Historical Roots of Confusion among Beginning Algebra Students: A Newly Discovered Manuscript

Helena M. Pycior

doi:10.2307/2690081

An Excel–lent Card Trick

Mathematics Teacher ◽

10.5951/mt.104.7.0526 ◽

2011 ◽

Vol 104 (7) ◽

pp. 526-530

Author(s):

Holly S. Zullo

Keyword(s):

Mathematical Explanation ◽

Microsoft Excel ◽

Mathematical Ideas ◽

Algebra Students ◽

Beginning Algebra ◽

Composite Functions ◽

Floor Function

Card tricks based on mathematical principles can be a great way to get students interested in exploring some important mathematical ideas. Bonomo (2008) describes several variations of a card trick that rely on nested floor functions, but these generally go beyond the reach of beginning algebra students. However, a simple spreadsheet implementation shows students why the card trick works and allows them to explore several variations. As an added bonus, students are introduced to composite functions, the floor function, and iteration, and they learn how to use formulas and the INT function in Microsoft Excel. The depth of the mathematical explanation can be varied according to students' background.

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Mathematical Conversations to Transform Algebra Class

Mathematics Teacher ◽

10.5951/mathteacher.108.9.0656 ◽

2015 ◽

Vol 108 (9) ◽

pp. 656-661

Author(s):

Jennifer Earles Szydlik

Keyword(s):

Classroom Discussions ◽

Algebra Students ◽

Beginning Algebra ◽

Algebra Class

Three topics worthy of classroom discussions help beginning algebra students create meaning and build understanding as a community.

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What Are These Things Called Variables?

Mathematics Teacher ◽

10.5951/mt.76.7.0474 ◽

1983 ◽

Vol 76 (7) ◽

pp. 474-479

Author(s):

Sigrid Wagner

Keyword(s):

Algebra Students ◽

Beginning Algebra ◽

Literal Symbols

We all know some of the problems that beginning algebra students have in working with literal symbols, or variables. Two articles in this journal (Herscovics and Kieran 1980; Rosnick 1981) have discussed certain difficulties related to variables and have offered suggestions for overcoming them.

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Early Secondary Mathematics: The Use of Intrigue to Enhance Mathematical Thinking and Motivation in Beginning Algebra

Mathematics Teacher ◽

10.5951/mt.96.2.0092 ◽

2003 ◽

Vol 96 (2) ◽

pp. 92-96

Author(s):

Marjorie L. Lewkowicz

Keyword(s):

Conceptual Understanding ◽

Mathematical Thinking ◽

Secondary Mathematics ◽

Algebra Students ◽

Beginning Algebra

IN AN EFFORT TO HELP MY BEGINNING ALGEBRA STUDENTS further develop their conceptual understanding of variables, the language of algebra, and other important topics,

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Some Research Support for a Second Chance for Beginning Algebra Students

The Two-Year College Mathematics Journal ◽

10.2307/3026571 ◽

1974 ◽

Vol 5 (2) ◽

pp. 50

Author(s):

Paul W. Merritt

Keyword(s):

Research Support ◽

Algebra Students ◽

Beginning Algebra ◽

Second Chance

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Take Time for Action: From Kinesthetic Movement to Algebraic Functions

Mathematics Teaching in the Middle School ◽

10.5951/mtms.14.7.0388 ◽

2009 ◽

Vol 14 (7) ◽

pp. 388-391

Author(s):

Mary G. Goral

Keyword(s):

Algebraic Function ◽

Physical Models ◽

Algebraic Reasoning ◽

Mathematical Functions ◽

Spatial Intelligence ◽

Algebra Students ◽

Beginning Algebra ◽

Geometric Thinking ◽

And Algebra ◽

Pictorial Representations

Are students able to work through a series of geometric spatial activities, discover a pattern, and find an algebraic function? Can they move from using spatial intelligence to number sense to algebraic reasoning? Are they able to connect geometric thinking and algebra, physical models, and numeric relationships? Friel, Rachlin, and Doyle (2001) state, “Explorations that develop from problems that can be solved by using tables, graphs, verbal descriptions, concrete or pictorial representations or algebraic symbols offer opportunities for students to build their understandings of mathematical functions” (p. v). Further, combining physical spatial activities with algebraic reasoning can better engage beginning algebra students in the task at hand. According to Jensen (2001), the kinesthetic arts can provide a significant vehicle that can enhance content-area learning.

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What is Going on in Your School?: An experiment in teaching

Mathematics Teacher ◽

10.5951/mt.48.5.0360 ◽

1955 ◽

Vol 48 (5) ◽

pp. 360-365

Author(s):

Beatrice Buzzetti

Keyword(s):

High School ◽

Higher Learning ◽

First Year ◽

Algebra Students ◽

Beginning Algebra ◽

Institutions Of Higher Learning ◽

School Career ◽

Eighth Grade Students ◽

School Guidance ◽

Guidance Department

In the Bremerton school system only those eighth-grade students who receive an arithmetic grade of B or above and those recommended by their mathematics teachers are permitted to study algebra in the ninth grade. Since our senior high-school guidance department urges all students who hope to attend institutions of higher learning to elect beginning algebra sometime during their high-school career, Bremerton gets an older group but a slower group of first-year algebra students.

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