Making Collective Sense of Data: Item and Error Analysis ... · Sim School: Grade 6 Mathematics,...

Making Collective Sense of Data: Item and Error AnalysisSample DataPresented by Nancy Love Research for Better TeachingActon, Massachusetts, USA

Near East South Asia Council of Overseas SchoolsBangkok, Thailand

5 April 2014

Research for Better Teaching, Inc. • One Acton Place, Acton, MA 01720 • +1-978-263-9449 • [email protected]

Copyright © 2014 by Research for Better Teaching, Inc.

The material in this handout from or adapted from Nancy Love, Katherine E. Stiles, Susan Mundry, & Kathryn DiRanna, The Data Coach’s Guide to Improving Learning for All Students: Unleashing the Power of Collaborative Inquiry (Thousand Oaks, CA: Corwin Press, 2008) is used with the permission of Corwin Press.

Research for Better Teaching, Inc.One Acton PlaceActon, MA 01720

President: Jon SaphierExecutive Director: Sandra SpoonerProgram Director: Nancy Love

© 2014 Research for Better Teaching, Inc. • One Acton Place • Acton, MA 01720 • Phone +1-978-263-9449 • [email protected]

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Making Collective Sense of Data:Item and Error Analysis

Table of Contents

Sim School: Grade 6 Mathematics, Multiple-Choice Item Results, 2014 - Prediction Template .........................1

Sim School: Grade 4 English Language Arts, Multiple-Choice Item Results, 2014 - Prediction Template .........2

Released Items for Patterns, Relations, and Algebra .............................................................................................3

Mathematics: Student Work Samples: Question 34 ...............................................................................................9

English Language Arts Reading Comprehension: “Into the Volcano” ................................................................16

Sim School: Grade 6 Mathematics, Multiple-Choice Item Results, 2014 ...........................................................23

Sim School: Grade 4 English Language Arts, Multiple-Choice Item Results, 2014 ...........................................24

Grade 4 Mathematics: Fraction Pre-Assessment: Student Work: Item 2 .............................................................25

Middle School Science: Floating Logs Probe ......................................................................................................28

Middle School Science: Floating Logs Probe - Sample Middle School Student Responses (N=23) ..................29


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Sim School: Grade 6 Mathematics Task 9

Released Items for Patterns, Relations, and Algebra - CCSS

CCSS.Math.Content.6.EE.A.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations)...

CCSS.Math.Content.6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. CCSS.Math.Content.6.RP.A.3b Solve unit rate problems including those involving unit pricing and constant speed...

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CCSS.Math.Content.6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. CCSS.Math.Content.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reason-ing about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.CCSS.Math.Content.6.RP.A.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

CCSS.Math.Content.6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given num-ber in a specified set makes an equation or inequality true.

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●ID:217534 D Common

ID:221625 C Common

ID:217505 PB0006_rectangle.eps D Common

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Mathematics Session 2

What is the value of n that makes the equation below true?

n 5 12 3

A. 4

B. 9

C. 15

D. 36

At one time, the world population was 6,034,627,105. What digit is in the millions place of 6,034,627,105?

A. 0

B. 3

C. 4

D. 6

● Jon and his friends painted a mural in 23 art class. The shaded part of the figure below represents the part of the mural that Jon painted.

Which of the following best represents the percent of the mural that Jon painted?

A. 20%B. 25%C. 33%D. 40%

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CCSS.Math.Content.6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers...CCSS.Math.Content.6.RP.A.3b Solve unit rate problems including those involving unit pricing and constant speed...


(cont. next page)


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CCSS.Math.Content.6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation...

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CCSS.Math.Content.6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Extended application of CCSS.Math.Content.6.EE.A.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity...

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Source: Adapted from the Massachusetts Department of Elementary and Secondary Education’s Massachusetts Comprehensive Assessment System (MCAS), 2007. www.doe.mass.edu.


CCSS.Math.Content.6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which val-ues from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.CCSS.Math.Content.6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.


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Sample 134.

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Sample 2

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Sample 3

34.

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Sample 4

34.

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Sample 5

34.

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Sample 6

34.

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Sample 734.

Source: Adapted from the Massachusetts Department of Elementary and Secondary Education’s Massachusetts Comprehensive Assessment System (MCAS), 2007, p. 304. www.doe.mass.edu.


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Reading Comprehension

Some Like It Hot

H awaii’s Kilauea volcano rumbles under my feet with thunder I feel in my stomach. The air reeks of burning metal. A towering dark steam cloud looms over me. Without warning, a football-sized

chunk of gooey lava drops out of the cloud and plops onto the ground near me. I duck and run as more hissing red chunks splatter everywhere. These “lava bombs” could crush a skull as if it were an eggshell. What on Earth am I doing here, on the world’s most active volcano?

T here were no volcanoes where I grew up. Our family lived in a quiet, little town in rural New England where the cows outnumbered the people. I was the eldest of three children and spent my childhood

exploring the forests and fields.My favorite pastime was sitting safe and dry on our porch watching

violent summer thunderstorms rage through the Connecticut River Valley. Our springer spaniel, Dinney, would cower under my chair in fright, but the louder the thunder and brighter the lightning, the more thrilled I was.

In school I loved earth science and biology, but my guidance counselor suggested I take typing classes and become a secretary. That didn’t interest me. Fortunately, I was artistic, so instead I majored in creative arts—painting, photography and writing. To this day I still can’t type.

1

2

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Donna O’Meara studies and photographs volcanoes. Read the selection to find out how she became interested in volcanoes and answer the questions that follow.

from Into the Volcanoby Donna o’Meara

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1730


In the 1970s I moved to Boston and worked for magazine and book publishers. But something was missing in my life. Although getting out into the countryside helped, I finally decided I had to make some changes. I wanted to learn about the earth and the sky and the stars, where they all came from and where they were going.

At age 32, I went back to college. My teacher, Stephen James O’Meara, opened my eyes to science when he described how our solar system was shaped by geological forces. One of the most dynamic forces, Steve said, was volcanism. I pictured Earth, with its 1500 or more volcanoes spewing lava, as it spun dizzily around our sun.

Steve studied volcanoes to learn how planets formed and to search for clues that might help predict when a volcano will erupt here on Earth. So far, no single scientific method can accurately predict deadly eruptions. Any new discoveries would be important scientifically and could save lives.

Steve’s daring tales of exploring erupting volcanoes held me spellbound. When he passed around a piece of rough, hardened lava, I held it tight, closed my eyes and imagined myself climbing an erupting volcano in an exotic foreign country. Now that sounded like a good job for me!

Weeks after class ended, Steve and I had dinner. He described how he’d once jumped over a moving lava flow to save his life. I could barely believe what I was hearing. Asleep that night I dreamed of volcanoes.

On December 23, 1986, around noon, my office phone rang. It was Steve.“Donna, have you ever seen an erupting volcano?”No, of course I hadn’t.“I’m on my way to Kilauea and need a field assistant.”“Kilauea, Hawaii? When do we leave?”I said “aloha” to my magazine boss and was on a plane to Hawaii before

sunset that same night.

My First Volcano

At noon on December 24, 1986, Steve and I strapped ourselves into a helicopter without doors and bounced on air drafts over a sizzling Hawaiian lava lake.

The lake had formed when a new vent, called Kupaianaha, had burst open on the east side of Kilauea volcano. A vent is an opening through which a volcano erupts lava and ash from inside the Earth.

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1831


Helicopters take volcano hunters where the action is. This one approaches a smoking crater. It’s similar to the one we took to see the lava lake — only our chopper didn’t have doors!

Fresh lava smells like burning metal. Here, it wipes out a road. I didn’t know then that molten lava can be 1150°C (2100°F) when it erupts out of the earth.

Lava oozed out of the vent, filling a huge depression to overflowing and creating a lava lake. The lava gushing into the lake from the vent caused sloshing waves.

As our pilot tilted the chopper to give us a better view, I clutched at the seat cushion for fear I would slide across the smooth leather and right out the open door. Below us a red lake the size of two football fields bubbled like a pot of oatmeal. Only this wasn’t oatmeal. It was burning hot molten lava.

The chopper whirled down to the edge of the sizzling lake. Hot, glowing rock oozed from the earth like toothpaste out of a cracked tube. The helicopter cabin got hotter, and a burnt metal smell filled the air. Our pilot expertly dodged chunks of spatter the volcano flung at us. We landed on the ground with a soft thump.

Steve and the pilot jumped out and ducked the rotors, leaving the engine running for a fast getaway. I thought about the gasoline in the engine near this heat.

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1932


Explosive Facts

Name of volcano: Kilauea

Location: Hawaii, U.S.A.

Status: active

Type: shield volcano

Height: 1222 m (4009 ft.)

Known people killed: about 120

Into the Volcano by Donna O’Meara. Text copyright © 2005 by Donna O’Meara. Photographs copyright © by Stephen James O’Meara and Donna O’Meara. Reprinted by permission of Kids Can Press Ltd.

I watched as Steve walked right up to the creeping lava flow—and survived. The scientist in me said “Hey, isn’t this what you went back to school for?” The artist in me had to admit the lake was strangely beautiful. Glowing pinkish-orange lava was creeping along, hissing and popping as if it were alive. This was the opportunity I had been waiting for my whole life. I grabbed my camera and jumped out of the chopper. I felt heat through the soles of my sneakers. I changed lenses and started shooting.

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ID:279972 A Common

●7 What is the main purpose of paragraph 1 in the selection?

A. to grab the reader’s interest

B. to explain the main problem

C. to introduce the main character

D. to answer the reader’s questions

ID:279978 D Common

●8 Based on paragraph 5, which of the following is most likely true about the author?

A. She is scared of things that are new to her.

B. She is upset about things she cannot control.

C. She is satisfied with things that remain the same.

D. She is curious about things she does not understand.

CCSS.ELA-Literacy.CCRA.R.6 Assess how point of view or purpose shapes the content and style of a text.


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2033


ID:279990 D Common

●11 Read the sentence from paragraph 20 in the box below.

Hot, glowing rock oozed from the earth like toothpaste out of a cracked tube.

In the sentence, the lava is compared to toothpaste to show

A. how hot the lava feels to the touch.

B. how clean the lava looks on the ground.

C. how sticky the lava looks against the rocks.

D. how slowly the lava flows from the ground.

ID:279981 B Common

●9 Based on the selection, what first made the author interested in volcanoes?

A. She saw a volcano erupting.

B. She studied volcanoes in college.

C. She wrote a book about volcanoes.

D. She heard about a volcano as a child.

ID:279987 C Common

●10 According to paragraph 19, why did the helicopter turn?

A. to visit a different volcano

B. to find another landing spot

C. to help the passengers see better

D. to keep the passengers in their seats

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ID:279990 D Common


Hot, glowing rock oozed from the earth like toothpaste out of a cracked tube.

In the sentence, the lava is compared to toothpaste to show

A. how hot the lava feels to the touch.

B. how clean the lava looks on the ground.

C. how sticky the lava looks against the rocks.

D. how slowly the lava flows from the ground.

ID:279981 B Common

●9 Based on the selection, what first made the author interested in volcanoes?

A. She saw a volcano erupting.

B. She studied volcanoes in college.

C. She wrote a book about volcanoes.

D. She heard about a volcano as a child.

ID:279987 C Common

●10 According to paragraph 19, why did the helicopter turn?

A. to visit a different volcano

B. to find another landing spot

C. to help the passengers see better

D. to keep the passengers in their seats

CCSS.ELA-Literacy.CCRA.R.1 Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.


CCSS.ELA-Literacy.CCRA.L.5 Demonstrate understanding of figurative language, word relatioships and nuances in word meanings.

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2134


ID:279995 C Common

●12 Which of the following events from the selection happened last?

A. The author rode in a helicopter.

B. The author studied painting in school.

C. The author photographed the volcano.

D. The author worked for a book publisher.

ID:279994 C Common

●13 What is the main purpose of the “Explosive Facts” box?

A. to explain the dangers of Kilauea

B. to describe the appearance of Kilauea

C. to give more information about Kilauea

D. to list other volcanoes found around Kilauea

ID:279997 B Common

●14 Which of the following best shows that the selection is from an autobiography?

A. The author teaches facts about volcanoes.

B. The author describes events from her own life.

C. The author persuades readers to protect nature.

D. The author makes up a story about a famous scientist.

34


ID:279995 C Common

●12 Which of the following events from the selection happened last?

A. The author rode in a helicopter.

B. The author studied painting in school.

C. The author photographed the volcano.

D. The author worked for a book publisher.

ID:279994 C Common

●13 What is the main purpose of the “Explosive Facts” box?

A. to explain the dangers of Kilauea

B. to describe the appearance of Kilauea

C. to give more information about Kilauea

D. to list other volcanoes found around Kilauea

ID:279997 B Common

●14 Which of the following best shows that the selection is from an autobiography?

A. The author teaches facts about volcanoes.

B. The author describes events from her own life.

C. The author persuades readers to protect nature.

D. The author makes up a story about a famous scientist.


CCSS.ELA-Literacy.CCRA.R.5 Analyze the structure of texts, including how specific sen-tences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.


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ID:280000 C Common


I pictured Earth, with its 1500 or more volcanoes spewing lava, as it spun dizzily around our sun.

Which of the following words from the sentence is a verb?

A. volcanoes

B. lava

C. spun

D. around

ID:279999 D Common


Steve studied volcanoes to learn how planets formed and to search for clues that might help predict when a volcano will erupt here on Earth.

Based on the sentence, what does predict mean?

A. to describe changes

B. to hear something clearly

C. to find something that was lost

D. to tell what will happen in the future

Source: Adapted from the Massachusetts Department of Elementary and Secondary Education’s Massachusetts Comprehensive Assessment System (MCAS), 2007, p. 304. www.doe.mass.edu.

CCSS.ELA-Literacy.CCRA.L.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and con-sulting general and specialized reference materi-als, as appropriate.

CCSS.ELA-Literacy.CCRA.L.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.


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Assessment/Data Studying Skillful Teaching: Using Data Day to Day

© 2010 Research for Better Teaching, Inc. • One Acton Place • Acton, MA 01720 • Phone 978-263-9449 • www.RBTeach.com205

FLOATING LOGS PROBE

Name _____________________________________ Date _______________________

Source: Page Keeley, Francis Eberle, and Joyce Tugel. 2007. Uncovering Student Ideas in Science: 25 More Formative Assessment Probes, vol. 2. Arlington, VA: NSTA Press, p. 27. Used with permission.

(cont. next page)(cont. next page)

Middle School Science: Floating Logs Probe


29



FLOATING LOGS PROBE—SAMPLE MIDDLE SCHOOL STUDENT RESPONSES (N=23)

Response A (More than half of the larger log fl oats above the water surface):

Student #1: I think that more than half of the larger log fl oats above the water surface because I know that the longer or wider they are, that the log won’t sink.

Student #2: I think more than half the larger logs fl oats above the water surface because a tree produces oxygen and I think that they would fl oat better because they have or give off more oxygen and air doesn’t sink it fl oats really well.

Response B (Half of the larger log fl oats above the water surface):

Student #3: My thinking on this matter is that size of the logs will not matter. The log will be half submerge, half on the surface. The reason for this “rule” is that all the logs have the [illegible] amount of fl oating material to have half of it fl oat. As example a small log will not [illegible] as much fl oatation as a larger log. Every log or piece will equally have enough to half submerge it half fl oat it.

Student #4: If this log is twice the size of the other nothing change for the buoyancy.

Student #5: It’s the same as the smaller log. Half of the log is in water the other half is out of water. I guessed using things I’ve used before.

Student #6: For it is made of the same material as the smaller log. And these materials fl oat, and it is the same type of wood.

Student #7: I think the half of the larger log fl oats above the surface. I think this because if the smaller one fl oated like that and this one is twice as long and twice as wide it should be balanced. I just made an inference to fi gure this out.

Student #8: I think the answer is it will be halfway out of the water because the log is rolling. I have also seen pencils short and long that are all half way out when in water.

Student #9: I think that half of the bigger log will fl oat because when they used to transport logs on water before we had vehicles to do it for them. Another reason I believe they both fl oat the same is because the fl oating is to do with the depth of the water.

Student #10: The rule for this is mass even though log is heavier it will still stay the same because logs fl oat it might be a little bit lower.

Student #11: Half of the larger log fl oats above because the log is still going to be the same as the other. The log is just the same shape only wider and longer. Just because your bigger doesn’t mean your worse or better, for example if you threw a 5 year old kid tied up in a deep pool it will sink, the same for an adult, you will sink if you don’t move. This is why I believe this answer.

Student #12: There will still be half of the log in the water because it is bigger in diameter so it has more area to be able to fl oat half in the water.

Student #13: Even though the log is bigger it has more density which would cause it to be the same as the smaller one.

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Middle School Science: Floating Logs Probe - Sample Middle School Student Responses (N=23)


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Student #14: I have chosen that half of the larger log fl oats above the water surface because it was twice as large as the fi rst one and was wider also. Just like when your on ice, you spread yourself out and since the log is wider, it is kind of like it is spreading itself on the water so it wasn’t sink/fall through.

Response C (Less than half of the larger log fl oats above the water surface):

Student #15: I think most of the log would be under water. I think that would happen because the bigger one is heavier and more dense.

Student #16: I think the bigger log will fl oat less then half way above the surface because the log is heavier and heavier objects sink so obviously the heavier log will sink more than the lighter one.

Student #17: This is the rule of fl oating. Heavy things sink and light things fl oat. So the larger log would sink more than the smaller log.

Student #18: Well water can only hold so much weight. As the weight increase the object may sink for example a cinderblock may sink to the waters bottom. While a beach ball will barely go underwater. So the log will sink farther than the less dense one.

Student #19: I think because the log is larger it will sink a little more. I think this because more weight is put on the water because the log is larger, so it causes the log to sink. If the log was light I think it would fl oat more, and if it was in between large and little, it would fl oat equally.

Student #20: I think that since it is twice the size it is twice the weight. So I think that would make the log sink twice as much and almost the whole log would be underwater.

Student #21: I think that less of log was above the water surface because the longer the log the more it is going to weigh. If the log was smaller it would weigh less.

Student #22: The bigger it is the more density it has. Although it is heavy it has a lot of density so it can fl oat.

Student #23: No matter the size of the log it will always fl oat. The larger and heavier the log is determines how well it fl oats. There are many different types of logs that are different materials. Some fl oat more than others. I think if a small log had half in and half out then a larger log would half less out of the water because of its size and weight.

Source: Adapted with permission from the Curriculum Topic Study Project (http://www.curriculumtopicstudy.org/).

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