Study Guide

Field 114: Physics 
Sample Constructed-Response Assignment

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Test Directions for the Constructed-Response Assignment

This section of the test consists of one constructed-response assignment. You are to prepare a written response of approximately  300 to 600  words on the assigned topic. You should use your time to plan, write, review, and edit your response to the assignment.

Read the assignment carefully before you begin to write. Think about how you will organize your response.

As a whole, your response must demonstrate an understanding of the knowledge and skills of the field. In your response to the assignment, you are expected to demonstrate the depth of your understanding of the content area through your ability to apply your knowledge and skills rather than merely to recite factual information.

Your response to the assignment will be evaluated based on the following criteria.

 start bold PURPOSE: end bold  the extent to which the response achieves the purpose of the assignment
 start bold SUBJECT KNOWLEDGE: end bold  appropriateness and accuracy in the application of subject knowledge
 start bold SUPPORT: end bold  quality and relevance of supporting evidence
 start bold RATIONALE: end bold  soundness of argument and degree of understanding of the subject area

The constructed-response assignment is intended to assess subject matter knowledge and skills, not writing ability. However, your response must be communicated clearly enough to permit valid judgment of the scoring criteria. Your response should be written for an audience of educators in this field. The final version of your response should conform to the conventions of edited American English. Your written response must be your original work, written in your own words, and not copied or paraphrased from some other work.

Be sure to write about the assigned topic. You may not use any reference materials during the test. Remember to review what you have written and make any changes you think will improve your response.

Sample Constructed-Response Assignment

Competency 0010 
Analyze a lesson plan and student work sample for a learning standard in the Oklahoma Academic Standards for Science or the Next Generation Science Standards and describe differentiated follow-up that addresses student needs.

 start bold Use the information provided in the exhibits to complete the assignment that follows. end bold 

Using your knowledge of standards-based learning goals and scientific investigations, prepare a response of  300 to 600  words in which you:

Be sure to utilize all of the exhibits in your response.

Exhibit 1: Class Context

In a high school physics class, students learn about the particle nature of light through Planck's modeling of blackbody radiation, the photoelectric effect, and the Compton effect. In this lesson, students are asked to apply their knowledge of wave and particle behavior, gather evidence supporting the particle nature of light by performing a photoelectric experiment, and experimentally determine Planck's constant.

Exhibit 2: Lesson Plan

The following is an excerpt from a high school physics lesson plan.

Unit Subject: The Particle Nature of Light and Energy Quantization—The Photoelectric Effect

Subject of the Lesson: Exploring the particle nature of light and energy quantization through the photoelectric effect and determining Planck's constant through measurements

Oklahoma Standard: Exploring the particle nature of light and energy quantization through the photoelectric effect and determining Planck's constant through measurements

Lesson Objectives:

Safety Procedures: One needs to be careful when handling electricity. Do not use the power supply except as instructed to do so.

Materials:

Procedure:

Table depicting the results of a student lab assignment
Color of Light
[laser pointer or mercury lamp]		 Wavelength
(units = nanometers)		 Stopping Potential
(units = blank)		 Variation in Stopping Potential
(units = blank)
yellow 578.0 empty cell empty cell
green 546.1 empty cell empty cell
blue 435.8 empty cell empty cell
violet 404.7 empty cell empty cell
ultraviolet 365.5 empty cell empty cell

Data Analysis: Using your data, and the equation describing the photoelectric effect, H F equals K subscript max plus W subscript metal, create a linear plot and calculate Planck's constant from the best fit line of your data.

Assessment: Students will be assessed based on connecting concepts in their responses to questions, observations, data collection, data analysis and presentation, and conclusions drawn.

Exhibit 3: Student Sample

Pre-lab Questions

1.  Waves carry energy. What parts of a wave change if the wave carries more energy?

The amplitude might be larger. Like ocean waves with bigger amplitudes have a lot more energy. Alternatively, the frequency could be larger. Like when you make a wave on a spring toy with a higher frequency, you work a lot harder.

2.  How are waves added together?

By adding the amplitudes of the waves.

3.  Light has both a particle and wave nature. How does the photoelectric effect show the particle nature of light rather than its wave nature?

One way we saw in class is if you shine light on the metal, sometimes no electrons are ejected even when the amount of light was increased. And if the light you picked did produce photoelectrons, doubling the light would just produce twice as many, but they wouldn't be any faster. So, doubling the amount of light is like having twice as many particles of light rather than having the effect of adding wave amplitudes; those particles all have the same energy so they can't give any electrons more than they have.

4.  The equation for the photoelectric effect is given by:

H F equals K subscript max plus W subscript metal

(a) Describe each variable in this equation.
(b) What conservation law is represented in this equation?
(c) In this lab you are measuring wavelength and stopping potential. Rewrite the equation to show these variables.

(a) h is Plank's constant, f is the frequency of the light, K is the kinetic energy of the ejected electron, and W is the work function of the metal.
(b) This is a restatement of conservation of momentum, the electron is knocked out of the metal.
(c) H C over lambda equals E V subscript stop plus W subscript M

Student Data

Table depicting the results of a student lab assignment
Color of Light
[laser pointer or mercury lamp]		 Wavelength
(units = nanometers)		 Stopping Potential
(units = volts)		 Variation in Stopping Potential
(units = volts)
yellow 578.0 0.56 0.01
green 546.1 0.70 0.01
blue 435.8 1.16 0.01
violet 404.7 1.30 0.01
ultraviolet 365.5 1.57 0.01
a graph depicting wavelength versus stopping voltage

A graph titled wavelength versus stopping voltage is shown. The vertical axis runs from zero to 1.8. The horizontal axis runs from zero to 7 times 10 to the power of 7. Five data points are plotted with a straight line of best fit whose equation is labeled y equals the quantity negative 5 times 10 to the power of 6 times x plus 3.1912

Student Responses to Analysis Section of Investigation

Our data showed the expected increase in stopping voltage for light with more energy. However, I'm color-blind and relied on my lab partners for this, but I think they were doing things right. From plotting our data, we find that Planck's constant is the negative of the slope or 5 times 10 to the power of 6 electron volts, which is very different from the accepted value of 4.1 times 10 to the power of negative 15 electron volts, so we must have done something wrong. We also find the work function of the metal to be 3.2 volts.

Sample Strong Response to the Constructed-Response Assignment

 start bold Please note: The sample response provided below is for review purposes only and should not be used in a response on an operational exam. Use of the exact words and phrases presented in this sample response will result in a score of "U" (Unscorable) due to lack of original work. end bold 

In this lesson, students answer prelab questions using concepts of light modeled as a wave and a particle. They use the particle model with the photoelectric effect to collect data to determine the value of Planck's constant. This fits the Oklahoma Standard (Lesson Plan) which essentially says light can be modeled as waves or particles.

The student sample shows this student's strengths include a good understanding of how the photoelectric effect demonstrates the particle nature of light. The answers in prelab questions 1to3 provided clear explanations and included a reference to a previous class demonstration to help understand the phenomenon. The student also correctly identified the variables in the equation for the photoelectric effect and could rewrite the equation in a form that used the variables measured during the experiment. Lastly, they understood that lower wavelengths mean higher energy waves, and this results in increased stopping voltage.

A weakness in the student sample, as shown in the prelab, is that the equation represents the conservation of energy, not the conservation of momentum. The conservation of momentum does hold for the photoelectric effect, but that is not what this equation describes.

More serious issues are shown in the graph and the analysis. First, in converting the wavelengths from nanometers to meters, there should be a negative 7 exponent, not positive 7 exponent. It is also possible the student wanted the x-axis to represent 1 divided by wavelength but did not take the inverse properly. As written, the slope will not equal Planck's constant since the student needs to properly convert wavelength to meters and adjust the value by c, and the y-intercept is not equal to the work function. Thus, the axes need to be labeled with both names and units of measurement, and their values need to be checked. The work function should be reported in units of electron volt, not volt.

To address this need, students can rewrite the equation with units and identify how the variables match the equation of a line, y = m x plus b. Students can predict what the line would look like in three cases: graphing V subscript stop versus wavelength, versus 1 divided by wavelength, and versus frequency, and determine which graph most directly represents the equation. This should allow students to see the slope change direction and understand that the slope value could be directly equal to Planck's constant. The student groups could choose which graph to use and redesign the data table to make it easier to plot their chosen graph.

I would add some prelab questions after #3. Where does the energy go for photons that do not produce photoelectrons? What do we call the energy level at which photoelectrons are first detected? I think these questions will help the students conceptualize the experiment and understand how it relates to the equation.

Once students have a strong understanding of the energy equation and have correctly determined Planck's constant, they can calculate the momentum for the photon and electron at different frequencies.

For future instruction, students could explore what happens with an increase in light intensity rather than changing frequency. Students could predict what this would look like in graph form using voltage versus current in the circuit attached to the instrument, and then confirm the curve by measuring voltage and current. Another approach would be to explore different experiments where we model light as a wave. For example, the classic double-slit experiment relates to this lab since we used a lens/grating system to isolate different wavelengths of light. Some of these experiments could be done online. The video demonstrations could include embedded quizzes (for points or for fun prizes) and could also delve into modern applications of the concepts.

Rationale for the Sample Strong Response

Please note that the response is evaluated based upon the four performance characteristics of Purpose, Subject Matter Knowledge, Support, and Rationale. Please also note how the score point descriptions are based upon how the examinee attends to the performance characteristics. You should be very familiar with the CEOE performance characteristics and score scale and refer to them when reviewing this rationale.

The purpose of this assignment is largely achieved as the response addresses all four bullet points of the prompt. For instance, the standard is related to the learning goals, and most aspects of the student work were analyzed with evidence cited. In addition, strengths and needs were identified, and subsequent differentiated instructional strategies related to those strengths and needs were discussed. Lastly, future instruction options were described.

The candidate shows a general command of the subject matter by accurately identifying important strengths and needs in the student work and by suggesting appropriate instructional strategies that directly address those identified strengths and needs. Most notably, the strategies addressing student needs expand the way the student works with the information. The future instruction then explores related physics experiments showing the scope of the candidate's subject matter knowledge.

In each of the bullet points of the prompt the ideas of the candidate are generally well supported with specific examples. In particular, details provided for the differentiated instructional strategies and the suggested future instruction convey how well the candidate understands the topic. These explanations and examples are presented throughout the response. They are appropriately applied, reflect logical reasoning, and demonstrate a general understanding of the topic. A stronger response would include more evidence and additional high-quality examples throughout. Overall, this response reflects a general understanding of the subject matter.

Sample Weak Response to the Constructed-Response Assignment

Both the lesson plan and the standard focus on light, but the subject of the lesson only talks about the particle nature of light. The Oklahoma Standard includes both the wave model and the particle model.

This student work shows some strengths and some needs. Some of their strengths are their knowledge of light waves and energy, as shown in the answer to questions #1 and #3. The rest of the answers to the questions are correct, too. Some of their needs are in graphing. The graph needs to have their axes labeled so we, the readers, can follow along. The values for the wavelengths are too large for light waves (beyond radio waves?!), so I also wonder what the units are on the graph. The slope on the graph should be the other way (positive) because Planck's constant is a positive number in the equation, so there is definitely a problem there too.

The answers to the questions are correct so the student does not need to go back through those ideas, but since the student knows there is a problem with the calculated value for Planck's constant, then they should go back through the lab work and find the problem. If this is not the only student with this problem, then a class review of drawing graphs might be worthwhile.

Also, in the student analysis there is no mention of c, the speed of light, so we would need to discuss where c fits into the calculations. Another idea is to rearrange the groups so that in rerunning the experiment, some of the students that struggle could be helped by their peers.

Once everyone is caught up then we can do some other experiments with this setup. I would ask the students what they would like to change but could suggest that we use a different metal. That should give us the same value for Planck's constant but a different value for the work function.

In the future, I would want to address experiments with light as a wave model since that is what is in the Oklahoma Standard. I would also include prelab questions that include graphing since that was a problem.

Rationale for the Sample Weak Response

Please note that the response is evaluated based upon the four performance characteristics of Purpose, Subject Matter Knowledge, Support, and Rationale. Please also note how the score point descriptions are based upon how the writer attends to each of the performance characteristics. You should be very familiar with the CEOE performance characteristics and score scale and refer to them when reviewing this rationale.

The purpose of this response is only partially achieved. Although all four bullet points are addressed in this response, there is limited explanation and support for much of the material, so the purpose is considered to be only partially achieved. The subject matter knowledge is considered limited. The candidate does correctly identify the major weaknesses demonstrated in the graphing of the data, but there is little explanation of why these are problems as they relate to the photoelectric effect equation. For example, the candidate realizes that the values of the wavelengths are large, even for radio waves, but they do not discuss where the problem occurred, nor do they mention how that affects determination of the work function. So, appropriate application of subject matter is missing. Similarly, the last two bullet points are very weak, with no support provided, and so there can be limited to little rationale to evaluate. As an example, in order to address the needs of the student, the candidate suggests reworking the assignment as is. That shows no additional knowledge from the candidate and certainly will be of very limited help to the student. This limited amount of subject matter knowledge, along with the lack of depth in the response, explains why this is considered a weak response. Overall, this response reflects a limited, poorly reasoned understanding of the topic.

Performance Characteristics

The following characteristics guide the scoring of responses to the constructed-response assignment.

Characteristics that guide the scoring of responses
Purpose The extent to which the response achieves the purpose of the assignment
Subject Matter Knowledge The accuracy and appropriateness in the application of subject matter knowledge
Support The quality and relevance of supporting details
Rationale The soundness of argument and degree of understanding of the subject matter

Scoring Scale

Scores will be assigned to each response to the constructed-response assignment according to the following scoring scale.

Score Scale with description for each score point.
Score Point Score Point Description
4  start bold The "4" response reflects a thorough knowledge and understanding of the subject matter. end bold 
  • The purpose of the assignment is fully achieved.
  • There is a substantial, accurate, and appropriate application of subject matter knowledge.
  • The supporting evidence is sound; there are high-quality, relevant examples.
  • The response reflects an ably reasoned, comprehensive understanding of the topic.
3  start bold The "3" response reflects a general knowledge and understanding of the subject matter. end bold 
  • The purpose of the assignment is largely achieved.
  • There is a generally accurate and appropriate application of subject matter knowledge.
  • The supporting evidence generally supports the discussion; there are some relevant examples.
  • The response reflects a general understanding of the topic.
2  start bold The "2" response reflects a partial knowledge and understanding of the subject matter. end bold 
  • The purpose of the assignment is partially achieved.
  • There is a limited, possibly inaccurate or inappropriate application of subject matter knowledge.
  • The supporting evidence is limited; there are few relevant examples.
  • The response reflects a limited, poorly reasoned understanding of the topic.
1  start bold The "1" response reflects little or no knowledge and understanding of the subject matter. end bold 
  • The purpose of the assignment is not achieved.
  • There is little or no appropriate or accurate application of subject matter knowledge.
  • The supporting evidence, if present, is weak; there are few or no relevant examples.
  • The response reflects little or no reasoning about or understanding of the topic.
U The response is unscorable because it is illegible, not written to the assigned topic, written in a language other than English, or lacking a sufficient amount of original work to score.
B There is no response to the assignment.