Imani Goffney - Profile on Academia.edu (original) (raw)

Papers by Imani Goffney

arXiv (Cornell University), Dec 13, 2023

Cognitive modeling commonly relies on asking participants to complete a battery of varied tests i... more Cognitive modeling commonly relies on asking participants to complete a battery of varied tests in order to estimate attention, working memory, and other latent variables. In many cases, these tests result in highly variable observation models. A near-ubiquitous approach is to repeat many observations for each test independently, resulting in a distribution over the outcomes from each test given to each subject. Latent variable models (LVMs), if employed, are only added after data collection. In this paper, we explore the usage of LVMs to enable learning across many correlated variables simultaneously. We extend LVMs to the setting where observed data for each subject are a series of observations from many different distributions, rather than simple vectors to be reconstructed. By embedding test battery results for individuals in a latent space that is trained jointly across a population, we can leverage correlations both between disparate test data for a single participant and between multiple participants. We then propose an active learning framework that leverages this model to conduct more efficient cognitive test batteries. We validate our approach by demonstrating with realtime data acquisition that it performs comparably to conventional methods in making item-level predictions with fewer test items.

A standard approach for evaluating a cognitive variable involves designing a test procedure targe... more A standard approach for evaluating a cognitive variable involves designing a test procedure targeting that variable and then validating test results in a sample population. To extend this functionality to other variables, additional tests are designed and validated in the same way. Test batteries are constructed by concatenating individual tests. This approach is convenient for the designer because it is modular. However, it is not scalable because total testing time grows proportionally with test count, limiting the practical size of a test battery. Cross-test models can inform the relationships between explicit or implicit cognitive variables but do not shorten test time and cannot readily accommodate subpopulations who exhibit different relationships than average. An alternate modeling framework using probabilistic machine learning can rectify these shortcomings, resulting in item-level prediction from individualized models while requiring fewer data points than current methods. To validate this approach, a Gaussian process probabilistic classifier was used to model young adult and simulated spatial working memory task performance as a psychometric function. This novel test instrument was evaluated for accuracy, reliability and efficiency relative to a conventional method recording the maximum spatial sequence length recalled. The novel method exhibited extremely low bias, as well as test-retest reliability 30% higher than the conventional method under standard testing conditions. Efficiency was consistent with other adaptive psychometric threshold estimation strategies, with 30-50 samples needed for consistently reliable estimates. While these results demonstrate that similar spatial working memory tasks can be effectively modeled as psychometric functions by any method, the advantage of the novel method is that it is scalable to accommodate much more complex models, such as those including additional executive functions. Further, it was designed with tremendous flexibility to incorporate informative theory, ancillary data, previous cohort performance, previous individual performance, and/or current individual performance for improved predictions. The result is a promising method for behavioral modeling that can be readily extended to capture complex individual task performance.

Inferences about executive functions (EFs) are commonly drawn via lengthy serial administration o... more Inferences about executive functions (EFs) are commonly drawn via lengthy serial administration of simple independent assessments. Classical methods for EF estimation often require excessive measurements and provide little or no flexibility to dynamically adjust test length for each individual. In order to decrease test duration and mitigate respondent burden, active testing modalities that incorporate more efficient data collection strategies are indispensable. To this end, we propose sequential analysis to improve upon traditional testing methods in behavioral science. In this paper, we show that sequential testing can be used to rapidly screen for a difference in the EF of a given individual with respect to a baseline level. In cognitive tests consisting of repeated identical tasks, a sequential framework can be utilized to actively detect significant differences in cognitive performance with high confidence more rapidly than conventional non-sequential approaches. Ultimately, sequential analysis could be applied to a variety of problems in cognitive and perceptual domains to improve efficiency gains and achieve substantial test length reduction.

Promoting Computational Thinking, Computational Participation, and Spatial Reasoning with LEGO Robotics

Canadian Journal of Science, Mathematics and Technology Education

Equitably Teaching and Mathematically Preparing

Proceedings of the 2022 AERA Annual Meeting

Equity in Mathematics Methods Coursework: A Necessary Pairing

Proceedings of the 2020 AERA Annual Meeting

Rehumanizing Mathematics for Black, Indigenous, and Latinx Students

National Council of Teachers of Mathematics, 2018

In this essay, the authors, as participants of the Privilege and Oppression in the Preparation of... more In this essay, the authors, as participants of the Privilege and Oppression in the Preparation of Mathematics Teachers Educators conference, reflect on tensions inherent in standing with and speaking on behalf of communities in an attempt to build and signal solidarity with them. They describe this tension in relation to their membership in the community of researchers who study equity in mathematics education. A particular exchange that arose during whole group discussion at the conference seeded a conversation around other situations they have encountered in this community, and led to the development of a set of "cautionary tales" for the field.

Mathematics teaching produces and reproduces social injustice. It also has the potential to disru... more Mathematics teaching produces and reproduces social injustice. It also has the potential to disrupt patterns of inequity and advance just communities of practice. Drawing from literature on equitable mathematics teaching, we analyze the work of leading a discussion of student solutions in ways that nurture healthy identities, relationships and societies. From a conceptual analysis of a Norwegian mathematics lesson, we first identify dynamics of race and gender at play, then identify three key aspects of mathematics teaching that can serve to disrupt these dynamics while creating opportunities for alternative identities, relationships and futures: (i) having regard for property and its use; (ii) taking up student thinking as participatory citizenship; and (iii) orchestrating collective mathematical work. We discuss nuances of this work and implications for research on teaching.

A Retrospective Look at Where We’ve Been and Where We Might Go: The Research Committee Reflects Upon the Judith Jacob Lectures and the Early Career Award Articles

Considering Hybrid Mathematics Content and Methods Courses for Preservice Teachers Introduction

Designing the Online Portion of Hybrid Pedagogy and Content Courses for Preservice Elementary Teachers

The Complexities of Teaching About Issues of Equity, Diversity, Social Justice, and Multicultural Education in an Online Course

Soccer for Real

Mathematics Teaching in the Middle School, 2019

My name is Naima Goffney, and I am an eleven-year-old seventh grader at Julius West Middle School... more My name is Naima Goffney, and I am an eleven-year-old seventh grader at Julius West Middle School. I am taking algebra 1 this year. I wanted to write the Math for Real because in math class I do not always think that what we are learning is related to the real world. At home, my mom shows me all the different ways I am mathematically smart, which makes me want to try harder in school during the “rougher” days. We can use math to know more about how to improve our skills and find the math we learn in school more interesting and more related to our real world as middle schoolers.

Math smarts in Wordles

Teaching Children Mathematics, 2016

Postscript items are designed as rich grab-and-go resources that any teacher can quickly incorpor... more Postscript items are designed as rich grab-and-go resources that any teacher can quickly incorporate into his or her classroom repertoire with little effort and maximum impact. Increase mathematical confidence by creating ways for students to show they are “smart” in math through Smartness Wordles™, collections of words in graphic representation.

did not just teach academic subjects. They taught their pupils skills and knowledge to help devel... more did not just teach academic subjects. They taught their pupils skills and knowledge to help develop them as individuals and as members of a collective. Subject matters offered important resources for these social goals: they and their students read literature in the voices of a wide range of people, about experiences both similar to and different from theirs. They studied other cultures and learned about work, life, and practice in a variety of societies and settings. And they learned that issues of voice, experience, culture, and setting were important threads in the tapestry of what it means to be human. The work they did with their pupils across these academic subjects was, of course, also aimed at developing the children’s skills and knowledge, their capacity to interpret texts and

Measuring Teacher Quality in Practice

Measurement Issues and Assessment for Teaching Quality

Validating Measures Validating Measures of of Content Knowledge for Teaching Mathematics: Content Knowledge for Teaching Mathematics: A Validity Argument Approach A Validity Argument Approach

Validating the Ecological Assumption: The Relationship of Measure Scores to Classroom Teaching and Student Learning

Measurement: Interdisciplinary Research and Perspectives, 2007

Assessing Elemental and Structural Validity: Data from Teachers, Non-teachers, and Mathematicians

Measurement: Interdisciplinary Research and Perspectives, 2007

Validation efforts typically focus around what, exactly, is measured by an instrument (s), and wh... more Validation efforts typically focus around what, exactly, is measured by an instrument (s), and whether what is measured corresponds to the theoretical domain (s) originally specified. In this paper, we conduct a first analysis into these issues. Our goal is building instruments ...

arXiv (Cornell University), Dec 13, 2023

Cognitive modeling commonly relies on asking participants to complete a battery of varied tests i... more Cognitive modeling commonly relies on asking participants to complete a battery of varied tests in order to estimate attention, working memory, and other latent variables. In many cases, these tests result in highly variable observation models. A near-ubiquitous approach is to repeat many observations for each test independently, resulting in a distribution over the outcomes from each test given to each subject. Latent variable models (LVMs), if employed, are only added after data collection. In this paper, we explore the usage of LVMs to enable learning across many correlated variables simultaneously. We extend LVMs to the setting where observed data for each subject are a series of observations from many different distributions, rather than simple vectors to be reconstructed. By embedding test battery results for individuals in a latent space that is trained jointly across a population, we can leverage correlations both between disparate test data for a single participant and between multiple participants. We then propose an active learning framework that leverages this model to conduct more efficient cognitive test batteries. We validate our approach by demonstrating with realtime data acquisition that it performs comparably to conventional methods in making item-level predictions with fewer test items.

A standard approach for evaluating a cognitive variable involves designing a test procedure targe... more A standard approach for evaluating a cognitive variable involves designing a test procedure targeting that variable and then validating test results in a sample population. To extend this functionality to other variables, additional tests are designed and validated in the same way. Test batteries are constructed by concatenating individual tests. This approach is convenient for the designer because it is modular. However, it is not scalable because total testing time grows proportionally with test count, limiting the practical size of a test battery. Cross-test models can inform the relationships between explicit or implicit cognitive variables but do not shorten test time and cannot readily accommodate subpopulations who exhibit different relationships than average. An alternate modeling framework using probabilistic machine learning can rectify these shortcomings, resulting in item-level prediction from individualized models while requiring fewer data points than current methods. To validate this approach, a Gaussian process probabilistic classifier was used to model young adult and simulated spatial working memory task performance as a psychometric function. This novel test instrument was evaluated for accuracy, reliability and efficiency relative to a conventional method recording the maximum spatial sequence length recalled. The novel method exhibited extremely low bias, as well as test-retest reliability 30% higher than the conventional method under standard testing conditions. Efficiency was consistent with other adaptive psychometric threshold estimation strategies, with 30-50 samples needed for consistently reliable estimates. While these results demonstrate that similar spatial working memory tasks can be effectively modeled as psychometric functions by any method, the advantage of the novel method is that it is scalable to accommodate much more complex models, such as those including additional executive functions. Further, it was designed with tremendous flexibility to incorporate informative theory, ancillary data, previous cohort performance, previous individual performance, and/or current individual performance for improved predictions. The result is a promising method for behavioral modeling that can be readily extended to capture complex individual task performance.

Inferences about executive functions (EFs) are commonly drawn via lengthy serial administration o... more Inferences about executive functions (EFs) are commonly drawn via lengthy serial administration of simple independent assessments. Classical methods for EF estimation often require excessive measurements and provide little or no flexibility to dynamically adjust test length for each individual. In order to decrease test duration and mitigate respondent burden, active testing modalities that incorporate more efficient data collection strategies are indispensable. To this end, we propose sequential analysis to improve upon traditional testing methods in behavioral science. In this paper, we show that sequential testing can be used to rapidly screen for a difference in the EF of a given individual with respect to a baseline level. In cognitive tests consisting of repeated identical tasks, a sequential framework can be utilized to actively detect significant differences in cognitive performance with high confidence more rapidly than conventional non-sequential approaches. Ultimately, sequential analysis could be applied to a variety of problems in cognitive and perceptual domains to improve efficiency gains and achieve substantial test length reduction.

Promoting Computational Thinking, Computational Participation, and Spatial Reasoning with LEGO Robotics

Canadian Journal of Science, Mathematics and Technology Education

Equitably Teaching and Mathematically Preparing

Proceedings of the 2022 AERA Annual Meeting

Equity in Mathematics Methods Coursework: A Necessary Pairing

Proceedings of the 2020 AERA Annual Meeting

Rehumanizing Mathematics for Black, Indigenous, and Latinx Students

National Council of Teachers of Mathematics, 2018

In this essay, the authors, as participants of the Privilege and Oppression in the Preparation of... more In this essay, the authors, as participants of the Privilege and Oppression in the Preparation of Mathematics Teachers Educators conference, reflect on tensions inherent in standing with and speaking on behalf of communities in an attempt to build and signal solidarity with them. They describe this tension in relation to their membership in the community of researchers who study equity in mathematics education. A particular exchange that arose during whole group discussion at the conference seeded a conversation around other situations they have encountered in this community, and led to the development of a set of "cautionary tales" for the field.

Mathematics teaching produces and reproduces social injustice. It also has the potential to disru... more Mathematics teaching produces and reproduces social injustice. It also has the potential to disrupt patterns of inequity and advance just communities of practice. Drawing from literature on equitable mathematics teaching, we analyze the work of leading a discussion of student solutions in ways that nurture healthy identities, relationships and societies. From a conceptual analysis of a Norwegian mathematics lesson, we first identify dynamics of race and gender at play, then identify three key aspects of mathematics teaching that can serve to disrupt these dynamics while creating opportunities for alternative identities, relationships and futures: (i) having regard for property and its use; (ii) taking up student thinking as participatory citizenship; and (iii) orchestrating collective mathematical work. We discuss nuances of this work and implications for research on teaching.

A Retrospective Look at Where We’ve Been and Where We Might Go: The Research Committee Reflects Upon the Judith Jacob Lectures and the Early Career Award Articles

Considering Hybrid Mathematics Content and Methods Courses for Preservice Teachers Introduction

Designing the Online Portion of Hybrid Pedagogy and Content Courses for Preservice Elementary Teachers

The Complexities of Teaching About Issues of Equity, Diversity, Social Justice, and Multicultural Education in an Online Course

Soccer for Real

Mathematics Teaching in the Middle School, 2019

My name is Naima Goffney, and I am an eleven-year-old seventh grader at Julius West Middle School... more My name is Naima Goffney, and I am an eleven-year-old seventh grader at Julius West Middle School. I am taking algebra 1 this year. I wanted to write the Math for Real because in math class I do not always think that what we are learning is related to the real world. At home, my mom shows me all the different ways I am mathematically smart, which makes me want to try harder in school during the “rougher” days. We can use math to know more about how to improve our skills and find the math we learn in school more interesting and more related to our real world as middle schoolers.

Math smarts in Wordles

Teaching Children Mathematics, 2016

Postscript items are designed as rich grab-and-go resources that any teacher can quickly incorpor... more Postscript items are designed as rich grab-and-go resources that any teacher can quickly incorporate into his or her classroom repertoire with little effort and maximum impact. Increase mathematical confidence by creating ways for students to show they are “smart” in math through Smartness Wordles™, collections of words in graphic representation.

did not just teach academic subjects. They taught their pupils skills and knowledge to help devel... more did not just teach academic subjects. They taught their pupils skills and knowledge to help develop them as individuals and as members of a collective. Subject matters offered important resources for these social goals: they and their students read literature in the voices of a wide range of people, about experiences both similar to and different from theirs. They studied other cultures and learned about work, life, and practice in a variety of societies and settings. And they learned that issues of voice, experience, culture, and setting were important threads in the tapestry of what it means to be human. The work they did with their pupils across these academic subjects was, of course, also aimed at developing the children’s skills and knowledge, their capacity to interpret texts and

Measuring Teacher Quality in Practice

Measurement Issues and Assessment for Teaching Quality

Validating Measures Validating Measures of of Content Knowledge for Teaching Mathematics: Content Knowledge for Teaching Mathematics: A Validity Argument Approach A Validity Argument Approach

Validating the Ecological Assumption: The Relationship of Measure Scores to Classroom Teaching and Student Learning

Measurement: Interdisciplinary Research and Perspectives, 2007

Assessing Elemental and Structural Validity: Data from Teachers, Non-teachers, and Mathematicians

Measurement: Interdisciplinary Research and Perspectives, 2007

Validation efforts typically focus around what, exactly, is measured by an instrument (s), and wh... more Validation efforts typically focus around what, exactly, is measured by an instrument (s), and whether what is measured corresponds to the theoretical domain (s) originally specified. In this paper, we conduct a first analysis into these issues. Our goal is building instruments ...