Anticipating Student Thinking

So another question we asked students was this one…

The times and positions of an object are given in the table below. What’s a good estimate for the speed of the object at the instant t=2?

t(s) x(m)
0 2
1 4
2 10
3 20
4 34
5 52

Here’s what I’m interested in knowing…


If you had to write a multiple-choice version of this question, what options would you give students, and why? In other words, what approach or thinking underlies each choice? Are any of your choices degenerate?– meaning that the answer could point to very different thinking/approaches?


What’s something you would want to ask a student as follow up (either generally or to particular answers)?

Baby SBG Jump

So I have the green light to turn my reading quizzes into a mini-sbg experiment next semester. Each standard will end up being counted for 3pts of what was a 5pt reading quiz, the other 2 pts will come from students completing ungraded online questions about the reading (JiTT style). Every standard will be graded yes or no, and it can’t be taken away from the student once they get a yes. I’ll be allowing students to request reassessments through the exam that covers that material. If they show mastery of any standard from their work on that test, or any later test, they can ask me to change it, but I’m not allowing infinite reassessments.

The standards are an attempt to balance basic things students need to know, things I think are important, and things they need to be able to do to perform well on the exam (which I have no control over). “Synthesis” is not a standard, but is basically what they can expect to be able to do on the exam. It also reflects the kind of problems we practice in class as groups. It is not part of the standards, but it points to what they should practice after they have passed all the standards.

Through Test 1

Motion 1: Back-and-forth Motion

M 1.1   I can distinguish position, change in position, and distance

M 1.2   I can interpret position versus time graphs

M 1.3   I understand the difference between average speed and average velocity

Synthesis: I can solve a multi-stage constant velocity problem


Motion 2: Accelerated Motion

M 2.1   I can distinguish average velocity from velocity at an instant

M 2.2   I understand and can apply the concept of acceleration

M 2.3   I can interpret and set-up 1-D acceleration word problems

Synthesis: I can solve 1D acceleration word problems


Motion 3: Freefall

M 3.1   I understand the signing conventions for the acceleration due to gravity

M 3.2   I can describe and show how velocity changes for an object in free fall

M 3.3   I can set-up and organize information for a 1D free-fall problem

Synthesis: I can solve 1D free-fall problems


Interactions (1 dimensional)

I 1.1  I can identify when forces must be (un)balanced given description of motion

I 1.2  I can identify the direction of net force given a description of motion

I 1.3  I can identify the Newton’s 3rd law pairs corresponding to an interaction

Through Test 2


Trigs and Vectors

T 1.1   Given all sides of a triangle, I can calculate sine, cosine, and tangent

T 1.2   I can find components of vectors given magnitude and angle

T 1.3  I can find magnitude and angle of a vector given its components


Projectile Motion

PM 1.1   I can indicate velocity, acceleration, & net force along path of PM

PM 1.2   I can reason about projectile motion as superposition of two motions

PM 1.3   I can set up a projectile motion problem

Synthesis: I can set-up and solve problems involving projectile motion


Forces 1: Identifying and Summing Forces

F 1.1   I can identify forces acting an object and draw a free-body diagram

F 1.2   I can write a sum of forces statement given a free-body diagram

F 1.3   I can make inferences about unknown forces using Newton’s 2nd law


Forces 2: Understanding Empirical Force Models

F 2.1   I understand and can apply empirical force models for friction

F 2.2   I understand and can apply empirical force models for springs

F 2.3   I can find the components of weight along and perpendicular to a ramp

Synthesis: I can setup and solve  “forces on ramp” problems


Uniform Circular Motion

UCM 1.1   I understand and can apply relationships among T, f, and ω

UCM 1.2  I can identify the direction of acceleration & velocity for UCM

UCM 1.3  I can identify centripetal component of net force for UCM

Synthesis: I can solve a uniform circular motion problem


Through Test 3


Energy 1: Work and Stored Energy

E 1.1  I can identify when a force is and isn’t doing work in a given situation

E 1.2  I can calculate the work done by a force & relate to energy transfer in/out of system

E 1.3  I can identify factors that indicate that energy is stored in KE, PEg, & ,PEel


Energy 2: Energy Conservation

 E 2.1  I can identify whether or not energy of a system is constant or not

E 2.2  I can identify the kinds of energy that are relevant in a given situation

E 2.3  I can use COE to write an expression relating two states of a system

Synthesis: I can set-up and problems involving work and energy.



M 1.1  I can identify systems that do and don’t have total momentum conserved

M 1.2  I understand the difference between elastic and inelastic collisions

M 1.3  I can write a COM expression for completely inelastic collisions

Synthesis: I can solve a multi-part problem involving COE and COM


 Angular Kinematics

 AK 1.1   I can relate angular position, angular velocity, & angular acceleration

AK 1.2   I can relate angular quantities to their tangential counter-parts

AK 1.3   I can determine the direction of torque due to a force around a pivot

Synthesis: I can solve angular kinematics problems


Static Equilibrium

SE 1.1   I can calculate the torque due to force that is not perpendicular to r

SE 1.2   I can state and apply the conditions for static equilibrium

SE 1.3   I can write correct sum of force and sum of torque statements

Synthesis: I can solve a static equilibrium problem


Rotational Dynamics

RD 1.1   I can use the rolling-without-slipping relationship to relate v and ω

RD 1.2   I can make qualitative comparisons of moment of inertia

RD 1.3   I can write apply COE to write a relating expression for rolling motion


Through Last day of Class


Oscillations 1: SHM

O 1.1   I can show how energy changes through SHM

O 1.2   I can show how (net) force changes throughout SHM

O 1.3   I understand the factors that do and do not influence frequency


Oscillation 2:Waves

O 2.1   I can relate wavelength, frequency, and wave speed

O 2.2   I can reason about the factors that do and do not influence wave speed

O 2.3   I can write expressions relating wavelength to length for standing waves


Fluids 1: Static Fluids

F 1.1   I can make inferences based on force, pressure, and area relationships

 F 1.2   I can quantitatively reason about pressure changes in a liquid

 F 1.3   I can qualitatively reason about densities and buoyant forces


Fluids 2: Dynamic Fluids

F 2.1   I can reason about the flow rate of incompressible fluids in pipes

 F 2.2   I can reason about changes to pressure and speed relate in air flow



T 1.1   I can identify what changes and what’s constant in a given a gas process

T 1.2   I can relate the concept of specific heat to energy transfer


Participation Requested: Anticipating Student Approaches

An undergraduate student I work with gave the following problem to a bunch of students enrolled in two different calculus-based physics course.

An object undergoes constant acceleration. Data from the object’s motion is shown below.

Time (s)

Velocity (m/s)













How far did the object travel during those 5 seconds?



I’m curious, how you initially think about / approach this problem.


I’m curious what you would predict are all the different things students did (both correct and incorrect).


I’m also curious if there are any viable methods that you think were not likely be taken by students.

Transforming Content

In the intro physics course I teach, students take FCI on first day of class, and then again just yesterday. I don’t expect very high gains.

Although, there are many interactive features of the classroom (e.g., clickers, white-boarding, small-group discussion), the course content, materials, and pacing is very traditional. Thus, the same old physics course has been dressed up in reforms, but very little has fundamentally changed.

Often, interactive classrooms can facilitate three kinds of changes to content:

  • First, they can facilitate a transformation of what physics content is. Often this begin with a teacher who is starting to reconceptualize what that content is, and the interactive features of the classroom serve as a catalyst to drive that “content-reconceptualization” reaction.
  • Second, they can facilitate a change in the relationship between students and that transformed content. By giving students places to create, share, and negotiate the meaning of physics content in public ways, the possibility emerges that they become authors of content, not merely passive consumers.
  • Third, they can facilitate a change in the way teachers view the relationship between themselves, their students, and the content. Whether it be a view that students arrive in the classroom with misconceptions that impede learning or they arrive with resources that are assets for learning, the views are one in which students are viewed as already having a relationship with physics content–one that must be attended to as part of their learning.

These three changes are all about physics content–What the content of a physics course is? Who makes the content of a physics course? And where the raw materials of physics content lie?

This is the biggest obstacle I see for this course–not what new reforms practices to put in place, but how to begin a transformation of the content of the course. The three transformations above speak to different entry points to such change–changing teachers views of content, changing the contact students make with content (curriculum), and changing teachers views of learners of that content.


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