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Charles W Anderson - One of the best experts on this subject based on the ideXlab platform.

  • developing Learning Progression based teacher knowledge measures
    Journal of Research in Science Teaching, 2015
    Co-Authors: Hui Jin, Hyojeong Shin, Michele E Johnson, Jinho Kim, Charles W Anderson
    Abstract:

    This study developed Learning Progression-based measures of science teachers’ content knowledge (CK) and pedagogical content knowledge (PCK). The measures focus on an important topic in secondary science curriculum using scientific reasoning (i.e., tracing matter, tracing energy, and connecting scales) to explain plants gaining weight and exchanging gases. Using a design-based research approach, we conducted the research in four cycles. The findings reported in this article were based on the data collected in the last two cycles (year 2011–2012 and year 2012–2013). This study contains two parts. First, 194 teachers participated in professional development workshops and completed a teacher assessment measuring CK and PCK. A Learning Progression-based scoring system was developed for these measures. Second, a subgroup of 25 teachers participated in a teaching experiment. These teachers taught a Learning Progression-based unit on plant growth and functioning. Their students took written assessments both before and after the teaching intervention. In this process, validity evidence from multiple sources was obtained and analyzed to evaluate the claim that the assessment scores tell how well teachers understand the knowledge essential for teaching the science topic. This validity argument supports our interpretations that led to three results. First, teachers' overall performance on CK was a bit higher than PCK, but not significantly different. Second, two challenges confronting teachers are adaptively applying scientific principles and understanding students' intuitive ideas. Third, there was a statistically significant relationship between teachers' measured CK and PCK and students' Learning from the plant unit. © 2015 Wiley Periodicals, Inc. J Res Sci Teach 52: 1269–1295, 2015.

  • developing a fine grained Learning Progression framework for carbon transforming processes
    International Journal of Science Education, 2013
    Co-Authors: Hui Jin, Li Zhan, Charles W Anderson
    Abstract:

    Science educators have called for using the Learning Progression approach to align curriculum, instruction, and assessment. In line with this trend, we conducted both assessments and teaching experiments with students from grades 4 to 12 (717 students participated in the pre-assessments and 682 students participated in the post-assessments). The goal of the study is to develop a Learning Progression framework that provides effective guidance for curriculum and instruction on carbon-transforming processes in socio-ecological systems. We conducted the study in three research cycles. We developed a matter-and-energy Learning Progression framework during the first two cycles. This Learning Progression framework was used to guide the teaching intervention in the third research cycle. Clinical interviews and written assessments were implemented before and after the teaching intervention. In the process of data analysis, we found that the matter-and-energy Learning Progression framework did not provide a fine-gr...

  • a Learning Progression for water in socio ecological systems
    Journal of Research in Science Teaching, 2012
    Co-Authors: Kristin L Gunckel, Beth A Covitt, Ivan Salinas, Charles W Anderson
    Abstract:

    This article reports on our work of developing a Learning Progression focusing on K-12 students' performances of using energy concept in their accounts of carbon-transforming processes in socio-ecological systems. Carbon-transforming processes—the ecological carbon cycle and the combustion of biomass and fossil fuels—provide all of the energy for living systems and almost 90% of the energy for human economic activities. Energy, as a crosscutting concept across major disciplines, is a tool for analysis that uses the principle of energy conservation to constrain and connect accounts of processes and systems. Drawing on ideas from cognitive linguistics, the history of science, and research on students' energy conceptions, we identify two crucial practices that both scientists and students engage in when accounting for carbon-transforming processes: association and tracing. Using association and tracing as progress variables, we analyzed student accounts of carbon-transforming processes in 48 clinical interviews and 3,903 written tests administered to students from fourth grade through high school. Based on our analysis we developed a Learning Progression Framework that describes a Progression from accounts that use energy as an ephemeral “force” that enables actors to make events happen to energy as a scientific tool for analysis. Successful students developed a sense of necessity with respect to accounts of carbon-transforming processes—a sense that energy MUST be conserved and degraded in every individual process and in the system as a whole. This level of success was achieved by <3% of the students in our sample. Implications for science standards, curriculum, and instruction are discussed. © 2012 Wiley Periodicals, Inc. J Res Sci Teach 49: 1149–1180, 2012

  • developing a multi year Learning Progression for carbon cycling in socio ecological systems
    Journal of Research in Science Teaching, 2009
    Co-Authors: Lindsey Mohan, Jing Chen, Charles W Anderson
    Abstract:

    This study reports on our steps toward achieving a conceptually coherent and empirically validated Learning Progression for carbon cycling in socio-ecological systems. It describes an iterative process of designing and analyzing assessment and interview data from students in upper elementary through high school. The product of our development process—the Learning Progression itself—is a story about how learners from upper elementary grades through high school develop understanding in an important and complex domain: biogeochemical processes that transform carbon in socio-ecological systems at multiple scales. These processes: (a) generate organic carbon (photosynthesis), (b) transform organic carbon (biosynthesis, digestion, food webs, carbon sequestration), and (c) oxidize organic carbon (cellular respiration, combustion). The primary cause of global climate change is the current worldwide imbalance among these processes. We identified Levels of Achievement, which described patterns in the way students made progress toward more sophisticated reasoning about these processes. Younger learners perceived a world where events occurred at a macroscopic scale and carbon sources, such as foods and fuels, were treated as enablers of life processes and combustion rather than sources of matter transformed by those processes. Students at the transitional levels—levels 2 and 3—traced matter in terms of materials changed by hidden mechanisms (level 2) or changed by chemical processes (level 3). More advanced students (level 4) used chemical models to trace matter through hierarchically organized systems that connected organisms and inanimate matter. Although level 4 reasoning is consistent with current national standards, few high school students reasoned this way consistently. We discuss further plans for conceptual and empirical validation of the Learning Progression. © 2009 Wiley Periodicals, Inc. J Res Sci Teach 46: 675–698, 2009

  • focus article implications of research on children s Learning for standards and assessment a proposed Learning Progression for matter and the atomic molecular theory
    Measurement: Interdisciplinary Research & Perspective, 2006
    Co-Authors: Carol L Smith, Charles W Anderson, Marianne Wiser, Joseph Krajcik
    Abstract:

    The purpose of this article is to suggest ways of using research on children's reasoning and Learning to elaborate on existing national standards and to improve large-scale and classroom assessments. The authors suggest that Learning Progressions—descriptions of successively more sophisticated ways of reasoning within a content domain based on research syntheses and conceptual analyses—can be useful tools for using research on children's Learning to improve assessments. Such Learning Progressions should be organized around central concepts and principles of a discipline (i.e., its big ideas) and show how those big ideas are elaborated, interrelated, and transformed with instruction. They should also specify how those big ideas are enacted in specific practices that allow students to use them in meaningful ways, enactments the authors describe as Learning performances. Learning Progressions thus can provide a basis for ongoing dialogue between science Learning researchers and measurement specialists, leadi...

Victoria Krupnik - One of the best experts on this subject based on the ideXlab platform.

  • Stephanie’s Development of Reasoning by an Inductive Argument to Solve Tower Tasks: Part 2 of 3 (Grade 4)
    2020
    Co-Authors: Victoria Krupnik
    Abstract:

    Author Victoria Krupnik (Rutgers University - graduate) Overall Description This analytic is the second of three analytics that showcase Stephanie’s development of an argument by induction to solve a counting task over three school years. The three analytics focus on the reasoning, argumentation, and mathematical representations constructed by Stephanie in a variety of settings over time, in the third (Part 1), fourth (Parts 1 and 2), and fifth grades (Part 3). The first analytic begins with events where third grader Stephanie is working with a partner, in a whole class setting, building towers that are 3- and 4-tall, with plastic cubes available in two colors. This is followed by events in which Stephanie is working in a one-on-one interview with a researcher in the third and then fourth grade. The second analytic follows with events where fourth-grader Stephanie participates in a small group formative assessment and works on a summative assessment with a partner. The third analytic follows with events where fifth grader Stephanie is working with a partner, in a whole class setting, and then presenting her ideas to a small group and then to the whole class. In this analytic (the second of three), Stephanie’s Learning Progression is shown as she builds a justification for her solution to Tower Tasks by inductive reasoning. In fourth grade Stephanie presents an observed doubling pattern between Tower Tasks to a small group of students, presents a shortcut method to finding taller towers, and applies the doubling pattern as a rule to solve Tower Tasks up to 11-tall, selecting from two colors, in the partner summative assessment. Her problem solving is presented in events that serve to focus, in detail, on the explanations, reasoning, and argumentation Stephanie offers during her problem solving. Events 1-3 are retrieved from a small-group assessment interview (“Gang of Four”), facilitated by Researcher Maher (R2) on March 10, 1992. Stephanie presented her generalization of the doubling rule to taller towers up to 10-tall and a shortcut method for obtaining the number of towers of any height. Event 4 is retrieved from a June 15, 1992 session in which Stephanie and her partner, Milin, solved the 3-tall Tower Task written summative assessment at the end of the fourth grade. They applied the doubling rule to verify the numerical solution of the 3-tall Tower Task. The following definitions and background information about the Tower Task are offered: Doubling rule: The total number of different tower combinations of height k would be double the total number of tower combinations of height k–1. Argument by Induction An induction argument for the justification of the general solution 2^n includes the basic step (n=1) in which a participant states that the total number of 1-tall towers created when selecting from two colors is 2 (i.e. one of only blue and one of only yellow). The second step describes that the total number of towers of a given height can be found by placing either a yellow or blue cube on the top of each of the towers of the previous height, therefore doubling the total number of towers created in the previous height. Three-tall Tower Task (selecting from 2 colors): You have plastic cubes of 2 colors available to build towers. Your task is to make as many different looking towers as possible, each exactly 3 cubes high. Find a way to convince yourself and others that you have found all possible towers 3 cubes high, and that you have no duplicates [repetition of same color and order]. Record your towers below and provide a convincing argument why you think you have them all. After completing the Task for Towers 3-tall, describe and justify the approach you have chosen. (The Tower Task can be generalized to towers of any height “n-tall”). Video and Transcript References (in chronological order of Stephanie’s journey): B41, The Gang of Four (Jeff and Stephanie view), Grade 4, March 10, 1992, raw footage. Retrieved from: https://doi.org/doi:10.7282/T3CV4FWP B75, Towers Assessment, WV, Grade 4, Jun 15, 1992, raw. Retrieved from: https://doi.org/doi:10.7282/t3-tpqc-b71

  • Stephanie’s Development of Reasoning by an Inductive Argument to Solve Tower Tasks: Part 1 of 3 (Grades 3 & 4)
    2020
    Co-Authors: Usufu Nyakoojo, Victoria Krupnik
    Abstract:

    Author Victoria Krupnik (Rutgers University - graduate) Overall Description This analytic is the first of three analytics that showcase Stephanie’s development of an argument by induction to solve a counting task over three school years. The three analytics focus on the reasoning, argumentation, and mathematical representations constructed by Stephanie in a variety of settings, over time, in the third (Part 1), fourth (Parts 1 and 2), and fifth grades (Part 3). The first analytic begins with events where third grader Stephanie is working with a partner, in a whole class setting, building towers that are 3- and 4-tall, with plastic cubes available in two colors. This is followed by events in which Stephanie is working in a one-on-one interview with a researcher in third and then in fourth grade. The second analytic follows with events where fourth grader Stephanie participates in a small group formative assessment and works on a summative assessment with a partner. The third analytic follows with events where fifth grader Stephanie is working with a partner, in a whole class setting, and then presenting her ideas to a small group and then to the whole class. In this analytic (the first of three), Stephanie’s Learning Progression is shown as she builds a justification for her solution to Tower Tasks by inductive reasoning. In third grade, as she compares solutions to Tower Tasks of two heights, selecting from two colors, and, then in fourth grade, when she discovers a doubling pattern between Tower Tasks, Stephanie applies a doubling rule to solve Tower Tasks up to 11-tall. She is introduced to an inductive method to generate taller towers from shorter towers. Her problem solving is presented in events that serve to focus, in detail, on the explanations, reasoning, and argumentation Stephanie offers during her problem solving. Events 1 and 2 of this analytic are retrieved from a third-grade class session, facilitated by Researcher Alston (R1), on October 12, 1990. Partners Stephanie and Dana explore the 3-tall Tower Task after completing the 4-tall Tower Task. Event 3 is retrieved from a post-interview, facilitated by Researcher Martino (R3), on the same day, when Stephanie uses generic reasoning to justify why the number of 3-tall towers is fewer than the number of 4-tall towers. These events are shown for the purpose of presenting her early third-grade explorations building towers of two different heights. Events 4-7 are retrieved from a one-on-one interview facilitated by Researcher Maher (R2) that occurred on March 6, 1992. In this interview, Stephanie recognizes a doubling relationship between consecutive tower height solutions and applied this doubling pattern to predict the solutions of Tower Tasks up to 10-tall. She is also introduced by the researcher to an inductive method to account for the doubling pattern. She uses the physical tower models to solve the Outfit Task selecting from two colors of up to five clothing options by generating outfits inductively. The following definitions and background information about the Tower and Outfit Tasks are offered: Doubling rule The total number of different tower combinations of height k would be double the total number of tower combinations of height k–1. Argument by Induction An induction argument for the justification of the general solution 2^n includes the basic step (n=1) in which a participant states that the total number of 1-tall towers created when selecting from two colors is 2 (i.e. one of only blue and one of only yellow). The second step describes that the total number of towers of a given height can be found by placing either a yellow or blue cube on the top of each of the towers of the previous height, therefore doubling the total number of towers created in the previous height. Three-tall Tower Task (selecting from 2 colors): You have plastic cubes of 2 colors available to build towers. Your task is to make as many different looking towers as possible, each exactly 3 cubes high. Find a way to convince yourself and others that you have found all possible towers 3 cubes high, and that you have no duplicates [repetition of same color and order]. Record your towers below and provide a convincing argument why you think you have them all. After completing the Task for Towers 3-tall, describe and justify the approach you have chosen. (The Tower Task can be generalized to towers of any height “n-tall”). The original 3rd-grade Outfit (aka Shirts and Pants) Task: Stephen has a white shirt, a blue shirt and a yellow shirt. He has a pair of blue jeans and a pair of white jeans. How many different outfits can he make? Video and Transcript References (in chronological order of Stephanie’s journey): Towers Group Sharing, Clip 3 of 6: Guessing how many towers can be built three cubes high, continued. Retrieved from: https://doi.org/doi:10.7282/T30K26ZR Towers Group Sharing, Clip 6 of 6: Discussing their findings of how many towers can be built three cubes high. Retrieved from: https://doi.org/doi:10.7282/T3736P9W Stephanie Grade 3 Towers interview excerpts. Retrieved from: https://doi.org/doi:10.7282/T3FJ2F7X 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. Retrieved from: https://doi.org/doi:10.7282/T3SF30S

  • Michelle’s Longitudinal Problem Solving and Development of Reasoning About Tower Tasks: : Part 3 of 3 (Grade 5)
    2020
    Co-Authors: Victoria Krupnik
    Abstract:

    Author: Victoria Krupnik, Rutgers University Overall Description This analytic is the third of three analytics that showcase the problem solving of a counting task by a student, Michelle, over two school years. The analytics focus on the development of reasoning, argumentation, and mathematical representations constructed by Michelle in a variety of settings, over time, in the fourth (Parts 1 & 2) and fifth (Part 3) grades. The first analytic begins with Michelle working with a partner, in a whole class setting, building towers with plastic cubes that are 5-tall, selecting from cubes available in 2 colors. This is followed by events from a first and second one-on-one interview with researchers. The second analytic continues with events when Michelle participated in a small group formative assessment interview and with a partner on a summative assessment. The third analytic includes events when Michelle worked with a partner, Milin, in a whole class setting, using towers to solve an application task. In this analytic (the third of three analytics), Michelle’s Learning Progression in building “proof-like” justifications to Towers Tasks shows Michelle, in the fifth grade, listening to other arguments by induction and reasoning by induction to solve 3- and 4-tall Tower Tasks, selecting from two colors. Her problem solving is presented in a series of events that serve to focus, in detail, on the explanations, reasoning, and argumentation she offers during her problem solving. Events 1-4 are retrieved from a fifth-grade class session with partners Michelle and Milin as they work on a Guess My Tower (GMT) task on February 26, 1993. Solving the problem promotes revisiting the 3- and 4-tall tower outcome possibilities. Michelle indicates uncertainty of the 4-tall tower total, whereas Milin claims it to be 16. The events illustrate the dissemination of Milin’s idea about the doubling pattern that is recognized as they build towers of consecutive heights, supporting Milin’s inductive reasoning. Facilitated by R2, Milin explains his idea to Michelle in Event 1, Michelle displays her understanding in Events 2-3, and then demonstrates her reasoning with Stephanie and Matt in Event 4. The following definitions and background information about the Towers and Guess My Tower Tasks are offered. Argument by induction An induction argument for the justification of the general solution 2^n includes the basic step (n=1) in which a participant describes that the total number of 1-tall towers created when selecting from two colors is 2 (i.e. one of only blue and one of only yellow). The second states that the total number of towers of a given height can be found by placing either a yellow cube or a blue cube on the top of all of the towers of the previous height, therefore doubling the total number of towers created in the previous height. Case organization and/or argument In an organization and/or argument by cases, a statement is demonstrated by showing all the smaller subsets of statements that make up the whole. For example, the solution to the 3-tall Tower Task when selecting from two colors (i.e. blue and red) can be justified by separating the towers into cases using a characteristic of the tower. One such characteristic is the number of cubes of a specific color that the towers contain. In this situation, the towers can be broken down into four cases: 1) towers containing no red (towers with a single color); 2) three towers containing one red (towers with exactly one of color); 3) three towers containing 2 red cubes (within cases (2) and (3) can be cubes of the same color adjacent to or separated from each other); 4) one tower containing 3 reds or all red cubes. An argument by cases includes an exhaustive enumeration of the total number of towers in each case. Tower Task: You have plastic cubes of 2 colors available to build towers. Your task is to make as many different looking towers as possible, each exactly 3 (n) cubes high. Find a way to convince yourself and others that you have found all possible towers 3 (n) cubes high, and that you have no duplicates [repetition of same color and order]. Record your towers below and provide a convincing argument why you think you have them all. After completing the Task for Towers 3-tall, describe and justify the approach you have chosen. Guess My Tower Task: You have been invited to participate in a TV Quiz Show and have the opportunity to win a vacation to Disneyworld. The game is played by choosing one of the four possibilities for winning and then picking a tower out of a covered box. If the tower matches your choice, you win. You are told that the box contains all possible towers three tall that can be built when you select from cubes of two colors, red and yellow and that there is only one of each tower. There are no duplicates in the box. You are given the following possibilities for a winning tower: a. All cubes are exactly the same color; b. there is only one red cube; c. exactly two cubes are red; d. at least two cubes are yellow. Question 1. Which choice would you make and why would this choice be any better than any of the others? Question 2. Assuming you won, you can play again for the Grand Prize which means you can take a friend to Disneyworld. But now your box has all possible towers that are four tall with no duplicates (built by selecting from the two colors, yellow and red). You are to select from the same four possibilities for a winning tower. Which choice would you make this time and why would this choice be better than any of the others?" Video and Transcript References (in chronological order of Michelle’s journey): Building Towers, Selecting from two colors for Guess My Tower, Clip 3 of 5: Milin introduces an inductive argument. Retrieved from: https://doi.org/doi:10.7282/T3RN371

  • Michelle’s Longitudinal Problem Solving and Development of Reasoning About Tower Tasks: Part 2 of 3 (Grade 4)
    2020
    Co-Authors: Victoria Krupnik
    Abstract:

    Author: Victoria Krupnik, Rutgers University Overall Description This analytic is the second of three analytics that showcase the problem solving of a counting task by a student, Michelle, over two school years. The analytics focus on the development of reasoning, argumentation, and mathematical representations constructed by Michelle in a variety of settings, over time, in the fourth (Parts 1 & 2) and fifth (Part 3) grades. The first analytic begins with Michelle working with a partner, in a whole class setting, building towers with plastic cubes that are 5-tall, selecting from cubes available in two colors. This is followed by events from a first and second one-on-one interview with researchers. The second analytic continues with events when Michelle participated in a small group formative assessment interview and with a partner on a summative assessment. The third analytic includes events when Michelle worked with a partner, Milin, in a whole class setting, using towers to solve an application task. In this analytic (the second of three analytics), Michelle’s Learning Progression in building “proof-like” justifications to Towers Tasks shows Michelle, in the fourth grade, listening to the arguments of others by induction and cases and reasoning by cases with her partner. Her problem solving is presented in a series of events that serve to focus, in detail, on the explanations, reasoning, and argumentation she offers during her problem solving. Events 1-4 are retrieved from a small-group assessment interview (Gang of Four), facilitated by Researcher Maher (R2), on March 10, 1992. In this session, the students are asked to convince the researcher and each other of their solution to the 3-tall Tower Task, selecting from two colors. In Event 1, Michelle makes a claim for the numerical solutions to the Towers Tasks of heights one through five. After Milin and Stephanie offer explanations of solutions for finding all possible 3-tall tower outcomes, when selecting from two colors, Michelle displays her understanding of their arguments, engaging in justifications, as well as the review and evaluation of Milin’s inductive argument (Event 2) and Stephanie’s argument by cases (Event 3). The small group members provide rationales for the value of “looking for patterns.” Michelle contributes to the arguments offered, providing warrants to affirm the validity of the claims offered by her group members. In Event 4 Michelle applies Milin’s inductive reasoning to explain how the 4-tall Towers Task solution emerges from the 3-tall Towers solution. Events 5-6 are retrieved from a June 15, 1992 session in which Michelle and her partner, Jeff, work to solve the 3-tall Towers Task at the end of the fourth grade during a written assessment. Michelle and Jeff collaborate to jointly produce a written solution that includes an explanation, written by Michelle, along with drawings of towers organized by cases, drawn by Jeff. Event 5 illustrates their methodology by arranging 3-tall towers by elevator and color opposite patterns. Event 6 serves to illustrate their collaboration for their final solution and argument. The following definitions and background information about the Tower Task are offered. Strategies of locally exhaustive, systematic enumeration: Color “Opposites” (children’s language) Each element in a combination is replaced with the opposite element. The opposite of a tower in two colors is a tower of the same height where each position holds the opposite color of the cube in the corresponding position of the first tower. For example, a four-tall tower with yellow, blue, blue, blue and one with blue, yellow, yellow, yellow are opposites (Maher, Sran, & Yankelewitz, 2011). “Elevator” strategy (Jeff’s language) The elevator pattern is used when finding all possible towers containing one cube of one color and the remaining cubes of the other color. The single colored cube is placed in the first position of the first tower. To create a second tower, the cube is then moved to the second position. The cube is continuously lowered one position to create new towers until it is placed in the final position (Maher, Sran & Yankelewitz, 2011). Argument by induction An induction argument for the justification of the general solution 2^n includes the basic step (n=1) in which a participant describes that the total number of 1-tall towers created when selecting from two colors is 2 (i.e. one of only blue and one of only yellow). The second states that the total number of towers of a given height can be found by placing either a yellow cube or a blue cube on the top of all of the towers of the previous height, therefore doubling the total number of towers created in the previous height. Case organization and/or argument In an organization and/or argument by cases, a statement is demonstrated by showing all the smaller subsets of statements that make up the whole. For example, the solution to the 3-tall Tower Task when selecting from two colors (i.e. blue and red) can be justified by separating the towers into cases using a characteristic of the tower. One such characteristic is the number of cubes of a specific color that the towers contain. In this situation, the towers can be broken down into four cases: 1) towers containing no red (towers with a single color); 2) three towers containing one red (towers with exactly one of color); 3) three towers containing 2 red cubes (within cases (2) and (3) can be cubes of the same color adjacent to or separated from each other); 4) one tower containing 3 reds or all red cubes. An argument by cases includes an exhaustive enumeration of the total number of towers in each case. Tower Task: You have plastic cubes of 2 colors available to build towers. Your task is to make as many different looking towers as possible, each exactly 3 (n) cubes high. Find a way to convince yourself and others that you have found all possible towers 3 (n) cubes high, and that you have no duplicates [repetition of same color and order]. Record your towers below and provide a convincing argument why you think you have them all. After completing the Task for Towers 3-tall, describe and justify the approach you have chosen. Video and Transcript References (in chronological order of Michelle’s journey): B41, The Gang of Four (Jeff and Stephanie view), Grade 4, March 10, 1992, raw footage. Retrieved from: https://doi.org/doi:10.7282/T3CV4FWP B42, The Gang of Four (Michelle and Milin view), Grade 4, March 10, 1992, raw footage. Retrieved from: https://doi.org/doi:10.7282/T3833Q5P B75, Towers Assessment, WV, Grade 3, Jun 15, 1992, raw. Retrieved from: https://doi.org/doi:10.7282/t3-tpqc-b71

  • Stephanie’s Development of Reasoning by an Inductive Argument to Solve Tower Tasks: Part 3 of 3 (Grade 5)
    2020
    Co-Authors: Victoria Krupnik
    Abstract:

    Author Victoria Krupnik (Rutgers University - graduate) Overall Description This analytic is the third of three analytics that showcase Stephanie’s development of an argument by induction to solve a counting task over three school years. The three analytics focus on the reasoning, argumentation, and mathematical representations constructed by Stephanie in a variety of settings over time, in the third (Part 1), fourth (Parts 1 and 2), and fifth grades (Part 3). The first analytic begins with events where third grader Stephanie is working with a partner, in a whole class setting, building towers that are 3- and 4-tall, with plastic cubes available in two colors. This is followed by events in which Stephanie is working in a one-on-one interview with a researcher in the third and then fourth grade. The second analytic follows with events where fourth-grader Stephanie participates in a small group formative assessment and works on a summative assessment with a partner. The third analytic follows with events where fifth grader Stephanie is working with a partner, in a whole class setting, and then presenting her ideas to a small group and then to the whole class. In this analytic (the third of three), Stephanie’s Learning Progression in building a justification by inductive reasoning to Tower Tasks shows Stephanie in the fifth grade recalling and testing a doubling pattern between Tower Tasks, observing Michelle and Matt present an inductive method to generate taller towers from shorter towers to justify the doubling pattern, and, finally, presenting an inductive argument for the growth of towers for any height. Her problem solving is presented in events that serve to focus, in detail, on the explanations, reasoning, and argumentation Stephanie offers during her problem solving. Events 1-7 are retrieved from a fifth-grade class session with partners Stephanie and Matt as they worked on a Guess My Tower (GMT) task on February 26, 1992. Solving the problem promoted revisiting the 3- and 4-tall tower outcome possibilities. Events 1-2 show Stephanie attempting to test a doubling rule that she recalls from prior Towers problem-solving experiences. Milin’s inductive approach to finding taller towers from shorter towers is disseminated to other students during this session, first to Michelle, then to Stephanie and Matt (Event 3), and then to the rest of the class (Events 4-7). The purpose of the GMT events is to explore Stephanie’s Learning of his idea. The events presented are evidence of Stephanie’s individual reasoning about the doubling pattern and her reconciliation between the doubling rule and why it worked. The following definitions and background information about the Tower and Guess My Tower tasks are offered: Doubling rule The total number of different tower combinations of height k would be double the total number of tower combinations of height k–1. Argument by Induction An induction argument for the justification of the general solution 2^n includes the basic step (n=1) in which a participant states that the total number of 1-tall towers created when selecting from two colors is 2 (i.e. one of only blue and one of only yellow). The second step describes that the total number of towers of a given height can be found by placing either a yellow or blue cube on the top of each of the towers of the previous height, therefore doubling the total number of towers created in the previous height. Three-tall Tower Task (selecting from 2 colors): You have plastic cubes of 2 colors available to build towers. Your task is to make as many different looking towers as possible, each exactly 3 cubes high. Find a way to convince yourself and others that you have found all possible towers 3 cubes high, and that you have no duplicates [repetition of same color and order]. Record your towers below and provide a convincing argument why you think you have them all. After completing the Task for Towers 3-tall, describe and justify the approach you have chosen. (The Tower Task can be generalized to towers of any height “n-tall”). Guess My Tower Task: You have been invited to participate in a TV Quiz Show and have the opportunity to win a vacation to Disneyworld. The game is played by choosing one of the four possibilities for winning and then picking a tower out of a covered box. If the tower matches your choice, you win. You are told that the box contains all possible towers three tall that can be built when you select from cubes of two colors, red and yellow and that there is only one of each tower. There are no duplicates in the box. You are given the following possibilities for a winning tower: a. All cubes are exactly the same color; b. There is only one red cube; c. Exactly two cubes are red; d. At least two cubes are yellow. Question 1. Which choice would you make and why would this choice be any better than any of the others? Question 2. Assuming you won, you can play again for the Grand Prize which means you can take a friend to Disneyworld. But now your box has all possible towers that are four tall with no duplicates (built by selecting from the two colors, yellow and red). You are to select from the same four possibilities for a winning tower. Which choice would you make this time and why would this choice be better than any of the others?" Video and Transcript References (in chronological order of Stephanie’s journey): B78,Guess My Tower task,Matt and Stephanie partner work (work view), Grade 5,February 26,1993,Raw footage. Retrieved from: https://doi.org/doi:10.7282/t3-hw4j-2f57 Building Towers, Selecting from two colors for Guess My Tower, Clip 2 of 5: Does the Number Double? Retrieved from: https://doi.org/doi:10.7282/T32V2FBZ Building Towers, Selecting from two colors for Guess My Tower, Clip 3 of 5: Milin introduces an inductive argument. Retrieved from: https://doi.org/doi:10.7282/T3RN371Z Building Towers, Selecting from two colors for Guess My Tower, Clip 4 of 5: Stephanie and Matt Rebuild the Argument. Retrieved from: https://doi.org/doi:10.7282/T3W958DV Building Towers, Selecting from two colors for Guess My Tower, Clip 5 of 5: Sharing with the Group. Retrieved from: https://doi.org/doi:10.7282/T36M361

Mark Wilson - One of the best experts on this subject based on the ideXlab platform.

  • improving Learning using a Learning Progression to coordinate instruction and assessment
    Frontiers in Education, 2021
    Co-Authors: Mark Wilson, Richard Lehrer
    Abstract:

    We describe the development and implementation of a Learning Progression specifying transitions in reasoning about data and statistics when middle school students are inducted into practices of visualizing, measuring, and modeling the variability inherent in processes ranging from repeated measure to production to organismic growth. A series of design studies indicated that inducting students into these approximations of statistical practice supported the development of statistical reasoning. Conceptual change was supported by close coordination between assessment and instruction, where changes in students’ ways of thinking about data and statistics were illuminated as progress along six related constructs. Each construct was developed iteratively during the course of design research as we became better informed about the forms of thinking that tended to emerge as students were inducted into how statisticians describe and analyze variability. To illustrate how instruction and assessment proceeded in tandem, we consider progress in one construct, Modeling Variability. For this construct, we describe how Learning activities supported the forms of conceptual change envisioned in the construct, and how conceptual change was indicated by items specifically designed to target levels of the construct map. We show how student progress can be monitored and summatively assessed using items and empirical maps of items’ locations compared to student locations (called Wright maps), and how some items were employed formatively by classroom teachers to further student Learning.

  • making measurement important for education the crucial role of classroom assessment
    Educational Measurement: Issues and Practice, 2018
    Co-Authors: Mark Wilson
    Abstract:

    Author(s): Wilson, M | Abstract: © 2018 by the National Council on Measurement in Education This article is a written version of the Presidential Address1 I gave at the annual meeting of the National Council on Measurement in Education (NCME) in April 2017. It is a call to NCME members (and others who read this, of course) to rebalance their focus so that classroom assessments are seen as being at least as important as large-scale assessments for education (in fact, in my view, they are more important). The article reviews research literature about the effects of classroom assessment to establish its importance for education. Then, the roles of large-scale assessment are reviewed, and, in particular, it is noted how these can have negative results when the large-scale assessments are not well aligned with sound curriculum and instructional and assessment practices grounded in theories of Learning. In the next two sections (a) the idea of a Learning Progression is described as a way to facilitate the coherence between classroom and large-scale assessment and (b) the idea of a “roadmap” is described, being the assessment components of the Learning Progression. This is followed by a description of an example of such a roadmap, developed for the Assessing Data Modeling and Statistical Reasoning project using the BEAR Assessment System (BAS). Finally, a concluding discussion reviews the ways that the coherence between large-scale and classroom assessments can be achieved using the BAS, and hence make measurement more important for education.

  • a construct modeling approach to develop a Learning Progression of how students understand the structure of matter
    Journal of Research in Science Teaching, 2017
    Co-Authors: Linda Morell, Tina Collier, Paul Black, Mark Wilson
    Abstract:

    Author(s): Morell, Linda; Collier, Tina; Paul, Black; Wilson, Mark | Abstract: This paper builds on the current literature base about Learning Progressions in science to address the question, “What is the nature of the Learning Progression in the content domain of the structure of matter?” We introduce a Learning Progression in response to that question and illustrate a methodology, the Construct Modeling (Wilson, 2005) approach, for investigating the Progression through a developmentally based iterative process. This study puts forth a Progression of how students understand the structure of matter by empirically inter-relating constructs of different levels of sophistication using a sample of 1,087 middle grade students from a large diverse public school district in the western part of the United States. The study also shows that student thinking can be more complex than hypothesized as in the case of our discovery of a substructure of understanding in a single construct within the larger Progression. Data were analyzed using a multidimensional Rasch model. Implications for teaching and Learning are discussed—we suggest that the teacher’s choice of instructional approach needs to be fashioned in terms of a model, grounded in evidence, of the paths through which Learning might best proceed, working toward the desired targets by a pedagogy which also cultivates students’ development as effective learners. This research sheds light on the need for assessment methods to be used as guides for formative work and as tools to ensure the Learning goals have been achieved at the end of the Learning period. The development and investigation of a Learning Progression of how students understand the structure of matter using the Construct Modeling approach makes an important contribution to the research on Learning Progressions and serves as a guide to the planning and implementation in the teaching of this topic. # 2017 Wiley Periodicals, Inc. J Res Sci Teach 54: 1024–1048, 2017

  • assessment of Learning in digital interactive social networks a Learning analytics approach
    Journal of asynchronous learning networks, 2016
    Co-Authors: Mark Wilson, Perman Gochyyev, Kathleen Scalise
    Abstract:

    This paper summarizes initial field-test results from data analytics used in the work of the Assessment and Teaching of 21st Century Skills (ATC21S) project, on the “ICT Literacy — Learning in digital networks” Learning Progression. This project, sponsored by Cisco, Intel and Microsoft, aims to help educators around the world enable students with the skills to succeed in future career and college goals. The paper begins with describing some expansions to a common definition of Learning analytics, then includes a review of the literature on ICT literacy, including the specific development that led to the ATC21S effort. This is followed by a description of the development of a “Learning Progression” for this project, as well as the logic behind the instrument construction and data analytics, along with examples of each. Data were collected in a demonstration digital environment in four countries: Australia, Finland, Singapore and the U.S. The results indicate that the new constructs developed by the project, and the novel item forms and analytics that were employed, are indeed capable of being employed in a large-scale digital environment. The paper concludes with a discussion of the next steps for this effort. Acknowledgements: We thank the ATC21S project and its funders for their support for the work reported in this report. We also acknowledge the expertise and creative input of the ATC21S Expert Panel in ICT Literacy: John Ainley (Chair), Julian Fraillon, Peter Pirolli, Jean-Paul Reeff, Kathleen Scalise, and Mark Wilson. Of course, the views and opinions expressed in this paper are those of the authors alone.

  • rethinking ict literacy from computer skills to social network settings
    Thinking Skills and Creativity, 2015
    Co-Authors: Mark Wilson, Kathleen Scalise, Perman Gochyyev
    Abstract:

    Abstract This paper starts from the perspective that the current conceptualization of educational assessment is out of date, but particularly with regard to conception of information and communication (ICT) literacy. We initially provide a brief summary of the idea of a 21st century skill, then trace the conceptual changes in the idea of ICT literacy in four main steps: First, we briefly describe a concentration of knowledge about computers and their use, coalescing into the concept of ICT literacy in the early years of the field. Second, we describe the transition to a view of ICT literacy as a broad set of skills that have links to many traditional and non-traditional school subjects, and the move to technology integration in education. Third, we see the next transition for ICT literacy expressed as progress variables that are essential tools for the design of curriculum and assessments. Fourth, we discuss the impact of the “social network” perspective on ICT literacy—the critical need for building the power of virtual skills through proficiency with networks of people, information, tools, and resources. In summary, we offer a new framework for assessing student ICT Learning, based on a Learning Progression and social networking point of view. Throughout, we use extensive examples to help illustrate our review of the broad sweep of this development, and, as a part of the conclusion, we speculate about the coming next steps.

Julia D Plummer - One of the best experts on this subject based on the ideXlab platform.

  • development of a Learning Progression for the formation of the solar system
    International Journal of Science Education, 2015
    Co-Authors: Julia D Plummer, Christopher Palma, Alice Flarend, Keri Ann Rubin, Yann Shiou Ong, Brandon Botzer, Scott P Mcdonald, Tanya Furman
    Abstract:

    This study describes the process of defining a hypothetical Learning Progression (LP) for astronomy around the big idea of Solar System formation. At the most sophisticated level, students can explain how the formation process led to the current Solar System by considering how the planets formed from the collapse of a rotating cloud of gas and dust. Development of this LP was conducted in 2 phases. First, we interviewed middle school, high school, and college students (N = 44), asking them to describe properties of the current Solar System and to explain how the Solar System was formed. Second, we interviewed 6th-grade students (N = 24) before and after a 15-week astronomy curriculum designed around the big idea. Our analysis provides evidence for potential levels of sophistication within the hypothetical LP, while also revealing common alternative conceptions or areas of limited understanding that could form barriers to progress if not addressed by instruction. For example, many students' understanding o...

  • building a Learning Progression for celestial motion an exploration of students reasoning about the seasons
    Journal of Research in Science Teaching, 2014
    Co-Authors: Julia D Plummer, L Maynard
    Abstract:

    We present the development of a construct map addressing the reason for the seasons, as a subset of a larger Learning Progression on celestial motion. Five classes of 8th grade students (N = 38) participated in a 10-day curriculum on the seasons. We revised a hypothetical seasons construct map using a Rasch model analysis of students' pre/post-assessments followed by a closer examination of individual student explanations. Our proposed construct map is consistent with the Framework for K-12 Science Education [National Research Council. (2012). Framework for K-12 Science Education. Washington, DC: National Academy Press] but includes a more nuanced discussion of critical conceptual and spatial connections. Movement up the construct map begins with Learning foundational concepts about the Earth's motion in space and how observational patterns of the Sun relate to temperature changes. Movement into the upper levels of the seasons construct map occurs as instruction supports students in making sense of how the space-based perspective of their location on a spherical Earth can be used to account for observable patterns of change. However, our findings suggest that making this connection between Earth-based observations of the Sun and the motions and perspectives of the Earth in space is one of the major challenges that limit student progress in this domain. Findings have implications for instruction designed to support astronomy education as described by the Next Generation Science Standards [NGSS Lead States. (2013) Next Generation Science Standards: For the States, By the States. Achieve, Inc. on behalf of the twenty-six states and partners that collaborated on the NGSS. Retrieved from: http://www.nextgenscience.org/next-generation-science-standards]. Instruction that supports progress along this construct map, and the larger celestial motion Learning Progression, must purposefully support the spatially complex connection between the Earth's motion in space and phenomena observed from the Earth's surface. © 2014 Wiley Periodicals, Inc. J Res Sci Teach 51:902–929, 2014.

  • spatial thinking as the dimension of progress in an astronomy Learning Progression
    Studies in Science Education, 2014
    Co-Authors: Julia D Plummer
    Abstract:

    The big idea of celestial motion, observational astronomy phenomena explained by the relative position and motion of objects in the solar system and beyond, is central to astronomy in primary and secondary education. In this paper, I argue that students’ progress in developing productive, scientific explanations for this class of astronomical phenomena can be defined by the increasing sophistication of spatial knowledge and reasoning in the domain. Drawing upon literature on children’s ideas about celestial motion, instruction that supports progress in that domain and literature on spatial thinking, I developed a Learning Progression (LP) framework that integrates cognition, instruction and assessment to understand student Learning in this domain. This framework was applied to a study of children Learning to explain the daily celestial motion of the Sun, Moon and stars, and the phases of the Moon. The application of the LP framework to analyse teaching sequences in astronomy extends this review by illustr...

  • building a Learning Progression for celestial motion elementary levels from an earth based perspective
    Journal of Research in Science Teaching, 2010
    Co-Authors: Julia D Plummer, Joseph Krajcik
    Abstract:

    Prior research has demonstrated that neither children nor adults hold a scientific understanding of the big ideas of astronomy, as described in standards documents for science education (National Research Council (1996). National science education standards. Washington, DC: National Academy Press; American Association for the Advancement of Science (1993). Benchmarks for science literacy. New York: Oxford University Press). This manuscript focuses on ideas in astronomy that are at the foundation of elementary students' understanding of the discipline: the apparent motion of the sun, moon, and stars as seen from an earth-based perspective. Lack of understanding of these concepts may hinder students' progress towards more advanced understanding in the domain. We have analyzed the logic of the domain and synthesized prior research assessing children's knowledge to develop a set of Learning trajectories that describe how students' initial ideas about apparent celestial motion as they enter school can be built upon, through successively more sophisticated levels of understanding, to reach a level that aligns with the scientific view. Analysis of an instructional intervention with elementary students in the planetarium was used to test our initial construction of the Learning trajectories. This manuscript presents a first look at the use of a Learning Progression framework in analyzing the structure of astronomy education. We discuss how this work may eventually lead towards the development and empirical testing of a full Learning Progression on the big idea: how children learn to describe and explain apparent patterns of celestial motion. 2010 Wiley Periodicals, Inc. J Res Sci Teach 47: 768-787, 2010

Amelia Wenk Gotwals - One of the best experts on this subject based on the ideXlab platform.

  • early elementary students understanding of complex ecosystems a Learning Progression approach
    Journal of Research in Science Teaching, 2016
    Co-Authors: Hayat Hokayem, Amelia Wenk Gotwals
    Abstract:

    Engaging in systemic reasoning about ecological issues is critical for early elementary students to develop future understanding of critical environmental issues such as global warming and loss of biodiversity. However, ecological issues are rarely taught in ways to highlight systemic reasoning in elementary schools. In this study, we conducted semi-structured interviews with 44 students from the first through fourth grades. Using an iterative process, we developed an empirically grounded Learning Progression that captures how elementary students use systemic reasoning to explain interactions in ecosystems. This Learning Progression contains five reasoning patterns: anthropomorphic reasoning, concrete practical reasoning, simple causal reasoning, semi-complex causal reasoning, and complex causal reasoning. The results also show that many students exhibited mixed-level reasoning, meaning that they used reasoning patterns at multiple levels to construct a single response. We discuss the implications of the study for Learning Progression research and teaching ecosystems at early elementary grades. © 2016 Wiley Periodicals, Inc. J Res Sci Teach 53: 1524–1545, 2016

  • validity evidence for Learning Progression based assessment items that fuse core disciplinary ideas and science practices
    Journal of Research in Science Teaching, 2013
    Co-Authors: Amelia Wenk Gotwals, Nancy Butler Songer
    Abstract:

    This article evaluates a validity argument for the degree to which assessment tasks are able to provide evidence about knowledge that fuses information from a Progression of core disciplinary ideas in ecology and a Progression for the scientific practice of developing evidence-based explanations. The article describes the interpretive framework for the argument, including evidence for how well the assessment tasks are matched to the Learning Progressions and the methods for interpreting students' responses to the tasks. Findings from a dual-pronged validity study that includes a think-aloud analysis and an item difficulty analysis are presented as evidence. The findings suggest that the tasks provide opportunities for students at multiple ability levels to show evidence of both successes and struggles with the development of knowledge that fuses core disciplinary ideas with the scientific practice of developing evidence-based explanations. In addition, these tasks are generally able to distinguish between different ability-level students. However, some of the assumptions in the interpretive argument are not supported, such as the inability of the data to provide evidence that might neatly place students at a given level on our Progressions. Implications for the assessment system, specifically, how responses are elicited from students, are discussed. In addition, we discuss the implications of our findings for defining and redesigning Learning Progressions. © 2013 Wiley Periodicals, Inc. J Res Sci Teach 50: 597–626, 2013.

  • how and when does complex reasoning occur empirically driven development of a Learning Progression focused on complex reasoning about biodiversity
    Journal of Research in Science Teaching, 2009
    Co-Authors: Nancy Butler Songer, Ben Kelcey, Amelia Wenk Gotwals
    Abstract:

    In order to compete in a global economy, students are going to need resources and curricula focusing on critical thinking and reasoning in science. Despite awareness for the need for complex reasoning, American students perform poorly relative to peers on international standardized tests measuring complex thinking in science. Research focusing on Learning Progressions is one effort to provide more coherent science curricular sequences and assessments that can be focused on complex thinking about focal science topics. This article describes an empirically driven, five-step process to develop a 3-year Learning Progression focusing on complex thinking about biodiversity. Our efforts resulted in empirical results and work products including: (1) a revised definition of Learning Progressions, (2) empirically driven, 3-year Progressions for complex thinking about biodiversity, (3) an application of statistical approaches for the analysis of Learning Progression products, (4) Hierarchical Linear Modeling results demonstrating significant student achievement on complex thinking about biodiversity, and (5) Growth Model results demonstrating strengths and weaknesses of the first version of our curricular units. The empirical studies present information to inform both curriculum and assessment development. For curriculum development, the role of Learning Progressions as templates for the development of organized sequences of curricular units focused on complex science is discussed. For assessment development, Learning Progression-guided assessments provide a greater range and amount of information that can more reliably discriminate between students of differing abilities than a contrasting standardized assessment measure that was also focused on biodiversity content. © 2009 Wiley Periodicals, Inc. J Res Sci Teach 46: 610–631, 2009