Mathematics


 * Mathematics Learning Activity Types **

Essentially, these mathematics activity types are designed to be //catalysts// to thoughtful and creative instruction by teachers. We have conceptualized seven genres of activity types for mathematics that are derived from the NCTM's process standards. ** The "Consider" Activity Types ** When learning mathematics, students are often asked to thoughtfully consider new concepts or information. This request is a familiar one for the mathematics student, and is just as familiar to the teacher. Yet, although such learning activities can be very important contributors to student understanding, the "Consider" activity types also often represent some of the lower levels of student engagement, and typically are manifested using a relatively direct presentation of foundational knowledge. The “Consider” Activity Types Some educational technologies can provide valuable assistance in helping students to practice and internalize important skills and techniques.  The “Practice” Activity Types Educational technologies can be used to help students investigate concepts and relationships more actively, and assist them in interpreting what they observe.  The “Interpret” Activity Types ** The "Produce" Activity Types ** When students are actively engaged in the study of mathematics, they can become motivated producers of mathematical works, rather than just passive consumers of prepared materials. The “Produce” Activity Types ** The "Evaluate" Activity Types ** When students evaluate the mathematical work of others, or self-evaluate their own mathematical work, they utilize a relatively sophisticated understanding of mathematical concepts and processes. Educational technologies can become valuable allies in this effort, assisting students in the evaluation process by helping them to undertake concept comparisons, test solutions or conjectures, and/or integrate feedback from other individuals into revisions of their work. The “Evaluate” Activity Types  ** The "Create" Activity Types ** When students are involved in some of the highest levels of mathematics learning activities, they are often engaged in very creative and imaginative thinking processes. Albert Einstein once suggested, “Imagination is more important than knowledge.” The “Great” Activity Types
 * ** Activity Type ** || ** Brief Description ** || ** Example Technologies ** ||
 * Attend to a Demonstration || Students gain information from a presentation, video clip, animation, interactive whiteboard or other display media || Powerpoint, Keynote, iMovie, YouTube, Teacher Tube, podcasts ||
 * Read Text || Students extract information from textbooks, or other written materials, in either print or digital form || Electronic textbooks, websites (i.e. the Math Forum), informational. pdfs ||
 * Discuss || Students discuss a concept or process with a teacher, other students, or an external expert || Ask-an-expert sites (e.g., Ask Dr. Math) Moodle forums, Edmodo, videoconferencing ||
 * Recognize a Pattern || Students examine a pattern presented to them and attempt to understand the pattern better || Graphing calculators, virtual manipulative sites (National Library of Virtual Manipulatives), spreadsheets ||
 * Investigate a Concept || Students explore or investigate a concept (such as fractals), perhaps by use of the Internet or other research-related resources || Web searching, Informational databases (Wikipedia), virtual worlds, simulations ||
 * Understand or Define a Problem || Students strive to understand the context of a stated problem or to define the mathematical characteristics of a problem || Web searching, [|www.bubbl.us], ||
 * <span style="color: black; mso-ascii-font-family: Cambria; mso-bidi-font-family: Times; mso-bidi-font-size: 11.5pt; mso-hansi-font-family: Cambria;">The "Practice" Activity Types **
 * ** Activity Type  ** || **  Brief Description  ** || **  Example Technologies  ** ||
 * Do Computation || Students undertake computation-based strategies using numeric or symbolic processing || Scientific calculators, graphing calculators, spreadsheets, Study Island ||
 * Do Drill and Practice || Students rehearse a mathematical strategy or technique, and perhaps uses computer-aided repetition and feedback in the practice process || Timez Attack, Online textbook supplements ||
 * Solve a puzzle || Students carry out a mathematical strategy or technique within the context of solving an engaging puzzle, which may be facilitated or posed by the technology || Virtual manipulatives, Web-based puzzles (magic squares), brainteaser Web sites - [|www.coolmath.com] ||
 * <span style="color: black; mso-ascii-font-family: Cambria; mso-bidi-font-family: Times; mso-bidi-font-size: 11.5pt; mso-hansi-font-family: Cambria;">The "Interpret" Activity Types **
 * ** Activity Type  ** || **  Brief Description  ** || **  Example Technologies  ** ||
 * Pose a Conjecture || <span style="color: black; mso-ascii-font-family: Cambria; mso-bidi-font-family: Times; mso-bidi-font-size: 11.5pt; mso-hansi-font-family: Cambria;">The student poses a conjecture, perhaps using dynamic software to display relationships || Geometer’s Sketchpad, Gizmos (Explore Learning) ||
 * Develop an Argument || The student develops a mathematical argument related to why they think that something is true. Technology may help to form and to display that argument. || Concept mapping software like inspiration, [|www.bubbl.us.com], powerpoint, keynote, blog, glog, Gaggle email ||
 * Categorize || The student attempts to examine a concept or relationship in order to categorize it into a set of known categories || Databases like Zoho creator, [|www.bubbl.us.com], [|www.prezi.com] , [|www.cosketch.com] ||
 * Interpret a Representation || <span style="color: black; mso-ascii-font-family: Cambria; mso-bidi-font-family: Times; mso-bidi-font-size: 11.5pt; mso-hansi-font-family: Cambria;">The student explains the relationships apparent from a mathematical representation (table, formula, chart, diagram, graph, picture, model, animation, etc.) || iMovie, GPS, 2D and 3D animations, powerpoint, keynote, activinspire ||
 * Estimate || The student attempts to approximate some mathematical value, by further examining relationships using supportive technologies || Scientific calculator, graphing calculator, spreadsheets (excel, google docs, Zoho) response systems like activexpression (clickers) ||
 * Interpret a Phenomenon Mathematically || <span style="color: black; mso-ascii-font-family: Cambria; mso-bidi-font-family: Times; mso-bidi-font-size: 11.5pt; mso-hansi-font-family: Cambria;">Assisted by technology as needed, the student examines a mathematics related phenomenon (such as velocity, acceleration, the Golden Ratio, gravity, etc.) || Digital cameras, video, probes, animations ||
 * ** Activity Type ** || ** Brief Description ** || ** Example Technologies ** ||
 * Do a Demonstration || The student makes a demonstration on some topic to show their understanding of a mathematical idea or process. || Promethean board, video using iMovie and digital video, document camera, podcast with Garageband, Powerpoint, Keynote, [|www.prezi.com], iStopmotion ||
 * Generate Text || The student produces a report, annotation, explanation, journal entry or document, to illustrate their understanding. || Collaborative documents like Google Docs, Moodle journals, online discussion like [|www.edmodo.com] ||
 * Describe an Object or Concept Mathematically || Assisted by the technology in the description or documentation process, the student produces a mathematical explanation of an object or concept || Logo graphics ([|www.cooltext.com]), [|www.prezi.com], [|www.bubb.us], ActivInspire, Word, Pages ||
 * Produce a Representation || The student develops a mathematical representation (table, formula, chart, diagram, graph, picture, model, animation, etc.) || Spreadsheet – excel, numbers, google docs, Zoho ; virtual manipulatives – digital geoboard @ nlvm, ActivInspire, powerpoint, keynote, graphing calculator ||
 * Develop a Problem || The student poses a mathematical problem that is illustrative of some mathematical concept, relationship, or investigative question || Word, Pages, Google docs, Moodle forum, [|www.edmodo.com] (for discussion) email ||
 * ** Activity Type ** || ** Brief Description ** || ** Example Technologies ** ||
 * Compare and Contrast || The student compares and contrasts different mathematical strategies or concepts, to see which is more appropriate for a particular situation. || Inspiration, [|www.bubbl.us], web searches, ActivInspire ||
 * Test a Solution || The student systematically tests a solution, and examines whether it makes sense based upon systematic feedback. || Scientific calculator, graphing calculator, spreadsheet – excel, google docs, numbers- ||
 * Test a conjecture || The student poses a specific conjecture and then examines the feedback of any interactive results to potentially refine the conjecture. || Geometer sketchpad, online calculators, robotics ||
 * Evaluate Mathematical Work || The student evaluates a body of mathematical work, through the use of peer or technology – aided feedback. || Online discussion – Moodle forums, Edmodo, blogs ||
 * ** Activity Type  ** || **  Brief Description  ** || **  Example Technologies  ** ||
 * Teach a Lesson || The student develops and delivers a lesson on a particular mathematics concept, strategy, or problem || ActivInspire, Powerpoint, Keynote, video, podcasts, [|www.voki.com] ||
 * Create a Plan || The student develops a systematic plan to address some mathematical problem or task || Inspiration, bubbl.us, ActivInspire, google docs (for collaboration), Word, Pages ||
 * Create a Product || <span style="mso-layout-grid-align: none; mso-pagination: none; tab-stops: 28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt; text-autospace: none;"> The student imaginatively engages in the development of a student project, invention, or artifact, such as a new fractal, tessellation, or other creative product. || Word, Pages, iStop Motion, [|www.mutpic.com], animation tools ||
 * Create a Process || The student creates a mathematical process that others might use, test or replicate, essentially engaging in mathematical creativity. || iMovie, flip video, [|www.vuvox.com], 3D animation in Blender  ||