Algebra Tiles Using tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra. Copyright 2011, National Council of Teachers of Mathematics Conic Section Explorer Explore the different conic sections and their graphs. Use the Cone View to manipulate the cone and the plane creating the cross section, and then observe how the Graph View changes. Copyright 2011, National Council of Teachers of Mathematics Interactive Calculus Tool Master calculus concepts in an interactive environment. Explore graphs of polynomial functions. Approximate tangent lines, derivative curves, and areas. Then, see the actual result of each. Modify graphs and parameters as you work to see if you can improve your approximations. Copyright 2011, National Council of Teachers of Mathematics Vector Investigation: Boat to the Island Move the boat around the water by changing the magnitude and direction of the boat's speed (blue vector) or the magnitude and direction of the water current (red vector). Try to land the boat on the island — but be careful not to hit the walls! Copyright 2011, National Council of Teachers of Mathematics Algebraic TransformationsThis applet allows you to transform a plus sign in eight different ways: rotate it ¼, ½, ¾, or a full turn, or flip it vertically, horizontally, or diagonally. Copyright 2011, National Council of Teachers of Mathematics The Mathematics of Garlic Nathan T. Moore and John C. Deming August 2010, Volume 104, Issue 1, Page 22 More than vegetables—proportional reasoning skills and an understanding of sophisticated statistical concepts—can grow from a backyard plot.
Mathematics Teacher, National Council of Teachers of Mathematics Alternative Approaches to Traditional Topics in Algebra John W. Coburn August 2010, Volume 104, Issue 1, Page 34 These new approaches to algebra, although atypical, can bring unreachable students into the classroom mix.
Mathematics Teacher, National Council of Teachers of Mathematics Funny Face Contest: A Formative Assessment Yong S. Colen August 2010, Volume 104, Issue 1, Page 50 Algebra students create their own funny faces onscreen after studying several parent functions and their transformations.
Mathematics Teacher, National Council of Teachers of Mathematics Activities for Students: How Long Does It Take for a Person to Sober Up? Some Mathematics and Science of DUI August 2010, Volume 104, Issue 1, Page 58 How many hours after consuming a six-pack of beer has the alcohol been flushed from one’s system? An activity module integrates health education, biology, physics, chemistry, social studies, driver education, and mathematics.
Mathematics Teacher, National Council of Teachers of Mathematics Mathematical Knowledge for Teaching in Planning and Evaluating Instruction: What Can Preservice Teachers Learn? Anne K. Morris, James Hiebert, and Sandy M. Spitzer November 2009, Volume 40, Issue 5, Page 491 The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an essential starting point for studying and improving one’s teaching.
Journal for Research in Mathematics Education, National Council of Teachers of Mathematics Area ToolUse this tool to determine how the length of the base and the height of a figure can be used to determine its area. Can you find the similarities and differences between the area formulas for trapezoids, parallelograms, and triangles? Copyright 2011, National Council of Teachers of Mathematics Cyclic Figures Students will recognize rotation symmetry in figures and examining various rotation symmetries. Copyright 2011, National Council of Teachers of Mathematics Dihedral Figures Use this activity to recognize dihedral symmetry and reflections in figures and examining various symmetries. Copyright 2011, National Council of Teachers of Mathematics Free Ride This applet allows you to vary the gear ratio of a bike. The distance traveled by a half-pedal is determined by the ratio of gears. Can you capture all five flags on a course? Copyright 2011, National Council of Teachers of Mathematics Geometric Solids This tool allows you to learn about various geometric solids and their properties. You can manipulate and color each shape to explore the number of faces, edges, and vertices, and you can also use this tool to investigate the following question: For any polyhedron, what is the relationship between the number of faces, vertices, and edges? What other questions can this tool help you answer? Copyright 2011, National Council of Teachers of Mathematics "A Study of Proof Conceptions in Algebra" Lulu Healy and Celia Hoyles Journal for Research in Mathematics Education This resource surveys the different conceptions algebra students have regarding proof.
JSTOR "Focusing on Informal Strategies When Linking Arithmetic to Early Algebra" Barbara A. Van Amerom Educational Studies in Mathematics Modeled on studies of students' own productions, a prototype pre-algebra learning strand was designed which takes students' informal (arithmetical) strategies as a starting point for solving equations.
JSTOR "Predicting Eighth-Grade Algebra Achievement" Barbara K. Flexer Journal for Research in Mathematics Education The relative importance of a group of cognitive variables in explaining the algebra achievement of high-ability eighth graders was investigated in this article.
JSTOR "Do not worry about your difficulties in mathematics, I assure you that mine are greater" Albert Einstein (1879-1955)"Mighty is geometry; joined with art, resistless" Euripides (485-406 B. C. E) to i: Get real! Teacher: What is 2k + k? Student: 3000! Volker Runde, Math Jokes Trigonometry for farmers: swine and coswine... Q: How does a mathematician induce good behavior in her children? Q: What is the first derivative of a cow? |
Congruence Theorems Investigate congruence by manipulating the parts (sides and angles) of a triangle. If you can create two different triangles with the same parts, then those parts do not prove congruence. Can you prove all the theorems? Copyright 2011, National Council of Teachers of Mathematics Function Matching See how well you understand function expressions by trying to match your function graph to a generated graph. Choose from several function types or select random and let the computer choose. Copyright 2011, National Council of Teachers of Mathematics LimitsA geometric series is a sum of numbers such that the ratio between consecutive terms is constant. For instance, 1/2 + 1/4 + 1/8 + … is a geometric series. In this activity, you can see a representation of several geometric series and their limits. Copyright 2011, National Council of Teachers of Mathematics A Geometric Investigation of (a + b)2 What is the value of (a + b)2? You might think it's a2 + b2, but it's not! Use this geometric demonstration to find out what it really is. Copyright 2011, National Council of Teachers of Mathematics Angle Sums Examine the angles in a triangle, quadrilateral, pentagon, hexagon, heptagon or octagon. Can you find a relationship between the number of sides and the sum of the interior angles? Copyright 2011, National Council of Teachers of Mathematics Transforming the Way We Teach Function Transformations Eileen Durand Faulkenberry and Thomas J. Faulkenberry August 2010, Volume 104, Issue 1, Page 29 Using transparencies helps students learn function transformations—through understanding, not memorization.
Mathematics Teacher, National Council of Teachers of Mathematics Cosby’s Rule: Connecting Summation Operations, Definite Integrals, and the Fundamental Theorem of Calculus Margaret H. Sloan August 2010, Volume 104, Issue 1, Page 45 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.
Mathematics Teacher, National Council of Teachers of Mathematics Mathematical Lens: Looking for Slope in All the Wrong Places August 2010, Volume 104, Issue 1, Page 18 Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month the photographs focus on slopes of roadways and trigonometry.
Mathematics Teacher, National Council of Teachers of Mathematics Delving Deeper: A Problem in Probability August 2010, Volume 104, Issue 1, Page 71 The authors take the old dart-board problem and examine why the density of random hits seems to be greater nearer the bull’s-eye.
Mathematics Teacher, National Council of Teachers of Mathematics Knowledge Needed by a Teacher to Provide Analytic Scaffolding During Undergraduate Mathematics Classroom Discussions Natasha M. Speer and Joseph F. Wagner November 2009, Volume 40, Issue 5, Page 530 Using case study analysis and a cognitive theoretical orientation, the authors examine elements of knowledge for teaching needed by a mathematician to orchestrate whole-class discussions in an undergraduate mathematics classroom. Examples of classroom teaching and interview data demonstrate that, despite having extensive teaching experience and possessing strong content knowledge, some instructors may still face challenges when trying to provide analytic scaffolding to move whole-class discussions toward a lesson’s mathematical goals. Journal for Research in Mathematics Education, National Council of Teachers of Mathematics Compound Interest Simulator This applet will allow you to investigate savings account earnings, credit card debt, and a stock market simulation. Copyright 2011, National Council of Teachers of Mathematics Diagonals to Quadrilaterals Two line segments can be drawn to intersect in various ways — they could be perpendicular, they could bisect one another, or both. Depending on the arrangement of these segments, various quadrilaterals can be formed by connecting the endpoints of the segments. This activity allows you to discover what types of quadrilaterals can be formed when the diagonals meet in various ways. Copyright 2011, National Council of Teachers of Mathematics Flowing Through Mathematics Simulate water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Copyright 2011, National Council of Teachers of Mathematics Frieze Patterns Students can experiment with the seven classes of Frieze patterns with this activity. They can explore the transformations that constitute each of the seven categories. Copyright 2011, National Council of Teachers of Mathematics Half Angle If you want to inscribe a circle within a triangle, where will the center of the circle lie? This applet allows you to find the incenter of a triangle, as well an a visual explanation of why it occurs where it does. Copyright 2011, National Council of Teachers of Mathematics "The Effects of a Graphing-Approach Intermediate Algebra Curriculum on Students'Understanding of Function" Jeannie C. Hollar and Karen Norwood Journal for Research in Mathematics Education In this study, we investigate the effects of a graphing-approach curriculum employing the TI-82 graphing calculator in an algebra classroom.
JSTOR "Effects of Standards-Based Mathematics Education: A Study of the Core-plus Mathematics Project Algebra and Functions Strand" Mary Ann Huntley, Chris L. Rasmussen, Roberto S. Villarubi, Jaruwan Sangtong, James T. Fey Journal for Research in Mathematics Education To test the vision of Standards-based mathematics education, a comparative study was conducted of the effects of the Core-Plus Mathematics Project (CPMP) curriculum and more conventional curricula on growth of student understanding, skill, and problem-solving ability in algebra. JSTOR "There are things which seem incredible to most men who have not studied Mathematics" Archimedes of Syracus (287-212 B. C. E)"There is no royal road to geometry" Euclid of Alexandria (325-265 B.C.E)"Mathematics is the queen of the sciences and number theory is the queen of mathematics" Carl Friedrich Gauss (1777-1855)-GermanAn infinite crowd of mathematicians enters a bar. Q: What does the zero say to the eight? A: Nice belt! Volker Runde, Math Jokes Life is complex: it has both real and imaginary components. Math problems? Call 1-800-[(10x)(13i)2]-[sin(xy)/2.362x]. Q: Why do you rarely find mathematicians spending time at the beach? |