Teaching Strategies in Mathematics

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<ul><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 1/75</p><p>INNOVATIVE TEACHING</p><p>STRATEGIESIN MATHEMATICS</p><p>By:</p><p>JOCELYN G. TAMARES</p><p>Maruhat national High School</p><p>Gapan City Division</p><p>MERCY LEGASPI</p><p>Mayapyap National High School</p><p>Cabanatuan City Division</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 2/75</p><p> A teachers primary job is touncover the important ideas</p><p>in subjects, not cover atextbook.</p><p>-Anonymous</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 3/75</p><p>Challenges in Teaching</p><p>Engaging the learners;</p><p>Empowering the teachers;</p><p>and</p><p>Enabling research.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 4/75</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 5/75</p><p>Promoting Inquiry</p><p>Inquiry Question Openers</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 6/75</p><p>What is an inquiry-based classroom?</p><p> It is a classroom which allows a student to play the</p><p>role of an experienced co-researcher rather than</p><p>of someone with all the answers.</p><p>Here, the teacher:</p><p> gives enough hints and poses probing questions;</p><p> offers encouragement for good thinking, not</p><p>just for right answers. treat answers, right and wrong, as discussion</p><p>topics until the class the research team - reaches</p><p>a consensus. </p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 7/75</p><p>An inquiry-based classroom demands flexibility</p><p>in responding to students ideas.</p><p>Here, the goal is for students to experience mathematics as a</p><p>process of finding and connecting ideas so that</p><p>justifying ideas and problem solving become moreimportant than the actual solutions;</p><p> the teacher spends time in planning and thinkingof how students might address the problem under</p><p>investigation; and</p><p> the teacher leads students to know that thethinking and problem-solving skills they develop</p><p>can serve them in all aspects of their lives. </p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 8/75</p><p>Some Effective Mathematics</p><p>Teaching Methods</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 9/75</p><p>Indicators of Effectiveness of a</p><p>Teaching Strategy/Method</p><p>Students ability to</p><p> perform the desired competencies;</p><p>transfer learning and use whateverconcepts and skills learned to solve a similaror related problem;</p><p>accomplish tasks that require higher orderthinking skills; and</p><p> appreciate the application of the concept</p><p>or principle to real-life situations.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 10/75</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 11/75</p><p>CONCEPT MAPPING</p><p>A concept map</p><p> is a diagram or network indicating</p><p>interrelationships among concepts and</p><p>representing conceptual frameworks within aspecific domain of knowledge (Novak, 1990).</p><p>Here, the nodes represent concepts, the lines</p><p>linking the nodes represent relationships, andthe labels on the lines represent the nature of</p><p>the relationships.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 12/75</p><p> generates and communicates ideas which can</p><p>aid collaborative projects (brainstorming, etc.);</p><p> aids learning by explicitly integrating new and</p><p>old knowledge;</p><p> helps in assessing understanding or diagnosing</p><p>misunderstanding;</p><p> enhances the problem-solving phases of</p><p>generating alternative solutions and options; encourages positive self-concept.</p><p>(Seaman, 1990; Gaines and Shaw, 1995;</p><p>Plotnick, 1997; Williams,1997 </p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 13/75</p><p>Sample Concept Map</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 14/75</p><p>FLOW CHARTING</p><p>an outline of the sequence of processes indiagram form</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 15/75</p><p>MINDS-ON HANDS-ON</p><p> , focusing on the core conceptsand critical thinking processes needed for</p><p>students to create and re-create</p><p>mathematical concepts and relationships intheir own minds.</p><p> , experimenting first-hand with</p><p>physical objects in the environment and</p><p>having concrete experience before learning</p><p>abstract mathematical concepts.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 16/75</p><p>PROBLEM-BASED LEARNING</p><p> This is a curriculum delivery system that</p><p>recognizes the need to develop problem</p><p>solving skills.</p><p> The teachers act as facilitators of learning.</p><p> The students are given guidelines on how to</p><p>approach the problem.</p><p>(Here, students act as professionals andconfront problems as they occur with fuzzy</p><p>edges, insufficient information - to determine</p><p>the best solution.) </p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 17/75</p><p>Problem-based Learning</p><p>EVALUATION</p><p>EXPLANATION</p><p>ELABORATION</p><p>ENGAGEMENT</p><p>EXPLORATION</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 18/75</p><p>Sample Problem</p><p>(Systems of Linear Equation)</p><p>You have decided to purchase a cell phone and areconsidering which company offers the mostaffordable plan for you.</p><p>Talk-a-lot charges P199.90 per month and</p><p>P15 per minute</p><p>Motor mouth charges P399.90 per month</p><p>and P5 per minute</p><p>1. Write an equation that represents each phonecompany.</p><p>2. Is there ever a time when both would charge the</p><p>same amount? When? How much? </p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 19/75</p><p>COOPERATIVE LEARNING Think-Pair-Share- a strategy designed to</p><p>provide students with food for thought ona given topic enabling them to formulateindividual ideas and share these ideas with</p><p>another student. Uses: Note check, vocabulary review, quiz</p><p>review, concept review, lecture check,</p><p> Management Ideas: Assign partners, changepartners, give think time, monitor discussion,timed-pair-share, randomly select students</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 20/75</p><p>CONSTRUCTIVIST TEACHING METHOD</p><p> Orientation Students are given the opportunity</p><p>to develop a sense of purpose and motivation forlearning the topic.</p><p> Elicitation Students are provided with questions</p><p>or problems for them to think about. Their initialideas about the concepts covered in the lessonare solicited as well as their answers to the givenquestions.</p><p> Discussion This includes (a) clarification andexchange of ideas; (b) construction of new ideas;and (c) evaluation of new ideas.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 21/75</p><p>Constructivist</p><p> Application Students are given the opportunity</p><p>to use their developed ideas in a variety ofsituations. In cooperative groups, they solve,</p><p>explain and justify the solution of practical and</p><p>textbook exercises. Summary and Reflection Students are asked to</p><p>summarize the principles learned and write their</p><p>reflections on how they learned the concepts andprinciples and how the method helped them in</p><p>dealing with mathematical activities.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 22/75</p><p>MATHEMATICAL INVESTIGATIONS</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 23/75</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 24/75</p><p>Profitable Activities in Teaching Mathematics</p><p>1. Use of Music2. Visualization</p><p>3. Games and Puzzles</p><p>4. Math Lab5. Arts and Aesthetics</p><p>6. Journal Writing</p><p>7. Mathematics in</p><p>Context: Story</p><p>Mathematics</p><p>8. MathematicalConnections</p><p>9. Using News Items and</p><p>Clippings10. Research Reports</p><p>and Projects</p><p>11. Integratingtechnology</p><p>12. Use of manipulatives</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 25/75</p><p> To make the students relaxed, entertained,and eager to learn, especially when they aretired of routine work in mathematics.</p><p>This technique works very well as long as thevolume remains low enough for the studentsnot to compete against but loud enough to be</p><p>heard and to eliminate squeaks and other littledistractions.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 26/75</p><p>2. Visualization</p><p>Provide projects and hands-on materials</p><p>and draw three-dimensional figures from</p><p>real models.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 27/75</p><p> Some manipulatives in the form of</p><p>mathematical games and puzzles aretangrams, Rubiks cube and Soma cubes,</p><p>and problems which can be solved</p><p>through logical reasoning.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 28/75</p><p>3. Games and Puzzles</p><p>useful in improving problem solving andvisualization skills;</p><p> promote high-level skills such as analysis</p><p>and synthesis; reinforce concepts and skills;</p><p> improve students attitude toward learning</p><p>math;</p><p> add variety to the instructional program.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 29/75</p><p>4. Math Lab</p><p>offers opportunity for math to come aliveand for students to get involved and see the</p><p>positive relationship between mathematics</p><p>and everyday life; provides opportunity for encouraging</p><p>creativity and social skills development.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 30/75</p><p>Sample Math Lab Activities</p><p>A. Assume that you have Php10,000 whichyou can spend for a party.</p><p>1. Using the ads of a certain restaurant,</p><p>plan your expenses.2. Draw up a budget that will include all</p><p>party expenses.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 31/75</p><p>B. Clip a recipe for cooking your favorite</p><p>dish and make a new recipe for 20 servings.</p><p> 1 lb spaghetti</p><p> cup heavy cream</p><p> 4 eggs</p><p> lb bacon, cut into-inch dice</p><p> 1 tsp extra virgin</p><p>olive oil</p><p> 2 Tbsp chopped</p><p>Italian parsley</p><p> Kosher salt and</p><p>freshly ground black</p><p>pepper, to taste</p><p> cup freshly grated</p><p>pecorino-romano</p><p>cheese (parmesan</p><p>may be substituted)</p><p>Serving: 4</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 32/75</p><p> Fill a large soup pot with cold water and add a</p><p>handful or so of Kosher salt. Stir and taste; it should</p><p>taste like seawater. Cover the pot and heat the</p><p>water until it boils.</p><p> Add the diced bacon to a cold saut pan and cook</p><p>slowly over a low heat for 10 to 15 minutes or until</p><p>crisp. Remove bacon from pan and drain on papertowels.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 33/75</p><p> Drop the spaghetti into the boiling salted</p><p>water and cook according to package</p><p>instructions, about 6 to 9 minutes or until aldente, or tender but still firm to the bite.</p><p> While the pasta cooks, combine the eggs,</p><p>cheese, cream and olive oil in a bowl and beatwith a whisk until completely mixed.</p><p> Drain pasta, toss with the egg and cream</p><p>mixture, then add the cooked bacon andchopped parsley. Serve right away, with</p><p>additional grated cheese if desired.</p>http://culinaryarts.about.com/od/glossary/g/Al-Dente.htmhttp://culinaryarts.about.com/od/glossary/g/Al-Dente.htmhttp://culinaryarts.about.com/od/glossary/g/Al-Dente.htmhttp://culinaryarts.about.com/od/glossary/g/Al-Dente.htm</li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 34/75</p><p>C. Turn to the Computers for Sale section</p><p>of the classified ads.</p><p>1. Figure out the average cost per</p><p>computer in four different outlets.</p><p>2. Draw a bar graph which shows theaverage cost per computer in the four</p><p>outlets.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 35/75</p><p>D. Have everyone in the class select a stock</p><p>and follow it up for a week.1. Each student follows the progress of his</p><p>chosen stock and draws a line graph</p><p>depicting its behavior.</p><p>2. Ask students to describe the behavior of</p><p>the said stock.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 36/75</p><p>E. Turn to the sports page of any newspaper</p><p>and find the standings of any professionalsport.</p><p>1. Add up the total number of wins and losses</p><p>for each division.2. Which division appears to be the</p><p>strongest? the weakest?</p><p>3. By how much do their average winnings</p><p>differ?</p><p>F Mathematical Magic</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 37/75</p><p>F. Mathematical Magic1. Ask a student volunteer to write down any</p><p>three- digit number whose first and last digitsdiffer by more than one.</p><p>2. Then form another three-digit number by</p><p>reversing the digits of the first number(i.e., 235 becomes 532).</p><p>3. Subtract the smaller number from the larger</p><p>number, reverse the digits of the answer, and</p><p>add this to the result of subtraction.</p><p>4. What is the sum? Justify your answer. </p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 38/75</p><p>5. Arts and Aesthetics</p><p>The use of art as teaching aid can lead studentstowards better understanding of, andappreciation for mathematics.</p><p> Tessellations, modular art, and</p><p>curve stitching may be done in</p><p>the classroom.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 39/75</p><p>6. Writing Math/Journal Writing</p><p> Give students the opportunity to create andcommunicate mathematics problems of their</p><p>own.</p><p>Write</p><p>- an algorithm, a definition, a problem;</p><p>- generalizing a concept/relationship;</p><p>- reporting a project;</p><p>- accomplishments, reactions</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 40/75</p><p>7. Mathematics in Context: Story</p><p>MathematicsPlace a mathematical topic in the context</p><p>of a brief story to further explain it and</p><p>motivate students to carry out problem-solving activities.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 41/75</p><p>Sample of Mathematics in Context</p><p> Suppose that a classical concert ticket</p><p>costs twice as much as a rock concert</p><p>ticket.</p><p> Is it cheaper, more expensive, or equally</p><p>expensive for you to take 100 friends to a</p><p>rock concert or two friends, 25 timeseach, to a classical music concert?</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 42/75</p><p>-Which of the regions in the Philippines is thelargest in land area?</p><p>-Which is the smallest?</p><p>-How many times greater is the largest?</p><p>Which region has the largest population?</p><p>-What is the population density (number of personsper square mile)of a particular region?</p><p>-What is the population density in persons per</p><p>hectare of the region in which you live? </p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 43/75</p><p>-What change in the area occurs in a leaf of a fast-</p><p>growing plant as the growing season advances?-What is the rate of the change based on a simple</p><p>graph of area versus time?</p><p>-How does the rate of change in the area comparewith the rate of change in the length of the leaf?</p><p>Ifthe distributed electric current through a metalstrip of uniform but irregular cross section is one</p><p>ampere, what is the current density per square</p><p>centimeter across the cross section?</p><p>9 News Items that Provide Real</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 44/75</p><p>9. News Items that Provide Real</p><p>Mathematical Experiences</p><p>Decimals can be computed from batting orshooting averages and percentage of passcompletions for a favorite sports activity.</p><p>Common fractions are found in recipes. Find arecipe serving six persons and have studentsconvert the quantities so the recipe will serve15 persons.</p><p> Metric system can be introduced or reviewedby reading and interpreting articles,especially from foreign news services.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 45/75</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 46/75</p><p> Graphs are common in most newspapers,</p><p>and students can draw their own from data</p><p>they find in articles.</p><p> Bar graphs may be constructed from sports</p><p>statistics such as baskets scored by each of</p><p>the baseball or basketball teams.</p><p> Election results can be depicted through a</p><p>circle graph in which sectors indicate thepercentages of vote received by each</p><p>candidate.</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 47/75</p><p> Line or bar graphs can record daily</p><p>temperatures of hours of daylight (from a</p><p>certain date to another), height of annualrainfall or the rise and fall of tide in the</p><p>locality, or the households monthly water</p><p>and energy consumption.</p><p>10 Use of Research Reports</p></li><li><p>7/31/2019 Teaching Strategies in Mathematics</p><p> 48/75</p><p>10. Use of Research, Reports,</p><p>and Projects</p><p> Encourage students to pursue individual areas of</p><p>interest and open up new dimensions of study for</p><p>them.</p><p>This provides teachers excellent opportunities to</p><p>know their students better and work with themon an individua...</p></li></ul>

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