answer to a problem is the most important component of the learning process – not the answer itself. Our need to make sure students think deeply about the subjects they study is one key reason The College Board AP Program is undergoing revisions of several courses and exams in history, science and world languages.

The science course changes are driven by data from a 2002 National Research Council report and aim to implement improvements in content and pedagogical approaches that represent best practices in teaching and learning.

The curriculum frameworks for the new science courses are organized around subject specific ‘Big Ideas’ with a strong focus on scientific reasoning and inquiry. The courses will emphasize depth over breadth and will include cutting edge areas of research within each discipline. The College Board recently released the new Biology curriculum framework.

For students to be successful in these courses, teachers will need to use instructional strategies that require higher-order thinking skills and help students develop a deeper conceptual understanding of the topics.

This is the first post in a blog series that will explore how the AP Science Practices can be integrated in the 21st century science classroom using a variety of strategies and digital tools. While the primary focus will be in physics, the series will have relevance for other courses such as biology, chemistry and environmental science and could be used at the middle and high school levels.

Scientific Problems and Representations

The first science practice states:

The student can use representations and models to communicate scientific phenomena and solve scientific problems.

Problem-solving is a major part of a physics course. When confronted with challenging problems it is common to hear students say: “If I had the formula, I could solve this.” After all, finding the right equation is a key element in most textbooks’ problem-solving strategies and is often reinforced in the classroom through lectures, quizzes and tests.

In most cases, by using appropriate equations, a student is able to find the correct answer, but I will argue that finding the correct answer to a problem does not necessarily reflect a deep understanding of physics concepts. There are several studies in Physics Education Research that substantiate this claim. See, for example, the works cited in “An investigation of introductory physics students’ approaches to problem solving.”

Effective Approaches to Problem-Solving

The ability to relate physics concepts to the situations presented by problems and questions is fundamental for success.  A powerful strategy in developing a deep conceptual understanding is the use of Multiple Representations of Knowledge.

The diagram below is an example commonly seen in kinematics problems. This example demonstrates how physics equations are only one representation of knowledge.

illustrated physics problem

The Power of Multiple Representations

Here as an analysis of each of the representations above and its usefulness in helping the students deepen their conceptual understanding:

The real situation is the context of the problem; i.e., a car moving down a hill. It is common to represent real scenarios with a pictorial representation such as a sketch. It helps the students that have a preference for visual learning.

A verbal representation could describe the motion of the car in the context of the problem, in this example students could say that the car speeds up as it travels down the hill, or the student can describe the energy transformation that occurs. It helps the students articulate what is happening in the given scenario to specific physics principles.

The equation that describes the velocity in an inclined plane is the mathematical representation. This equation is usually derived from a free-body diagram by analyzing the forces acting on the car while it is accelerating.

The situation can be represented in a numerical way by providing data of position and velocity with respect to time. Data acquisition is often done in physics labs where students have to opportunity to gather the information in a hands-on experiment.

The data obtained can be represented graphically in a velocity versus time graph. Graphical representations are commonly constructed from data collected in a lab experiment. Through graphs students can obtain information from the slopes, intercepts and areas under the curve. In this example the slope of the line represents the average acceleration and the area under the line yields displacement.

A motion diagram can be used to illustrate the velocity vectors. This is another example that helps the students visualize the situation (a car speeding up) =i.e. increasing arrows as velocity vectors.

Students can demonstrate a deeper level of understanding of physics concepts by their ability to translate (move back and forth) between different representations of knowledge.

Multiple Representation Resources

Rutgers University Physics and Astronomy Education Research (PAER) group has written a document with the rationale about using multiple representations in physics, how to implement them in the classroom and how to score them.

Multiple Representations in Physics

You can also download power points with multiple representation exercises:

1. Mechanics: kinematics, dynamics, energy, momentum and statics

2. Electricity and Magnetism: electrostatics, DC circuits and magnetism

Digital Tools for Multiple Representations

Verbal Representations
These tools can be used individually or in collaboration among students
Google Docs



Pictorial Representations
Image editors
Sketchcast (Record a sketch with or without voice)



Google Sketchup for 3D Modeling

Mathematical Representations
Google Docs includes an Equation Editor

LaTeX Equation Editor

Graphical Representations
Google Docs spreadsheets

Create a Graph


Another powerful tool that helps with the implementation of Multiple Representations is the use of virtual simulations. In my next post, I will be describing effective strategies for using simulations and a variety of resources for simulations in all core areas of science.

Figure adapted from: Redish, Edward F. Teaching Physics: with the Physics Suite. Hoboken, NJ: Wiley, 2002

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