bluuebunny/crossref_metadata_2025 huggingface dataset:
Spatial Reasoning and Pólya's Five Planes Problem
Authors: Madden Seán P. , Diaz Ricardo
Published: January 2021

“I watched the sky as we drove toward the town center…. Our galaxy is a huge disk of stars millions of light-years across, and the solar system is somewhere near the outside edge of the disk…. I like this fact. It is something you can work out in your own mind just by looking at the sky above your head at night and thinking without having to ask anyone.”—The Curious Incident of the Dog in the Night-time (Haddon 2003, pp. 9–10)
Activities for Students: Trigonometry through a Ferris Wheel
Authors: Kaplan Gail
Published: January 2021

In the traditional study of trigonometry, students graph the basic trigonometric functions. They study phase shifts, horizontal and vertical translations, and changes in period so that they can sketch the graph of generalized functions such as f(x) = acosb(x − c) + d by recognizing the information provided by the constants a, b, c, and d. Far too often, students master this material by memorizing it and thus have little comprehension of why and how each value in an equation affects the graph.
Technology Tips: A Fathom Activity for the Central Limit Theorem
Authors: Moyer Todd O. , Gambler Edward
Published: January 2021

The central limit theorem, the basis for confidence intervals and hypothesis testing, is a critical theorem in statistics. Instructors can approach this topic through lecture or activity. In the lecture method, the instructor tells students about the central limit theorem. Typically, students are informed that a sampling distribution of means for even an obviously skewed distribution will approach normality as the sample sizes used approach 30. Consequently, students may be able to use the theorem, but they may not necessarily understand the theorem.
Delving Deeper: Series Subjects
Authors: Suzuki Jeff
Published: January 2021

One of the most fascinating discoveries I made while a student was that, while the exact value of a quantity like π or √2 cannot be determined, we could use an infinite series to determine these numbers as precisely as we would like. Even more fascinating was the discovery that the ratio between successive terms of the Fibonacci sequence tended toward a limit; later I discovered that this limit was the same, regardless of what the initial terms of the sequence were. Sequences and series are also connected to the so-called perfect numbers, such as 6 or 28, which are equal to the sum of their proper divisors.
Sound Off!: Student Engagement and Teacher Guidance in Meaningful Mathematics: Enduring Principles
Authors: Freeman Gregory D. , Lucius Lisa B.
Published: January 2021

I learned to ride a bike at age six. The experiences leading to my first solo bike ride are still vivid memories. First, my father gave a wonderful explanation of bike riding. The mechanics of leg motion required to pedal were explained. Hand placement on the handlebars and the nuances of steering were described with clarity. Braking, maintaining balance, and every other conceivable aspect of bike riding were laid before me. Next, my brother modeled bike riding. Down the block he rode: peddling, steering, maintaining balance. He managed a 180-degree turn, returned, braked, and came to a perfect stop. Having gained a conceptual understanding of bike riding and having observed successful bike riding, I was able to ride the bike by myself at first attempt. I attribute my riding independence to my father's excellent explanation and my brother's superb modeling.
The Evolution of Pearson's Correlation Coefficient
Authors: Kader Gary , Franklin Christine
Published: January 2021

Studying the relationship between two quantitative variables is a standard topic in statistics. In high school and introductory college-level statistics, Pearson's correlation coefficient, r, is typically included as a measure of the direction and strength of the linear relationship between two quantitative variables. This article describes an activity that aids an intuitive development of the formula for r and its interpretation. Exploring scatter plots allows students to develop an intermediate measure of association called the quadrant count ratio (QCR), investigate properties of the QCR, and develop Pearson's r to address some of the QCR's shortcomings.
The Histogram-Area Connection
Authors: Gratzer William , Carpenter James E.
Published: January 2021

An alternative approach to the construction of histograms is based on the notion of using area to represent relative density in intervals of unequal length.
Media Clips: University Endowments; Deal or No Deal?
Authors: Hall Randy
Published: January 2021

Under Harvard University's initiative to cut tuition costs, families with incomes between $120,000 and $180,000 per year will be expected to contribute 10 percent of their income toward the cost of undergraduate tuition, and families with incomes below $120,000 will be expected to contribute amounts determined by a sliding scale that declines from 10 percent for those with incomes at $120,000 down to 0 percent for those with incomes at $60,000 and below. Harvard's tuition is about $31,000 per year. This figure does not include additional expenses (textbooks, supplies, room and board, etc.), which Harvard estimated to be about $15,000 for the 2007–2008 academic year (www.news.harvard.edu/gazette/ 2007/04.05/99-admissions.html).
Activities for Students: Using the CBR to Enhance Graphical Understanding
Authors: Herman Marlena , Laumakis Paul
Published: January 2021

Instructional standards promoted by the National Council of Teachers of Mathematics (NCTM) include the ideas that students at all levels should understand patterns, relations, and functions; represent and analyze situations with mathematical models; and analyze change in various contexts (NCTM 2000). Incorporated in these general standards are more specific expectations for the various grade levels that involve the use of words, tables, graphs, and equations for expressing mathematical relationships, with a focus on linear relationships at the middle school level and other classes of functions at the high school level. Past research shows that students' ability in these areas tends to be more procedural than conceptual. With respect to graphing abilities, for example, students have been able to produce graphs from ordered pairs but have insufficient ability to interpret graphs, even at the college level (Mokros and Tinker 1987). In a review of more recent studies, Skalsky and Pastel (2004) claim that many students enter college without an adequate grasp of how relationships are depicted by graphs; they have difficulties interpreting graphs and connecting graphs to real-world phenomena.
Enhancing Plane Euclidean Geometry with Three-Dimensional Analogs
Authors: Posamentier Alfred S. , Patton L. Raphael
Published: January 2021

Human beings are born with an ability to sense, perceive, and then remember, and as we grow and develop this ability matures through exercise and practice. Most of us can recall learning to see how circles and lines are tangent to one another, how midpoints and perpendiculars partition triangles, and how one might prove conjectures about these. Learning how to see literally, how to make images of the world, and how to perceive the world more completely and accurately is part of that educational process.
Sacred Cows Make the Best Hamburger
Authors: Barger Rita H. , McCoy Ann C.
Published: January 2021

Research indicates that teaching university mathematics courses via lecture is ineffective. The authors revamp a course that involved teaching volume and surface area to include hands-on manipulatives.
Using Lesson Study and Four-Column Lesson Planning with Preservice Teachers
Authors: Matthews Michael E. , Hlas Christopher S. , Finken Teresa M.
Published: January 2021

Incorporating four-column lesson planning into lesson study encourages preservice secondary school teachers to be more student centered and value collaboration.
Tangent Lines without Derivatives for Quadratic and Cubic Equations
Authors: Carroll William J.
Published: January 2021

The equation of the line tangent to the parabola at its y-intercept is extended to give a convenient method of finding tangent lines at any point on the graph of a quadratic or a cubic equation.
Delving Deeper: Derivatives of Generalized Power Functions
Authors: Johnson John M.
Published: January 2021

After several years of teaching multiple sections of first-semester calculus, it was easy for me to think that I had nothing new to learn. But every year and every class bring a new group of students with their unique gifts and insights. In a recent class, after covering the derivative rules for power functions and exponential functions, I asked the class about the derivative of a function like y = xsinx, which is neither a power function (the power is not constant) nor an exponential function (the base is not constant).
Media Clips: (Im)Perfect Storm; Best Math Ace
Authors: Metz James , Lesser Lawrence M.
Published: January 2021

[El Paso, Tex., city council representative] Eddie Holguin stated, “It's taken at face value that we have to pay for a 500-year flood construction project right away, but we still have 490 more years to deal with this and not tax people out of their home in order to get things done.”
Learning from Students' Thinking
Authors: Hodge Lynn Liao
Published: January 2021

Really listening to students reveals that how data analysis is taught affects their mathematical competence.
Cookies and Pi
Authors: Dempsey Michael
Published: January 2021

Even in an advanced mathematics class, teachers should look for ways to sweeten their teaching.
Delving Deeper: Decomposing Quintics
Authors: Kulkarni Raghavendra G.
Published: January 2021

Polynomial decomposition, also referred to as polynomial factorization, is the process of splitting a given polynomial of degree n into its constituent factors—that is, polynomials of lower degree. A reducible polynomial over a given field—such as the real (ℝ), complex (ℂ), or rational numbers (ℚ)—is one that can be factored into polynomials of lower degree with coefficients in that field; otherwise, it is irreducible over the field (Thangadurai 2007). From the fundamental theorem of algebra, we know that a polynomial with integer coefficients is completely reducible into linear factors over the complex field, whereas it is reducible to linear and quadratic factors over ℝ; however, it may be irreducible over ℚ. If a polynomial (with rational coefficients) can be factored over ℚ, Gauss's lemma states, it can be factored over the integers as well. The fundamental theorem of algebra is only an existence proof and does not provide any procedure for factoring a polynomial.
The Problem with the Snack Food Problem
Authors: Szydlik Stephen D.
Published: January 2021

Solving systems of linear equations when using real data can present surprising challenges.
An Intriguing Exponential Inequality
Authors: Perrin John Robert
Published: January 2021

An algebra problem with a graphical solution challenges precalculus and calculus students to determine an analytical solution.
Technology Tips: Using Maple to Enhance Students' Understanding of Numerical Integration
Authors: Scherger Nicole
Published: January 2021

Typically, calculus students are introduced to the simplest numerical approximations of the definite integral through the process of finding the areas of rectangles. Students are initially shown how to use the endpoints of each subinterval to find lower and upper sums, a process that gives them a bound on the actual area. They are then shown, sometimes through a series of labor-intensive computations or through visualization with graphs, that as the number of rectangles, or partitions, increases, the approximations become more and more accurate. Somewhere in this process students are probably also shown how to use midpoints to obtain slightly more accurate numerical approximations. At this point, most calculus courses lead students toward the fundamental theorem of calculus, at which time they learn that they can evaluate a definite integral by finding the antiderivative and evaluating between the limits of integration.
The Back Page: De-Icing a VW
Authors: Day Roger
Published: January 2021

I began my career in 1978 while still a college student, teaching precalculus as part of an extended work-study program. In 1979, as an undergraduate senior, I was a student in Paul Jorgensen's methods course at St. Olaf College. Problem solving was receiving lots of attention in mathematics education, and Dr. J was driving that bandwagon in Minnesota. He instilled in me a never-wavering focus on problem solving.
Want to Play Geometry?
Authors: Kaufmann Matthew L. , Bomer Megan A. , Powell Nancy Norem
Published: January 2021

Much axiomatic reasoning, the basis of proof, occurs while students play games.
The Back Page: Building the Unit Circle: A Patty Paper Approach
Authors: Spanik Anna
Published: January 2021

My favorite lesson evolved from a session at the 1995 NCTM Annual Meeting in Boston. We were a group of eight junior and senior high school teachers from Nova Scotia, most of us attending our first NCTM Annual Meeting. We planned our days to maximize exposure to sessions and would share our experiences every evening.
Proof Mapping
Authors: Linares Leanne A. , Smith Phil R.
Published: January 2021

Constructing geometry proofs through group–and self–reflection helps develop successful arguments by revealing underlying thought processes.
Preparing for Formal Proofs in Geometry
Authors: Johnson Art
Published: January 2021

Conclusion quickies and mystery problems precede and prepare for formal proof in geometry.
Sound Off!: The Alliance: Mathematics and the Arts
Authors: Suzuki Jeff
Published: January 2021

Stick to the curriculum. Teach to the test. Don't ask questions; just follow directions.
How Technology Can Motivate the Learning of Proof
Authors: Muller Kimberley O.
Published: January 2021

Using The Geometer's Sketchpad helps students learn about geometric proof through exploration, discovery, and conjecture.
Shooting Free Throws, Probability, the Golden Ratio
Authors: Goodman Terry
Published: January 2021

A probability exploration built on shooting basketball free throws leads unexpectedly to the golden ratio.
Delving Deeper: Triangulating Polygonal Numbers
Authors: MacKinnon Dan
Published: January 2021

Like touring an old city, exploring classical topics from school mathematics allows us to make discoveries and enjoy knowing that other like-minded travelers have been in the same place before. There are few better areas for rediscovering formerly well-traveled mathematical pathways than the roads opened up by polygonal numbers. Polygonal numbers were revered by the Pythagoreans, were studied thoroughly by Euler, and are used as motivating examples in many contemporary textbooks. Despite their long history and frequent mention, our guidebooks—the student texts—leave 20016out many of their interesting features, making them an ideal area for mathematical tourism.
Mathematical Lens: Making a Pitch for Slope
Authors: Rudolph Heidi
Published: January 2021

Heidi Rudolph teaches mathematics at Orange High School in Pepper Pike, Ohio, located across the street from the Orange City School District administration buildings (see photograph 1). The buildings' rooflines inspired her to develop questions related to the slopes of the roofs and to consider ways in which dynamic geometry software such as The Geometer's Sketchpad® (GSP) could be used to make measurements that would help answer her questions.
The Pascal-Fermat Correspondence: How Mathematics Is Really Done
Authors: Devlin Keith
Published: January 2021

A letter records how two of the greatest mathematicians of all time struggled for several weeks to solve a probability problem.
Delving Deeper: From Chords of Circles to Triangular Numbers to Volumes of Spheres
Authors: Walter Marion , Crossfield Don
Published: January 2021

This “Delving Deeper” is a bit different from others: It arose from a series of discussions (telephone and e-mail) inspired by a problem that Don Crossfield posed in The Oregon Mathematics Teacher and from which interesting mathematical discoveries emerged. The story of how these results came about is just as interesting as the results themselves.
Cosby's Rule: Connecting Summation Operations, Definite Integrals, and the Fundamental Theorem of Calculus
Authors: Sloan Margaret H.
Published: January 2021

What happened when a student in an AP Calculus class in a small school in rural Georgia discovered a way to bypass some laborious computations.
Technology Tips: The Free Microsoft Word 2007 Mathematics Add-In
Authors: Nord Gail
Published: January 2021

The algebraic and symbolic capabilities of the free mathematics add-in provided by Microsoft Word 2007™ can turn Word into a graphing calculator. This article will familiarize teachers with some of the features of this add-in, paying special attention to the power of the Animate command. This computer algebra system (CAS) is available as a free download to any legitimate institutional or individual license holder of Microsoft Word 2007.
The Back Page: My Favorite Lesson: The First Day of Class
Authors: Forringer Richard S.
Published: January 2021

When the responses start to slow down, I ask students to guess which one response has come up more often than any other word over the years that I have played this game.
Sound Off!: Measurement: The Forgotten Standard
Authors: Foley Gregory D.
Published: January 2021

Measurement is a fundamental process that spans all branches of mathematics and connects mathematics to the world around us. At the most basic level, “measurement is the assignment of a numerical value to an attribute of an object, such as the length of a pencil. At more-sophisticated levels, measurement involves assigning a number to a characteristic of a situation, as is done by the consumer price index” (NCTM 2000, p. 44). During high school, students' understanding of measurable attributes, systems of units, and measurement processes should grow in sophistication and depth.
Integrating Literature: A Novel Idea!
Authors: Smyth Theoni Soublis , Waid Brandie
Published: January 2021

Reading literature in mathematics classrooms helps students better comprehend word problems, expand their mathematical vocabulary, and hone their critical thinking skills.
Delving Deeper: Calculating Pythagorean Triples
Authors: Stocks Collin RM , Lamb Gerald
Published: January 2021

Curious young minds can sometimes inspire one beyond all expectation.
The Back Page: My Favorite Lesson: Unfolding the Solution of Linear Systems
Authors: Bush Sarah B.
Published: January 2021

I often think back to a vivid memory from my student-teaching experience. Then, I naively believed that the weeks spent with my first-year algebra class discussing and practicing the art of solving systems of linear equations by graphing, substitution, and elimination was a success. But just at that point the students started asking revealing questions such as “How do you know which method to pick so that you get the correct solution?” and “Which systems go with which methods?” I then realized that my instruction had failed to guide my students toward conceptualizing the big picture of linear systems and instead had left them with a procedure they did not know how to apply. At that juncture I decided to try this discovery-oriented lesson.
Delving Deeper: New Life for an Old Topic: Completing the Square Using Technology
Authors: Phelps Steve , Edwards Michael Todd
Published: January 2021

Mathematics teaching has always been a curious blend of the old and the new. As the use of technology becomes more commonplace in school classrooms, this blend becomes even more pronounced. When teachers and students revisit traditional topics using technology, they are afforded opportunities to connect mathematical ideas in powerful, previously unimagined ways. The National Council of Teachers of Mathematics (NCTM) captures the importance of connections clearly in its Principles and Standards for School Mathematics (2000): “The notion that mathematical ideas are connected should permeate the school Technologymathematics experience at all levels. As students progress through their school mathematics experience, their ability to see the same mathematical structure in seemingly different settings should increase” (p. 64).
Sound Off!: Why I Use Interactive Whiteboards
Authors: Picciotto Henri
Published: January 2021

In its January 27, 2010, online issue, Teacher magazine published “Why I Hate Interactive Whiteboards,” a passionate article by Bill Ferriter. Hatred seems like a strong reaction to an inanimate object, but here it is tied to frustration about budgetary priorities, the lck of evaluation of the effectiveness of interactive whiteboards (IWBs), and the lack of accompanying training.
Now We're Really Clicking!
Authors: Popelka Susan R.
Published: January 2021

Using clickers in a high school mathematics classroom—before, during, and after instruction—provides data on students' understanding and attitudes.
A Close Encounter with Infinity: Inventing New Mathematics
Authors: Nabb Keith A.
Published: January 2021

A nonroutine problem helps change how calculus students perceive and create mathematics.
Technology Tips: Investigating the Mathematics of Center-Pivot Irrigation
Authors: Ottman Larry
Published: January 2021

Flying across the United States on a sunny day, airline passengers in window seats may have noticed the seemingly endless fields of bright green circles dotting the landscape in parts of the West and Midwest. These circular fields are the result of a technology called fixed-length, center-pivot irrigation, in which a wheeled scaffolding of pipe, sometimes up to a half mile in length, rotates around a fixed point that is connected to a water source. Plots of land are seldom, if ever, circular. Usually, they are square, rectangular, or irregularly shaped. However, because farming is a profession that often has a low margin of profit, farmers must use their valuable resources as efficiently as possible. Hence, the issue is how to maximize the packing of these circles within the existing geographic constraints of terrain features, roads, rivers, and land boundaries.
Media Clips: Fence Percentages; Welcome to the Jungle
Authors: Ebert David , LePage-Kljajic Jana
Published: January 2021

“Media Clips” appears in every issue of the Mathematics Teacher, offering readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. All submissions should be sent to the editor. For information on the department and guidelines for submitting a clip, visit http://www.nctm.org/publications/content.aspx?id=10440#media.
When 95% Accurate Isn't: Exploring Bayes's Theorem
Authors: CadwalladerOlsker Todd D.
Published: January 2021

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Shaughnessy (1992) has commented, “There is a good deal of cognitive strain involved in reading the problem and keeping everything straight; it is difficult for students to interpret exactly what they are being asked to do” (p. 471).
Improving Teaching through Lesson Study Debriefing
Authors: Groth Randall E.
Published: January 2021

The lesson study model of professional development that originated in Japan is becoming increasingly popular in the United States (Lesson Study Research Group 2009; Stigler and Hiebert 1999). At its core, lesson study is a means of bringing teachers together to carry out the process of planning a lesson, implementing and observing it, and then examining it during a debriefing session (Yoshida 2008). The debriefing component is one of the most distinctive characteristics of this type of professional development. It provides a means–discussion–for reflecting on the strengths and weaknesses of the collaboratively planned lesson. As such, the debriefing component merits special attention from those currently engaged in lesson study as well as those considering using it.
An Excel–lent Card Trick
Authors: Zullo Holly S.
Published: January 2021

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.
The Teacher's Role in Effective Computer–Assisted Instruction Intervention
Authors: Snow David R.
Published: January 2021

In January 2006 the Billings (Montana) Public Schools adopted a computer–assisted instruction (CAI) intervention aimed at helping students recover credits that they had attempted but had not attained. I volunteered to teach the algebra component in my high school. Through the following seven semesters, I came to better understand the role of an effective teacher in a credit–recovery program that relies so heavily on CAI. This article is an effort to describe this effectiveness and the nature of success and failure in CAI interventions.
Delving Deeper: Pell Numbers: A Fibonacci–like Treasure for Creative Exploration
Authors: Koshy Thomas
Published: January 2021

Fibonacci, Lucas, and the ubiquitous Catalan numbers are delightful sources for experimentation, exploration, and conjecture (Askey 2005; Koshy 2001, 2006, 2008). Pell numbers are another similarly rich source. In this article, I will demonstrate some patterns associated with Pell numbers and then will show how they can be extracted from Pascal and Pascal–like triangles. I will provide a geometric interpretation of Pell numbers and conclude by citing a few opportunities for further exploration.
Flower Power – Sunflowers as a Model for Logistic Growth
Authors: Fernández Eileen , Geist Kristi A.
Published: January 2021

Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy (see fig. 1). The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population, capacity is defined as “the maximum population that the environment is capable of sustaining in the long run” (Stewart 2008, p. 628).
Delving Deeper – Cyclical Products: The Last Shall Be First
Authors: Hugen Mark A. , Gannon Gerald E. , Shultz Harris S.
Published: January 2021

“Delving Deeper” offers a forum for classroom teachers to share the mathematics from their own work with the journal's readership; it appears in every issue of Mathematics Teacher. Manuscripts for the department should be submitted via http://mt.msubmit.net. For more background information on the department and guidelines for submitting a manuscript, visit http://www.nctm.org/publications/content.aspx?id=10440#delving.
Media Clips: Breaking Even Is Hard to Do; How Much Money Should You Borrow?
Authors: Cibes Margaret , Greenwood James , Muttiah Daniel
Published: January 2021

This year's robust stock-market advance has done a lot to bolster investors' psyches. Too bad many people's portfolios still haven't recovered from last year.… The culprit is what money manager and newsletter editor Daniel Wiener calls “the tyranny of the mathematics of loss”: When you suffer a very large loss, you need a gigantic gain to get back to where you started.
Activities for Students: Becoming Mathematicians: Exploring an Unsolved Arithmetic Problem
Authors: Miller Catherine M. , Shaw Douglas
Published: January 2021

“Activities for Students” appears six times each year in Mathematics Teacher, often providing in reproducible formats activity sheets that teachers can adapt for use in their own classroom. Manuscripts for the department should be submitted via http://mt.msubmit.net. For more information on the department and guidelines for submitting a manuscript, please visit http://www.nctm.org/publications/content.aspx?id=10440#activities.
Proof as a Tool for Learning Mathematics
Authors: Knuth Eric J.
Published: January 2021

Proof is considered to be central to the discipline of mathematics and the practice of mathematicians. Yet its role in secondary school mathematics has traditionally been peripheral at best; the only substantial treatment of proof is limited to geometry. According to Wu (1996, p. 228), however, the scarcity of proof outside of geometry is a misrepresentation of the nature of proof in mathematics.
Sharing Teaching Ideas: Let's Get Linear
Authors: King Sybrina L.
Published: January 2021

Developing an understanding of the process of solving equations is one of the most important tasks undertaken by teachers of first-year algebra students. I have also found it to be one of the most challenging. Over the years, I have used algebra tiles, diagrams, handwritten t-charts, calculatorgenerated tables, and graphs to help my students develop a conceptual understanding of what it means to solve a linear equation. A variety of instructional approaches have given most of my students an understanding of the concept of equation solving. However, a number of beginning students still tried subtracting 6, instead of dividing by 6, to solve an equation similar to 6x = 2. Those students choosing division often made another common mistake: they divided the 6 by 2. They often made these mistakes in attempting avoid nonintegral answers. Discussions with colleagues convinced me that my students were not the only ones who seemed to suffer from “fractionphobia.” And although I was reassured to learn that I was not facing this challenge alone, I still did not have an effective strategy for helping my students eliminate these mistakes in their work.
Sharing Teaching Ideas: Not Just Another Theorem: A Cultural and Historical Event
Authors: McDaniel Michael
Published: January 2021

The typical student rarely gets a chance to hold an old, powerful piece of history. In mathematics, teachers have the opportunity to present just such museum pieces; and furthermore, the class can verify their truth. Too often, however, students cringe in the face of proof and thus miss their chance to appreciate the treasure. Mathematics teachers can impress these future doctors, lawyers, politicians, and journalists with some jewels of mathematics; and teachers do mathematics a disservice if they skimp on the presentation. Since students and teachers have the time, the intelligence, and the materials to demonstrate the validity of a theorem, they should take advantage of this opportunity and privilege. Significant results in the history of thought that students can understand should be occasions for great drama. The high school mathematics sequence includes proofs of the quadratic formula, the Pythagorean theorem, the fundamental theorem of integral calculus, and other results. In this article, I suggest rolling out the red carpet for the proof of an important theorem. I focus on the Pythagorean theorem; the interested reader can easily adapt the treatment to any theorem that is worthy of unusual notice.
Discovering Steiner Triple Systems through Problem Solving
Authors: Sriraman Bharath
Published: January 2021

Principles and Standards for School Mathematics (NCTM 2000) calls for instructional programs that emphasize problem solving and that have the goal of helping students develop sophistication with such mathematical processes as representation, mathematical reasoning, abstraction, and generalization. In particular, the Problem Solving Standard suggests that teachers should choose problems that further the mathematical goals of the class. Problem solving can be viewed as a process through which teachers can help students think mathematically, which Schoenfeld (1985, 1992) defines as developing a mathematical point of view. It includes valuing the processes of representation and abstraction and having the predisposition to generalize them. In this article, I describe my attempt to implement problem solving as a teacher of ninthgrade algebra. I had two explicit goals in mind. The first goal was to use carefully chosen problemsolving situations as a setting for an extended mathematical investigation that leads to the discovery of Steiner triple systems. The second goal was to use problem-solving situations to help students think mathematically, that is, to construct representations and to engage in mathematical reasoning, abstraction, and generalization.
Sharing Teaching Ideas: Identifying Features of Functions Stated in Graph Form or Equation Form
Authors: Goerdt Sonja L.
Published: January 2021

This article describes an activity that emphasizes identifying the features of functions. Such features include rates of change, intercepts, zeros, asymptotes, and local and global behavior. I designed this activity to enhance my students' understanding of functions and to detect any misconceptions they might have.
Max Liebermann: Assimilation and Belonging
Authors: Frank Mitchell B.
Published: January 2021

En raison de la nature très publique de sa vie à l’époque de l’Empire allemand et de la République de Weimar, le peintre juif allemand Max Liebermann (1847–1935) a souvent été considéré comme un représentant exemplaire de l’assimilation juive à la vie culturelle allemande. Plutôt que de traiter Liebermann comme le représentant d’un groupe, cet essai explore la complexité de son expérience individuelle d’appartenance afin de suggérer que son sentiment d’être chez lui, même avant 1933, n’a jamais été complètement résolu. La maison berlinoise de Liebermann, située au coeur de la ville, est un motif central dans cette étude de son sentiment d’appartenance. Cet essai explore également sa position sociale, son sens du langage, la réception de sa peinture et sa pratique d’autoportraits. Souvent mis en scène dans l’atelier que Liebermann avait construit au-dessus de sa maison berlinoise, ses autoportraits engagent un dialogue de proximité et de distance qui est à la base de son sentiment d’être chez lui et au coeur de sa position de peintre moderniste et de juif allemand assimilé.
Shoah y Spielberg: 25 años de un modelo narrativo para contar el Holocausto
Authors: López-Olano Carlos , Colomer Rubio Juan Carlos
Published: January 2021

La lista de Schindler representó un punto de inflexión en la narrativa sobre el Holocausto. A pesar de que fue bien recibida por crítica y público, algo nada habitual en la trayectoria de un Steven Spielberg al que se tildaba de autor infantil y bueno sólo como realizador de cine de aventuras, la película no lo fue tanto en los círculos intelectuales judíos. La crítica negativa a la fábula cruel pero esperanzada de Spielberg fue ejercida especialmente por el director de otra de las propuestas cinematográficas que desde el extremo opuesto formalmente, también sentó referencia en el género: Claude Lanzmann y su monumental Shoah. Ahora, un cuarto de siglo después, queremos analizar en este artículo que queda sobre la discusión y el modelo narrativo impuesto por Spielberg cuando se trata de recordar uno de los episodios más negros de la historia reciente: el intento de exterminio nazi de los judíos.
Cine documental y movimientos sociales en la era de Internet: discursos de control y prácticas de resistencia durante el G8 de Génova
Authors: Delle Donne Napoli Serena
Published: January 2021

El presente artículo se centra en analizar las relaciones de poder y resistencia que articulan nuestra contemporaneidad en situaciones de excepcionalidad política. Más concretamente, nuestro interés se dirige hacia el estudio de la relación entre globalización, Internet y producción de discursos a través de los audiovisuales en un contexto histórico, social y político determinado, esto es, la contra cumbre del G8 de Genova del año 2001.
Risas en la comodidad del hogar. Un análisis de las comedias para adultos realizadas para el mercado del video hogareño en Argentina hacia fines de la década de 1980 y comienzos de 1990
Authors: Fidanza Fabio Nicolás
Published: January 2021

En una serie de breves comentarios, Jesús Martín-Barbero (1987), postula lo cómico, junto con el melodrama, como una de las matrices de la cultura popular latinoamericana. Esta matriz cultural fue reelaborada por distintas disciplinas entre las que se destaca el cine. Cuando este la incorpora, y la reformula, da vida a diversas variantes entre las que se encuentra un tipo de comedia, centrada en lo sexual, que logró convertirse en uno de los subgéneros más populares de toda Latinoamérica. En la Argentina esta vertiente fue desde sus inicios una de las producciones cinematográficas más exitosas. Este modo, que emergió en los sesenta, continuó produciéndose hasta fines de los años ochenta y comienzos de los noventa cuando abandona los cines nacionales. Sin embargo, lejos de desaparecer encuentra refugio en el campo del video hogareño. Partiendo de estas consideraciones, la intención de este trabajo es abordar el desembarco del cine picaresco en el campo del video con el fin de analizar las continuidades y las rupturas que se produjeron en el traspaso a un nuevo medio, las reformulaciones que llevó a cabo de elementos de otras producciones con características similares (programas cómicos televisivos, el «Teatro de la Calle Corrientes») y los vínculos que estableció con otros géneros de la industria del video local como el video concert.
La vida de la Cultura o Contra la cultedad.
Authors: León Liquete Carlos
Published: January 2021

Francisco Silvera, La vida de la Cultura o Contra la cultedad. Sevilla: Editorial La Isla de Siltolá, [Libro de Tientos, 1], 2020, 165 págs.
Los escogidos
Authors: Angulo Egea María
Published: January 2021

Patricia Nieto, Los escogidos, Prólogo del Cristian Alarcón. Valencia: La Caja Books, 2020, 152 págs.
Infrapolítica. Instrucciones de uso
Authors: Aparisi Galán María
Published: January 2021

Alberto Moreiras, Infrapolítica. Instrucciones de uso. Madrid: Oficina de Arte y Ediciones, 2020, 248 págs.
Methotrexate attenuates vascular inflammation through an adenosine-microRNA-dependent pathway
Authors: Yang Dafeng , Haemmig Stefan , Zhou Haoyang , Pérez-Cremades Daniel , Sun Xinghui , Chen Lei , Li Jie , Haneo-Mejia Jorge , Yang Tianlun , Hollan Ivana , Feinberg Mark W
Published: January 2021

Endothelial cell (EC) activation is an early hallmark in the pathogenesis of chronic vascular diseases. MicroRNA-181b (Mir181b) is an important anti-inflammatory mediator in the vascular endothelium affecting endotoxemia, atherosclerosis, and insulin resistance. Herein, we identify that the drug methotrexate (MTX) and its downstream metabolite adenosine exert anti-inflammatory effects in the vascular endothelium by targeting and activatingMir181bexpression. Both systemic and endothelial-specificMir181a2b2-deficient mice develop vascular inflammation, white adipose tissue (WAT) inflammation, and insulin resistance in a diet-induced obesity model. Moreover, MTX attenuated diet-induced WAT inflammation, insulin resistance, and EC activation in aMir181a2b2-dependent manner. Mechanistically, MTX attenuated cytokine-induced EC activation through a unique adenosine-adenosine receptor A3-SMAD3/4-Mir181bsignaling cascade. These findings establish an essential role of endothelialMir181bin controlling vascular inflammation and that restoringMir181bin ECs by high-dose MTX or adenosine signaling may provide a potential therapeutic opportunity for anti-inflammatory therapy.
Perfluorooctane sulfonate exerts inflammatory bowel disease-like intestinal injury in rats
Authors: Liang Hai , Yang Miao , Zeng Cheng , Wu Wei , Zhao Liying , Wang Yu
Published: January 2021

Background

Perfluorooctane sulfonate (PFOS), a type of perfluorinated compounds (PFCs), can induce various organ toxicity, including hepatomegaly, immunotoxicity, and gut microbiota disorder. PFCs have been associated with inflammatory bowel disease (IBD). Yet, whether PFOS exposure causes IBD-like disorder and the underlying mechanism remains undefined. Here, we investigated the influence of PFOS exposure on the development of IBD-like disorder in rats.

Methods

Sprague-Dawley rats were intraperitoneally injected with PFOS (1 or 10 mg/kg) or normal saline (NS) every other day for 15 days. Body weight, serum concentrations of serum amyloid A (SAA) and high sensitivity C reactive protein (hsCRP) were measured. Pathological assessments of villi height and crypt depth in the proximal duodenum and jejunum were performed using H&E staining. Terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) staining was used to assay cell apoptosis in the jejunum. The infiltration of inflammatory cells and cytokines in the jejunum were detected by immunohistochemistry analysis.

Results

PFOS (10 mg/kg) significantly increased the body weight, SAA and hsCRP, whereas no significant differences were observed in PFOS 1 mg/kg group of rats. The villi height and crypt depth in the proximal duodenum and jejunum were significantly reduced upon PFOS exposure. PFOS induced higher histopathological score in intestinal tissues compared to NS. Notably, TUNEL-positive cells were significantly higher in the jejunum upon PFOS exposure. Further, neutrophil and macrophage accumulated, and inflammatory cytokines infiltration were also remarkably increased in rats exposed to PFOS.

Conclusion

PFOS induces IBD-like phenotypes in rats, with associated inflammatory infiltration to intestinal.
O diálogo de Hegel com as ciências modernas na lógica da essência a partir do aparecimento
Authors:   Pontifícia Universidade Católica do Rio Grande do Sul (PUCRS), Bavaresco Bavaresco Agemir
Published: January 2021

Hegel's Science of Logic concludes with the “absolute idea”. The end meets the beginning, at the same time, as a retrospective of logical foundation and perspective of opening to spatiotemporal and historical exteriority. The problem is how this process is made explicit through the dialectical method, that is, articulated by the contradiction between idealism and realism, in a categorical network of logical space and time that imply a reason that is justified as true insofar as the idea becomes effective in history. The research addresses critical points in the structure of the dialectical method and its relationship with the absolute idea; contextualizes the historical debate of Hegelian idealism and realism; explains the essential role of the moment of contradiction that moves the logical-historical process; thematizes the specific sense of time and logical space, and finally, describes the dialectical tension between reason and effectiveness and its modern and contemporary historical implications. The absolute idea is the leitmotiv that contains in itself the form and the content of the logical whole as a whole in motion always open to constitute new meanings and produce new figurations of meaning for the circles of the logical idea.
El signo en Spinoza: imágenes, palabras e ideas
Authors:   Universidad Alberto Hurtado (Chile), Barroso Rojo Maribel
Published: January 2021

Se expone la relación en la filosofía spinoziana entre el signo en tanto gnoseológicamente originado por las impresiones en el cuerpo y, en consecuencia, perteneciente al ámbito imaginativo; y semánticamente de carácter equívoco y ambiguo; con el propósito de examinar si el uso del lenguaje por parte de Spinoza para explicitar sus ideas, constituye un obstáculo o, por el contrario, posibilita la interpretación de su filosofía. Al respecto, se revisan tres posturas: (i) la de David Savan, quien sostiene la inadecuación del lenguaje para expresar verdades filosóficas debido a la vinculación spinoziana entre las palabras y la imaginación; (ii) la de G.H.R. Parkinson, quien afirma que el uso del lenguaje no es inconsistente con la expresión de las proposiciones filosóficas por parte de Spinoza, sino que, la mayor parte de lo propuesto en la Ética pertenece al conocimiento de razón y las nociones comunes y; (iii) la de Mogens Laerke, quien defiende la posibilidad de atribuir coherencia al uso del lenguaje, por un lado, y a la filosofía spinoziana, por el otro, a partir del recurso matemático de la demostración geométrica. Finalmente, se argumenta una interpretación propia que intenta conciliar estas tres interpretaciones, con base en el análisis semiótico del signo en Spinoza, a partir de la cual (i) es posible atribuirle al signo una función dentro del entendimiento, sin detrimento de su capacidad gnoseológica y semántica para alcanzar verdades filosóficas y, por consiguiente, (ii) validar el uso del lenguaje como medio para exponer su filosofía.
La evolución conceptual del ateísmo, sus dificultades en el siglo actual y el renacimiento del teísmo
Authors:   Universidad Nacional de Cuyo (Argentina), Torres Juan Manuel
Published: January 2021

En primer lugar, se clarifica la actual confusión entre las nociones de religión y teísmo. A continuación, se muestra la diferencia esencial que hay entre el clásico argumento cosmológico a favor de la existencia de Dios y dos pruebas actuales que también parten del orden natural: el principio antrópico y la teoría del diseño inteligente. Finalmente, se señalan los límites de estos dos argumentos y se propone cómo se puede avanzar en la elucidación de la naturaleza del principio inteligente de la vida y del diseño de un escenario para ella
Is dairy wastewater safe for production of edible microbial biomass: A case study of Saras Dairy plant at Jaipur, India
Authors: Gaur Suman , Mathur Nupur , Singh Anuradha , Bhatnagar Pradeep
Published: January 2021

Mismanagement of wastewater at large scale may lead to catastrophic environmental and health consequences. Microbial remediation of wastewater is one of the most effective low-cost solutions. There are also initiatives to use wastewater for production edible biomass as an alternative for protein diets. While much researches were oriented towards maximum recovery of biomass and applications, less were focused on mutagenicity of dairy wastewater. In this study, we examined wastewater of one of the largest dairy industries in Rajasthan for its suitability for microbial biomass production and mutagenicity. Influent wastewater was collected from Saras dairy plant, Jaipur, for over a week. Physiochemical properties of wastewater were examined, such as; temperature, pH, salinity, TSS, TDS, turbidity, conductivity, BOD, COD, total carbon, and total nitrogen. SOS chromotest and Salmonella fluctuation test (TA 98, TA 100 and TA 102) were carried out at variable concentration of wastewater to assess mutagenic activity. Results indicated ideal pH, temperature and salinity, for microbial remediation. High TOC and TKN were also observed in the investigated wastewater, which is few of the prerequisites for single cell production. The ratio of BOD and COD was between 0.3-0.4, making the wastewater ideal for microbial growth. No mutagenic activity was observed by SOS chromotest, all three concentrations (C 0.01, C 0.1, and C 0.2) investigated in this study were <1.5 IF. Likewise, mutagenic ratio for all three types of Salmonella revertants were below 1.2 threshold, for investigated concentrations (C 0.5, C 1, and C 10) of wastewater. Conclusively, examined influent wastewater is less likely to induce mutagenic activity at the investigated concentration. Through physiochemical analysis, the investigated wastewater assumed to be candidate substrate for microbial biomass production.