Mathematics.Games for drill and practice - Essay Example

Report on NCTM standard for number sense and operations d 30 March 2009 Since 1989, the National Council of Teachers ofMathematics has developed standards for Mathematics in the schools. Pre-Kindergarten through Grade 12 are included in these standards that relate to instruction, classroom materials, and student evaluation. The NCTM standards are more specific and detailed models of teaching procedures. The NCTM standards describe specific ways base ten blocks and other manipulative can be used to help students understand the certain concepts within the standards. In this essay four different activities are described. The first activity is called the Fish out of Water: In this particular game each student begins with 20 fish out of water. Each player rolls a die and counts out that many fish to return to the fish bowl. The first player to return all 20 of his/her fish to the bowl wins the game. The materials used are foam fish cutouts and a plastic bowl for a more realistic version of the game or download the directions, game mat and center icons for Fish out of Water. This game is designed especially for the pre-kindergarten kids who are very new to numbers and help children understand basic number concepts thus helping them to develop the number sense of basic counting. Also, the activity enhances the kid's ability to recognize the numbers better and remember them for a longer period of time. The set of instructions given for this game are very simple and easy to comprehend for the kids who are just learning to recognize the numbers. For example the instructor can show a video of the activity and then play with the help of the instructor and finally let them play on their own. The second activity is called Addition Top-It: This game can be played by two to three players and the materials required are: a set of number cards with four cards each of the numbers 0-10, a penny which is optional in the game. A player shuffles the cards and places the deck number-side down on the playing surface. Each player turns over two cards and calls out their sum. The player with the highest sum wins the round and takes all the cards. In the case of a tie, each player turns over two more cards and calls out their sum. The player with the highest sum then takes all the cards from both plays. Play ends when not enough cards are left for each player to have another turn. The player with the most cards wins the game. There is an option available with the game which allows the children to toss a penny to determine whether the player with the most or the fewest cards wins. The other variations are also available with this game are as follows: 1. Use a set of double-nine dominoes instead of a set of number cards to generate addition problems then place the dominoes facedown on the playing surface. Each player turns over a domino and calls out the sum of the dots on the two halves. The winner of a round takes all the dominoes then in play. 2. To practice addition with three addends, use three cards and play the same as described above. This game is suited for the students in grade one where they begin to learn the basic concept of addition, subtraction, multiplication etc. The number sense that the player is the addition of numbers which is the second step after the children can recognize the basic numbers and are ready to do more complex activities with the numbers. Also, by practicing these kind of exercises skills like calculator skills, money exchange and shopping skills, logic, geometric intuition, and intuition about probability and chance because many games involve numbers that are generated randomly are reinforced within the children. The instructions given at this level are easy and simple and also less as compared to the instructions given for the first activity as the understanding of the children increase. For example the teacher can display the video of the game and then allow them to take drills of the activity according to the comfort of the students like practicing it during breaks or after school. The third activity is the fractions: The game comprises of three parts as described under: 1. Area Model: In this the students divide shapes into the appropriate number of equal sections given by the denominator, then shade in the appropriate number of sections, given by the numerator to create a picture of the fraction. Further, equivalent fractions are also developed using this area model. Following are the manipulative used to develop the area model pattern blocks, circular fraction regions, pizzas, geo-boards, spinners and folded fraction pieces. 2. Measurement or Linear Model: In this game the students use the number line model found on rulers or divide fraction strips into the appropriate sections by length by using number line, rulers, linking cube trains, Cuisenaire rods, fraction bars and fraction strips. 3. Set Model: Students use individual shapes to match the fraction. For example, one student has 4 cubes in his/her bag and 1/2 of them are blue or John brought 6 toy cars to school and 1/3 of them are red etc. by using the manipulative like two-color counters, colored counters or bingo chips, centimeter or rainbow cubes and foam shapes. These activities are suited for the students of 3-5 grades as the games can motivate students and engage them in thinking about and applying concepts and skills. Also, by working on this activity, students have opportunities to think about how fractions are related to a unit whole, compare fractional parts of a whole, and find equivalent fractions. The above mentioned activities allow the students develop a rich concept of fractions that they can use to make sense of numbers, operations, measurement and probability. The instruction given has to in a well designed manner by first showing the activity in a video clip and then communicating the activity very well to the students and finally allowing the students to practice the activities to understand them completely. The fourth activity is to understand Distance, Speed, and Time Relationships Using Simulation Software: The activity includes a software simulation of two runners along a track where the students can control the speeds and starting points of the runners, watch the race, and examine a graph of the time-versus-distance relationship. The student has to set a starting position for the runners by dragging their icons along the tracks also; they can change the direction they face by clicking once on their icons. The activity is suitable for the 3-5 grade students who are capable of doing complex activities like fractions, and algebraic standards. The activity helps the students in the upper elementary grades understand ideas about functions and about representing change over time, as described in the algebra standards. This game allows students to analyze change by setting the starting positions and length of stride (speed) for two runners. Students can predict the effects on the graph of changing the starting position or the length of the stride of either runner. They can observe and analyze how a change in one variable, such as length of stride, relates to a change in speed. The instructor has to help them connect what is happening on the graph to what is happening on the track: How long does it take for the boy to go the same distance as the girl has traveled in fifty "seconds" How can you see this demonstrated on the track Where on the track does the girl catch up to the boy Etc. and has to supervise them during the entire simulation and help them understand the various aspects related to the activity. Thus it can be concluded that NCTM number and operations standard focuses on students developing further number sense. It also emphasizes that students solve problems that are meaningful. When they go about solving problems, students need to be encouraged to use informal strategies and to notice the informal strategies used by others. Following these current ideas and concepts is essential for teachers in the classroom now. In addition, this standard discusses many other new ways of thinking about teaching as well. Students should not merely fill out worksheets to practice number sense, but they should be given various opportunities to use their own number knowledge throughout the school day like understanding counting, addition, subtraction, fraction, area models etc. Thus it helps students to remember the numbers better and permanently and will benefit the most from procedural fluency and conceptual understanding. Yes, all the activities support differentiation of instruction depending on the level of understanding amongst the students of different grades the instructions given to them also differs as discussed in the end of each activity the kind of instructions that are usually provided to them by the teachers. References: 1. Everyday Mathematics (2008). Games for drill and Practice: Addition Top-It. Retrieved on 28 March 2009, from http://everydaymath.uchicago.edu/educators/em_games 2. Mathwire.com standards-based math activities (2008). Counting activities: Featured game, Fish Out of Water. Retrieved on 29 March 2009, from http://www.mathwire.com/games/countinggames.html 3. Mathwire.com standards-based math activities (2008). Fractions: Fraction models. Retrieved on 29 March 2009, from http://www.mathwire.com/fractions/fracmodels.html 4. The National Council of Teachers of Mathematics (2004). Principles and Standards for School Mathematics: Understanding Distance, Speed, and Time Relationships Using Simulation Software. Retrieved on 29 March 2009, from http://standards.nctm.org/document/eexamples/chap5/5.2/index.htm Read More