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  • Student affect towards mistakes in the context of counting

    Creator:
    McGee, Samantha
    Abstract:
    In this study, I seek to examine undergraduate STEM majors’ beliefs about and attitude towards mistakes in the context of counting. This is a particularly fruitful setting for such an investigation both because combinatorics is widely applicable to various fields such as physics, biology, chemistry, and computer science (Kapur, 1970),...
    Resource Type:
    Masters Thesis
    Full Text:
    profound reasoning” as well as “rich mathematical thinking” (Lockwood, 2015, p. 340), which not only

  • Characterizing and Understanding Semiotic Representations in Combinatorics Problems

    Creator:
    De Chenne, Adaline E.
    Abstract:
    Combinatorics is a field of mathematics that concerns enumeration and existence, and its most notable applications are in computer science and statistics. Most students are introduced to combinatorics through counting problems, where they are tasked with determining the cardinality of a set of outcomes. Such problems are well-known for being...
    Resource Type:
    Dissertation
    Full Text:
    . Abstract approved: ______________________________________________________ Elise N. Lockwood

  • Students' generalisation of function from single- to multivariable settings

    Creator:
    Dorko, Allison J.
    Abstract:
    Generalisation is a key component of mathematical activity. Mathematicians often seek general formulae or wonder if a rule that holds in a particular dimension also holds in dimension n. However, generalisation is not limited to professional mathematicians; kindergarteners engage in generalisation when they seek patterns and algebra is sometimes described...
    Resource Type:
    Dissertation
    Full Text:
    Multivariable Settings. Abstract approved: _________________________________ Elise Lockwood

  • Listing as a Potential Connection between Sets of Outcomes and Counting Processes

    Creator:
    Erickson, Sarah A.
    Abstract:
    Counting problems are rich in opportunities for students to make meaningful mathematical connections and develop non-algorithmic thinking; their accessible nature and applications to computer science make counting problems a valuable part of mathematics curricula. However, students struggle in various ways with counting, and while previous studies have indicated that listing...
    Resource Type:
    Masters Thesis
    Full Text:
    students (Lockwood, 2013, p. 255

  • Undergraduate Students' Generalizing Activity in Real Analysis : Constructing a General Metric

    Creator:
    Reed, Zackery K.
    Abstract:
    Generalization is a fundamental mathematical practice across all disciplines and content areas (Amit & Klass, 2005; Lannin, 2005; Pierce, 1902; Vygotsky, 1986; Ellis, Lockwood, Tillema & Moore, 2017). While a considerable amount of research has been conducted on students' generalizing activity in algebraic contexts (Amit & Klass 2005; Becker &...
    Resource Type:
    Dissertation
    Full Text:
    approved: ________________________________ Elise N. Lockwood Generalization is a

  • Investigating Provers' Understandings of Combinatorial Proof

    Creator:
    Erickson, Sarah A.
    Abstract:
    Enumerative combinatorics is an area of mathematics that is both highly accessible for students and widely applicable to other sciences and areas of mathematics (Kapur, 1970; Lockwood, Wasserman, & Tillema, 2020). One important class of problems in combinatorics is combinatorial proofs of binomial identities, which is a type of proof...
    Resource Type:
    Dissertation
    Full Text:
    : ___________________________________________________________ Elise N. Lockwood Enumerative combinatorics is an area of mathematics that

  • Creating Community: A Case Study of Students’ Experiences in Inquiry-Based Learning

    Creator:
    Schaub, Branwen
    Abstract:
    We now have broad consensus in the mathematics education research community that active, inquiry-based classrooms provide a wealth of learning benefits for students (Freeman et al., 2014; Laursen et al., 2014; Theobald et al., 2020). Classrooms that utilize inquiry throughout the entire structure of the course, as opposed to the...
    Resource Type:
    Dissertation
    Full Text:
    approved: ______________________________________________________ Elise N. Lockwood We now have

  • The Mathematical Knowledge for Teaching of First Year Mathematics Graduate Teaching Assistants : The Case of Exponential Functions

    Creator:
    Keeling, Matthew
    Abstract:
    A teacher's mathematical knowledge for teaching has been shown to have a positive correlation with their students' success (Monk, 1994). So, when half of the students that start out in a STEM major switch out to a non-STEM major before graduation to in large part to instructors pedagogical methods and...
    Resource Type:
    Masters Thesis
    Full Text:
    , Dr. Tom Dick, Dr. Elise Lockwood, and Dr. Paul Blakemore for their continuous support and

  • An Exploratory Study of Mathematics Disciplinary Practices in Advanced Mathematics

    Creator:
    Glover, Erin D.
    Abstract:
    Policy and research have increased attention in K12 mathematics education on core mathematical practices such as argumentation, justification, and proof, that are central to students learning and doing mathematics. One reason for this increased focus is the empirical evidence that engaging students in mathematical practices provide more equitable opportunities for...
    Resource Type:
    Dissertation
    Full Text:
    : ___________________________________________________________ Rebekah L. Elliott Policy and research have increased attention in K12

  • Learning about the Standards for Mathematical Practice: An Investigation of Opportunities within Two Teacher Education Contexts

    Creator:
    Stoddard, Elyssa R.
    Abstract:
    The Common Core State Standards for Mathematical Practice (SMPs) describe ways of thinking and doing mathematics that parallels how mathematicians engage with mathematics (National Governors Association for Best Practices, 2010). These standards reflect a broader goal in K-12 mathematics education focused on moving beyond K-12 learners acquiring knowledge of mathematical...
    Resource Type:
    Dissertation
    Full Text:
    : _____________________________________________________ Rebekah L. Elliott The Common Core State Standards for Mathematical Practice (SMPs