### Night Session, Pascal’s Identity, Clip 6 of 7: Examples of Pascal’s Identity in the notation for combinations

Carolyn Alexander Maher, Regina D. Kiczek & Elena Perrone Steencken
This is the sixth of seven clips from the night session. After Jeff draws Pascal’s Triangle in what the students call “choose” notation, the researcher asks the students to express an instance of the addition rule using that “choose” notation (the notation for selecting combinations). Michael gives an example, and then he and the other students discuss the meaning of other specific instances of Pascal’s Identity in “choose” notation, in terms of specific instances of...

### Zhengang Wang (王振刚) interview for the China Boom Project

Zhengang Wang & John Delury
Zhengang Wang, Former Vice Chairman of the Dandong Municipal Committee of the Chinese People's Political Consultative Conference, was interviewed by the Asia Society staff in Dandong, China on August 14, 2009.

### Shirts and Pants with Jamie and Michael, Clip 3 of 3: Recording a graphical representation of their solution

Amy Marie Martino & Alice S. Alston
In this clip, Jamie and Michael discuss their solutions to the Shirts and Pants Problem introduced in first clip in this series. They compare their individual solutions and find that they match. Researcher Alice Alston recommends that they depict a graphical representation of their solution on the large sheet in addition to the narrative solution which Jamie has already included. Jamie and Michael then work on drawing their solution of shirts and pants outfits on...

### Night session, Pascal's identity, clip 3 of 7: further explorations of factorials and combinations

Carolyn Alexander Maher, Regina D. Kiczek & Elena Perrone Steencken
This is the third of seven clips from the night session. The four students (Ankur, Jeff, Michael, and Romina) investigate the reason for dividing n! by (n-x)! and x! when calculating “n choose x.” In explaining the specific example of “5 choose 2,” they use two analogies: 1) arranging five people on a line when you are concerned about the positions of only two of the people and 2) counting the number of 5-tall towers...

### Alan's Infinity

Carolyn Alexander Maher
In this clip from 4th grade classroom study, students discuss the placement of numbers between zero and one on a number line. A debate ensues as to how many numbers exist between zero and one. Andrew suggests that a microscope can show more numbers than might be visible to the eye. Michael and Erik argue that the line would need to be made larger to include more numbers. Alan maintains that in any given interval,...

### Equine behavior: behavior test, walking on cardboard test, Genesis

No Name Supplied
Test conducted as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University, November, 2009. Subject was RU Genesis, a 6-month-old weanling draft cross born May, 2009. Test conducted by Dr. Sarah L. Ralston at the George H. Cook Campus, Rutgers University. Duration of test: 14 seconds. Overall score on a scale of 1-4 (4 is highest compliance): A-plus, according to sound track (4.25).

### Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 1 of 10: Combinatorics notation for selecting a particular number of items from a total of 4.

Carolyn Alexander Maher & Elena Perrone Steencken
In the first clip in a series of ten from the fifth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, the researcher, Carolyn Maher, introduces Stephanie to mathematical notation to represent the number of ways to select a specific number of objects from a set. Maher asks Stephanie to recall an earlier problem task, in which she was asked to determine the possible number of unifix "towers", four...

### Equine behavior: pasture play, multiple horses

No Name Supplied
Produced as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University, under the oversight of Dr. Sarah L. Ralston. Recorded at the George H. Cook Campus, Rutgers University, April, 2009.

### Equine behavior: behavior test, preliminary test 2 with student, Woodstock, draft-cross weanling gelding

No Name Supplied
Test conducted as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University, January 25, 2010. Subject was 6-month-old RU Woodstock, born May, 2009. Test conducted by Dr. Sarah L. Ralston, with Carly A. Painter, at the George H. Cook Campus, Rutgers University. Overall score on a scale of 1-2 (2 is highest compliance): 1.690909091

### Equine behavior: behavior test, vacuum cleaner test, Casanova, mustang yearling gelding

No Name Supplied
One of a series of tests conducted to compare behavioral responses of young draft horse crosses and Bureau of Land Management mustangs. Conducted as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University, February 16, 2010. Subject was RU Casanova, born ca. May, 2008. Test conducted by Dr. Sarah L. Ralston at the George H. Cook Campus, Rutgers University. In this test, Dr. Ralston introduces the horse to...

### Equine behavior: behavior tests, oats vs. TMR cubes test 2 with student and novel object test with dustbuster, Koda, mustang two-year-old gelding

No Name Supplied
Test conducted by Nadja Fischlechner at the George H. Cook Campus, Rutgers University as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University. One of a series of tests comparing behavior responses of mustangs fed a diet with oats versus behavior responses of mustangs fed a low starch diet(only total mixed ration cubes). In the second behavior test, four of the mustangs had been on an oats diet...

### Equine behavior: behavior test, scary aisle test, Firedance

No Name Supplied
Test conducted as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University. Subject was RU Firedance, a yearling draft cross born May, 2008. Test conducted by Dr. Sarah L. Ralston at the George H. Cook Campus, Rutgers University. Duration of test: 2 minutes. Overall score on a scale of 1-4 (4 is highest compliance): 3.464286.

### Equine behavior: behavior test, preliminary test 1 with student (Fall 2010, indoor), Sierra, mustang two-year-old female

No Name Supplied
Test conducted by Sarah Shaw at the George H. Cook Campus, Rutgers University as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University. One of a series of tests comparing behavior responses of mustangs fed a high starch diet versus behavior responses of mustangs fed a low starch diet. In the preliminary test, all the mustangs were on the same diet consisting of only forage (total mixed ration...

### Early algebra ideas involving one variable, Clip 4 of 11: Working on equations two and three

Davis, Robert B. (Robert Benjamin), Carolyn Alexander Maher, Alice S. Alston, Amy Marie Martino & Thomas LaMonde Purdy
In the fourth of eleven clips from the first day of the Early Algebra Ideas 6th grade class sessions, the students work in small groups to find and record solutions for the first two of a series of open sentences that have been presented as a worksheet by the researcher, Robert B. Davis. As the students test different values in the equations, Davis keeps track on the white board of answers that the students propose...

### Equine behavior: geldings eat at the feeder while fillies graze the pasture

No Name Supplied
Produced as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University, under the oversight of Dr. Sarah L. Ralston. Recorded at the George H. Cook Campus, Rutgers University, April, 2009.

### Early algebra, investigating linear functions, series 6 of &, Museum problem, Clip 5 of 6: James modeling the Museum problem with rods

No Name Supplied
In the fifth of six clips from an after-school enrichment session in an urban middle school, James, a &th grade boy completing a unit about linear functions, has finished his written solution for the Museum problem. When researcher Markus Hahkioniemi asks James if he could use the Cuisenaire rods to model this problem, James begins by building a "ladder" with two rungs and counts the rods as he had for the earlier Ladder problem. He...

### Shirts and Pants Group Sharing, Clip 2 of 3: Michael, Gerardo, Jeff, Brian, and Matt share their solutions

Alice S. Alston
In this clip, students continue to share their solutions to the Shirts and Pants Problem, which they have worked on in the Shirts and Pants series. Michael and Gerardo share their solution in which they have drawn lines between the shirts and pants, saying that their solution is more like Stephanie and Dana’s than Jamie and Michael’s. Jeff and Brian, who have drawn six outfits of shirts and pants without using lines, share their solution...

### B64, Stephanie third of three interview sessions when she used a case-based method for all heights below and including four-tall Towers problems (work view), Grade 4, March 6, 1992, raw footage

Carolyn Alexander Maher
This one-on-one interview between Researcher Carolyn Maher and Stephanie was an 85-minute discussion that occurred in the 4th grade about two weeks after Stephanie’s second interview with researcher Maher in that same school year. Prior to this interview and after the second interview Stephanie was given a home assignment to solve the four-tall towers problem, selecting from two colors of Unifix cubes, using her “new method” by cases that she had used to partly solve...

### Equine behavior: behavior test, oats vs. TMR cubes test 1 with student, Sierra, mustang two-year-old female

No Name Supplied
Test conducted by Joann Chien at the George H. Cook Campus, Rutgers University as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University. One of a series of tests comparing behavior responses of mustangs fed a diet with oats versus behavior responses of mustangs fed a low starch diet(only total mixed ration cubes). In the first behavior test, four of the mustangs had been on an oats diet...

### Word problems with addition and subtraction, Stephanie's group, Clip 6 of 9: Reconsidering problem 5

No Name Supplied
In the sixth of nine clips in a first grade classroom, four children: Stephanie, Gerardo, Sean and Aaron, revisit and reconsider their solution to Problem 5 of a set of 6 word problems involving addition and subtraction. Refer to clip 4 of the series for their initial work. Stephanie rereads the problem to the group, questioning whether their first answer of 5 is correct. Sean claims that the answer should be 5 plus 3 or...

### A86, Discovering equivalent fractions and introducing fraction notation (classroom view), Grade 4, October 4, 1993, raw footage

Carolyn Alexander Maher
Researcher Maher began the session by discussing the relative size of fractions within different models. Using the analogy of two different sized dioramas of children in a fishing boat, the class agreed that the proportions within each model need to be the same, but that the parts of the models cannot be interchanged. Then, the class worked in partners on the problem: Which is larger, one half or two thirds, and by how much? Meredith,...

### Early algebra, investigating linear functions, series & of &, Ariel's 8th grade interview, Clip 2 of 5: Ariel solving the Ladder problem

No Name Supplied
In the second of five clips from a follow-up interview about his participation in Informal Mathematics Learning (IML), an after-school enrichment program, Ariel, an 8th grade student in an urban middle school, is asked to solve the Ladders problem, which he had worked on as a &th grader in IML. Researcher Cecilia Arias asks Ariel to read the first parts of the problem and Ariel quickly determines the number of rods necessary to build ladders...

### Calvin Schwartz interviews La Principessa Maria Elettra Marconi Giovanelli

Calvin Barry Schwartz & Elettra Marconi
New Jersey author and journalist Calvin Barry Schwartz interviews Princess Elettra Marconi about her famous father, his role in saving Titanic survivors and her life, work, and interests, in an interview that took place at the Alexander Library of Rutgers University, June 1&, 2014.

### Equine behavior: obstacle test, Pardner, draft-cross yearling gelding

No Name Supplied
Conducted as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University, April, 2009. Subject was RU Pardner, an 11-month-old yearling draft cross born May, 2008. Conducted at the George H. Cook Campus, Rutgers University.

### Equine behavior: behavior test, preliminary test 2 (Fall 2010, indoor), Sassafras, mustang yearling female

No Name Supplied
Test conducted by Dr. Sarah L. Ralston at the George H. Cook Campus, Rutgers University as part of the Young Horse Teaching & Research Program of the Equine Science Center, Rutgers University. One of a series of tests comparing behavior responses of mustangs fed a high starch diet versus behavior responses of mustangs fed a low starch diet. In this second test, four mustangs have been on a high starch diet (total mixed ration cubes...

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