Dismantling Racism in Mathematics Instruction Exercises for Educators to Reflect on Their Own Biases to Transform Their Instructional Practice
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Ethnomathematics and the Aboriginal Leadership Year (--THIS SECTION DOES NOT PRINT--)
QUICK DESIGN GUIDE QUICK TIPS (--THIS SECTION DOES NOT PRINT--) Ethnomathematics and the Aboriginal Leadership Year (--THIS SECTION DOES NOT PRINT--) This PowerPoint 2007 template produces a 36”x48” This PowerPoint template requires basic PowerPoint professional poster. It will save you valuable time Dr. Bernadette Dececchi (version 2007 or newer) skills. Below is a list of placing titles, subtitles, text, and graphics. commonly asked questions specific to this template. Ms. Michela Ferguson If you are using an older version of PowerPoint some Use it to create your presentation. Then send it to template features may not work properly. PosterPresentations.com for premium quality, same day affordable printing. students were below the requirements of even the remedial class. Instead of starting Using the template BACKGROUND at the level where the students were functioning and bringing them to a more acceptable level, the students were expected to function at the level of the class We provide a series of online tutorials that will The Aboriginal Leadership Opportunity Year (ALOY) is a one year opportunity for more in line with year one classes. These students were lost and had a hard time Verifying the quality of your graphics guide you through the poster design process and selected First Nations, Inuit and Métis Aboriginal candidates from across Canada to following and had lost confidence I their ability to do well. This reinforced the feeling attend the Royal Military College of Canada (RMCC) in Kingston. At RMCC the that they were unable to do mathematics, as they were failing the remedial Go to the VIEW menu and click on ZOOM to set your answer your poster production questions. -
Reasoning About Equations Using Equality
Mathematics Instructional Plan – Grade 4 Reasoning About Equations Using Equality Strand: Patterns, Functions, Algebra Topic: Using reasoning to assess the equality in closed and open arithmetic equations Primary SOL: 4.16 The student will recognize and demonstrate the meaning of equality in an equation. Related SOL: 4.4a Materials: Partners Explore Equality and Equations activity sheet (attached) Vocabulary equal symbol (=), equality, equation, expression, not equal symbol (≠), number sentence, open number sentence, reasoning Student/Teacher Actions: What should students be doing? What should teachers be doing? 1. Activate students’ prior knowledge about the equal sign. Formally assess what students already know and what misconceptions they have. Ask students to open their notebooks to a clean sheet of paper and draw lines to divide the sheet into thirds as shown below. Create a poster of the same graphic organizer for the room. This activity should take no more than 10 minutes; it is not a teaching opportunity but simply a data- collection activity. Equality and the Equal Sign (=) I know that- I wonder if- I learned that- 1 1 1 a. Let students know they will be creating a graphic organizer about equality and the equal sign; that is, what it means and how it is used. The organizer is to help them keep track of what they know, what they wonder, and what they learn. The “I know that” column is where they can write things they are pretty sure are correct. The “I wonder if” column is where they can write things they have questions about and also where they can put things they think may be true but they are not sure. -
Arismendi-Pardi, Eduardo Jesus What Is Ethnomathematics And
DOCUMENT RESUME ED 430 804 SE 062 589 AUTHOR Arismendi-Pardi, Eduardo Jesus TITLE What Is Ethnomathematics and Why Should We Teach It? Crossing Cultures: Communicating through the Curriculum. PUB DATE 1999-04-00 NOTE 18p.; Paper presented to the National Conference of the Center for the Study of Diversity in Teaching and Learning in Higher Education (San Diego, CA, April, 1999). PUB TYPE Opinion Papers (120)-- Speeches/Meeting Papers (150) EDRS PRICE MF01/PC01 Plus Postage. DESCRIPTORS *Cultural Awareness; *Cultural Enrichment; *Curriculum Development; *Ethnography; Higher Education; Learning Strategies; *Mathematics Instruction; Teaching Methods IDENTIFIERS *Ethnomathematics ABSTRACT This paper defines ethnomathematics and reviews the methods used to incorporate this philosophy into the current teaching of mathematics. Ethnomathematics rejects inequity, arrogance, and bigotry while challenging the Eurocentric bias that denies the mathematical contributions and rigor of other cultures. A review of the literature shows that the teaching of ethnomathematics will bring awareness to students that Europe is not now nor was it ever the center of civilization. Ultimately, this methodwill present an accurate history of mathematics, use a variety of examples tosolve problems from a variety of cultures, and recognize that learning mathematics is a unique process for every individual. (CCM) ******************************************************************************** * Reproductions supplied by EDRS are the best that can be made * * from the original document. * ******************************************************************************** WHAT IS ETHNOMATHEMATICS AND WHY SHOULDWE TEACH IT? Crossing Cultures: Communicating Through the Curriculum U.S. DEPARTMENT OF EDUCATION PERMISSION TO REPRODUCE AND Office of Educational Research and Improvement DISSEMINATE THIS MATERIAL HAS E UCATIONAL RESOURCES INFORMATION BEEN GRANTED BY CENTER (ERIC) frpitni1ocument has been reproduced as received from the person or organization originating it. -
Radical Love As Praxis: Ethnic Studies and Teaching Mathematics for Collective Liberation
Journal of Urban Mathematics Education May 2021, Vol. 14, No. 1, pp. 71–95 ©JUME. https://journals.tdl.org/jume Radical Love as Praxis: Ethnic Studies and Teaching Mathematics for Collective Liberation Cathery Yeh Ricardo Martinez Chapman University University of Nebraska–Lincoln Sarah Rezvi Shraddha Shirude University of Illinois at Chicago Seattle Public Schools Ethnic studies is a growing movement for curricular and pedagogical practices that reclaim marginalized voices and histories and create spaces of healing for students of color; however, its application to mathematics education has been limited. In this essay, we provide a framework of five ethea of ethnic studies for mathematics education: identity, narratives, and agency; power and oppression; community and solidarity; resistance and liberation; and intersectionality and multiplicity. We de- scribe key concepts and examples of the ethos of ethnic studies. KEYWORDS: ethnic studies, love, mathematics for liberation, transformative resistance CATHERY YEH is an Assistant Professor at Chapman University in the Attallah College of Educational Studies, 1 University Dr., Orange, CA 92866; email: [email protected]. Her re- search focuses on critical mathematics education, humanizing practices, ethnic studies, and social justice teaching and organizing. RICARDO MARTINEZ is Assistant Professor in Mathematics Education in the Department of Teaching, Learning and Teacher Education at the University of Nebraska–Lincoln, 1430 Vine St., Lincoln, NE 68505; email: [email protected]. His research centers on paradigms of critical youth studies in mathematics education. SARAH REZVI is a doctoral student at the University of Illinois at Chicago in the College of Education, 1040 W. Harrison St., Chicago, IL 60607; email: [email protected]. -
From Ethnomathematics to Ethnocomputing
1 Bill Babbitt, Dan Lyles, and Ron Eglash. “From Ethnomathematics to Ethnocomputing: indigenous algorithms in traditional context and contemporary simulation.” 205-220 in Alternative forms of knowing in mathematics: Celebrations of Diversity of Mathematical Practices, ed Swapna Mukhopadhyay and Wolff- Michael Roth, Rotterdam: Sense Publishers 2012. From Ethnomathematics to Ethnocomputing: indigenous algorithms in traditional context and contemporary simulation 1. Introduction Ethnomathematics faces two challenges: first, it must investigate the mathematical ideas in cultural practices that are often assumed to be unrelated to math. Second, even if we are successful in finding this previously unrecognized mathematics, applying this to children’s education may be difficult. In this essay, we will describe the use of computational media to help address both of these challenges. We refer to this approach as “ethnocomputing.” As noted by Rosa and Orey (2010), modeling is an essential tool for ethnomathematics. But when we create a model for a cultural artifact or practice, it is hard to know if we are capturing the right aspects; whether the model is accurately reflecting the mathematical ideas or practices of the artisan who made it, or imposing mathematical content external to the indigenous cognitive repertoire. If I find a village in which there is a chain hanging from posts, I can model that chain as a catenary curve. But I cannot attribute the knowledge of the catenary equation to the people who live in the village, just on the basis of that chain. Computational models are useful not only because they can simulate patterns, but also because they can provide insight into this crucial question of epistemological status. -
First-Order Logic
Chapter 5 First-Order Logic 5.1 INTRODUCTION In propositional logic, it is not possible to express assertions about elements of a structure. The weak expressive power of propositional logic accounts for its relative mathematical simplicity, but it is a very severe limitation, and it is desirable to have more expressive logics. First-order logic is a considerably richer logic than propositional logic, but yet enjoys many nice mathemati- cal properties. In particular, there are finitary proof systems complete with respect to the semantics. In first-order logic, assertions about elements of structures can be ex- pressed. Technically, this is achieved by allowing the propositional symbols to have arguments ranging over elements of structures. For convenience, we also allow symbols denoting functions and constants. Our study of first-order logic will parallel the study of propositional logic conducted in Chapter 3. First, the syntax of first-order logic will be defined. The syntax is given by an inductive definition. Next, the semantics of first- order logic will be given. For this, it will be necessary to define the notion of a structure, which is essentially the concept of an algebra defined in Section 2.4, and the notion of satisfaction. Given a structure M and a formula A, for any assignment s of values in M to the variables (in A), we shall define the satisfaction relation |=, so that M |= A[s] 146 5.2 FIRST-ORDER LANGUAGES 147 expresses the fact that the assignment s satisfies the formula A in M. The satisfaction relation |= is defined recursively on the set of formulae. -
Part 3: First-Order Logic with Equality
Part 3: First-Order Logic with Equality Equality is the most important relation in mathematics and functional programming. In principle, problems in first-order logic with equality can be handled by, e.g., resolution theorem provers. Equality is theoretically difficult: First-order functional programming is Turing-complete. But: resolution theorem provers cannot even solve problems that are intuitively easy. Consequence: to handle equality efficiently, knowledge must be integrated into the theorem prover. 1 3.1 Handling Equality Naively Proposition 3.1: Let F be a closed first-order formula with equality. Let ∼ 2/ Π be a new predicate symbol. The set Eq(Σ) contains the formulas 8x (x ∼ x) 8x, y (x ∼ y ! y ∼ x) 8x, y, z (x ∼ y ^ y ∼ z ! x ∼ z) 8~x,~y (x1 ∼ y1 ^ · · · ^ xn ∼ yn ! f (x1, : : : , xn) ∼ f (y1, : : : , yn)) 8~x,~y (x1 ∼ y1 ^ · · · ^ xn ∼ yn ^ p(x1, : : : , xn) ! p(y1, : : : , yn)) for every f /n 2 Ω and p/n 2 Π. Let F~ be the formula that one obtains from F if every occurrence of ≈ is replaced by ∼. Then F is satisfiable if and only if Eq(Σ) [ fF~g is satisfiable. 2 Handling Equality Naively By giving the equality axioms explicitly, first-order problems with equality can in principle be solved by a standard resolution or tableaux prover. But this is unfortunately not efficient (mainly due to the transitivity and congruence axioms). 3 Roadmap How to proceed: • Arbitrary binary relations. • Equations (unit clauses with equality): Term rewrite systems. Expressing semantic consequence syntactically. Entailment for equations. • Equational clauses: Entailment for clauses with equality. -
Logic, Sets, and Proofs David A
Logic, Sets, and Proofs David A. Cox and Catherine C. McGeoch Amherst College 1 Logic Logical Statements. A logical statement is a mathematical statement that is either true or false. Here we denote logical statements with capital letters A; B. Logical statements be combined to form new logical statements as follows: Name Notation Conjunction A and B Disjunction A or B Negation not A :A Implication A implies B if A, then B A ) B Equivalence A if and only if B A , B Here are some examples of conjunction, disjunction and negation: x > 1 and x < 3: This is true when x is in the open interval (1; 3). x > 1 or x < 3: This is true for all real numbers x. :(x > 1): This is the same as x ≤ 1. Here are two logical statements that are true: x > 4 ) x > 2. x2 = 1 , (x = 1 or x = −1). Note that \x = 1 or x = −1" is usually written x = ±1. Converses, Contrapositives, and Tautologies. We begin with converses and contrapositives: • The converse of \A implies B" is \B implies A". • The contrapositive of \A implies B" is \:B implies :A" Thus the statement \x > 4 ) x > 2" has: • Converse: x > 2 ) x > 4. • Contrapositive: x ≤ 2 ) x ≤ 4. 1 Some logical statements are guaranteed to always be true. These are tautologies. Here are two tautologies that involve converses and contrapositives: • (A if and only if B) , ((A implies B) and (B implies A)). In other words, A and B are equivalent exactly when both A ) B and its converse are true. -
How Does Cigugur Indigenous People Using Calculations to Determine Good Day to Build Houses
EURASIA Journal of Mathematics, Science and Technology Education, 2021, 17(2), em1939 ISSN:1305-8223 (online) OPEN ACCESS Research Paper https://doi.org/10.29333/ejmste/9673 Exploring Ethnomathematics with Ethnomodeling Methodological Approach: How Does Cigugur Indigenous People Using Calculations to Determine Good Day to Build Houses Uba Umbara 1,2*, Wahyudin Wahyudin 2, Sufyani Prabawanto 2 1 Department of Mathematics Education, STKIP Muhammadiyah Kuningan, Kuningan, INDONESIA 2 Department of Mathematics Education, Universitas Pendidikan Indonesia, INDONESIA Received 25 March 2020 ▪ Accepted 10 January 2021 Abstract This article discusses Cigugur indigenous communities’ custom in carrying out calculation practices to determine the best time to start house construction activities. The realist ethnography approach was used in this study through exploratory research. The ethnomathematics design adopted four elements: generic questions, initial answers, critical constructs, and specific activities. Ethnomodelling was used to translate cultural mathematics ideas into academic mathematics through ethical, emic, and dialogical approaches. Based on ethnomathematics, the community practices the dimensions of necessary universal mathematical activities, such as counting, placing, and explaining. Based on ethnomodeling, mathematical ideas and practices carried out are relevant to the concepts of enumeration, integer operations, sets, relations, congruence, and modulo. The study results recommend the importance of ethnomodelling as a methodological -
Tool 1: Gender Terminology, Concepts and Definitions
TOOL 1 Gender terminology, concepts and def initions UNESCO Bangkok Office Asia and Pacific Regional Bureau for Education Mom Luang Pin Malakul Centenary Building 920 Sukhumvit Road, Prakanong, Klongtoei © Hadynyah/Getty Images Bangkok 10110, Thailand Email: [email protected] Website: https://bangkok.unesco.org Tel: +66-2-3910577 Fax: +66-2-3910866 Table of Contents Objectives .................................................................................................. 1 Key information: Setting the scene ............................................................. 1 Box 1: .......................................................................................................................2 Fundamental concepts: gender and sex ...................................................... 2 Box 2: .......................................................................................................................2 Self-study and/or group activity: Reflect on gender norms in your context........3 Self-study and/or group activity: Check understanding of definitions ................3 Gender and education ................................................................................. 4 Self-study and/or group activity: Gender and education definitions ...................4 Box 3: Gender parity index .....................................................................................7 Self-study and/or group activity: Reflect on girls’ and boys’ lives in your context .....................................................................................................................8 -
TEEM 2009 V1n1.Pub
ISSN# Volume 1, Issue 1, Fall 2009 Teaching for Excellence and Equity In Mathematics a publication of an Affiliate Organization of the National Council of Teachers of Mathematics From the Editors ¡Bienvenidos! It is an exciting privilege to welcome everyone to the debut issue of this refereed TODOS journal: Teaching for Excellence and Equity in Mathematics . Let us introduce our TEEM team of editors. Cynthia Anhalt has been an editor and contributor for Noticias de TODOS and is currently on the Instructional Faculty in Mathematics Education at The University of Arizona in Tucson, AZ. Larry LesserLesser has also been an editor and contribu- tor for Noticias de TODOS and is an Associate Professor of Mathematics Education at The Uni- versity of Texas at El Paso. Miriam Leiva is the founding president of TODOS, is Distinguished Professor of Mathematics Emerita at the University of North Carolina Charlotte, and is an au- thor of Houghton Mifflin Harcourt Mathematics. Collectively, the editors have served on sev- eral national editorial or research boards, have published on equity/ELL issues in mathematics and statistics education, and have precollege teaching experience. Since its launch in Spring 2005, the semiannual periodical Noticias de TODOS has served as much more than TODOS’ newsletter by also including quality peer-reviewed and invited arti- cles on pedagogical activities, curriculum, and issues on topics of interest. This past winter, the Board of TODOS voted to create TEEM as a separate (for now, annual) publication to focus on teacher-oriented articles to incorporate ideas for excellence and equity into teaching practices. As stated in the flyer released at the 2009 NCTM annual meeting, TEEM ’s intended audience includes math educators, practitioners, leaders, and administrators at all levels. -
Comparison Identity Vs. Equality Identity Vs. Equality for Strings Notions of Equality Order
Comparison Comparisons and the Comparable • Something that we do a lot Interface • Can compare all kinds of data with respect to all kinds of comparison relations . Identity . Equality Lecture 14 . Order CS211 – Spring 2006 . Lots of others Identity vs. Equality Identity vs. Equality for Strings • For primitive types (e.g., int, long, float, double, boolean) . == and != are equality tests • Quiz: What are the results of the following tests? • For reference types (i.e., objects) . "hello".equals("hello") true . == and != are identity tests . In other words, they test if the references indicate the same address . "hello" == "hello" true in the Heap . "hello" == new String("hello") false • For equality of objects: use the equals( ) method . equals( ) is defined in class Object . Any class you create inherits equals from its parent class, but you can override it (and probably want to) Notions of equality Order • A is equal to B if A can be substituted for B anywhere • For numeric primitives • For all other reference . Identical things must be equal: == implies equals (e.g., int, float, long, types double) • Immutable values are equal if they represent same value! . <, >, <=, >= do not work . Use <, >, <=, >= • Not clear you want them . (new Integer(2)).equals(new Integer(2)) to work: suppose we . == is not an abstract operation compare People • For reference types that Compare by name? • Mutable values can be distinguished by assignment. correspond to primitive Compare by height? class Foo { int f; Foo(int g) { f = g; } } weight? types Compare by SSN? Foo x = new Foo(2); . As of Java 5.0, Java does CUID? Foo y = new Foo(2); Autoboxing and Auto- .