El Conocimiento de Matemáticas Diarias

Presentación del tema: "El Conocimiento de Matemáticas Diarias"— Transcripción de la presentación:

1 El Conocimiento de Matemáticas Diarias

2 El 40% de adultos odiaban matemáticas en la escuela
Sabia Usted Que? El 40% de adultos odiaban matemáticas en la escuela El 84% de los estudiantes en la secundaria prefieren hacer “lo que sea” que hacer tarea de matemáticas Some of us love math. Many of us just hate it. According to an AP-AOL News poll of 1,000 adults, almost four in 10 of those surveyed said they hated math in school. That's twice as many as felt that strongly about any other school subject. And the dislike of math often trickles down to our children. A survey by Raytheon Co. found the vast majority of middle-school students would rather eat their vegetables, take out the garbage, clean their rooms or go to the dentist than study math. In fact, about 84 percent of students between the ages of 11 and 13 said they would rather do ``anything'' other than math homework, the survey showed. But, students CAN learn to love and appreciate math! To achieve this, the University of Chicago discovered that you have to teach math in a different way from they way most of us were taught.

3 Matemáticas Diarias en el Salón
Desarrollado por la Escuela de Proyectos en Matemáticas en la Universidad de Chicago Basado en investigaciones en como los estudiantes aprenden y desarrollan el poder en matemáticas Provee lo necesario en matemáticas del siglo 21 Everyday Mathematics is one way we’re doing it. The program was extensively researched and field-tested in classrooms before publication. It was developed by the University of Chicago School Mathematics Project as part of an effort to help children understand math better. The researchers found that children learn math best through hands-on activities that build on their interests and connect to their experiences. Young children can grasp math concepts traditionally saved for older students (for example, algebra) when concepts are explored with concrete materials and pictures. All this is so important because these children will live in a world where careers require the ability to access, evaluate, and use information to solve problems. Rote memorization and basic arithmetic (computation) are not enough.

4 Metas Fundamentales de UCSMP
Mejorar la educación de matemáticas para la mayoría de los estudiantes en los Estados Unidos. Industrias y Compañías Comunidades Escolares UCSMP presente Reconocer la necesidad Use el Currículo Proveer información

5 En Matemáticas Diarias, puede esperar:
solucionar problemas basados en situaciones diarias Children learn mathematics skills while solving problems that interest them. Explaining solutions and strategies to each other is one way students learn. Children are encouraged to solve problems in multiple ways, creating flexibility of thinking.

6 En Matemáticas Diarias, puede esperar:
solucionar problemas basados en situaciones diarias Un acercamiento en instrucción que revisa conceptos regularmente The program moves briskly and revisits key ideas and skills in slightly different contexts throughout the year. Multiple exposure to topics ensures solid comprehension. Strands are woven together - no strand is in danger of being left out. Mastery is developed over time. The “Content by Strand” poster depicts the interwoven design. Homework problems will have familiar format, but different levels of difficulty.

7 En Matemáticas Diarias, puede esperar:
solucionar problemas basados en situaciones diarias Un acercamiento en instrucción que revisa conceptos regularmente Practicas frecuentemente en habilidades básicas, normalmente con juegos Frequent practice is necessary to recall facts with accuracy and speed. Children of all ability levels find math games a fun way to practice. Focus is on understanding concepts behind basic facts, as well as mastering the facts themselves. Games are essential to the program, not optional or extra. Games are assigned as homework. (Families should expect to play!)

8 En Matemáticas Diarias, puede esperar:
solucionar problemas basados en situaciones diarias Un acercamiento en instrucción que revisa conceptos regularmente Practicas frecuentemente en habilidades básicas, normalmente con juegos Lecciones basadas en actividades y discusiones, no un libro de texto Children record, organize and demonstrate their learning in a math journal. Focus is on the learning process - most written material is aimed at the teacher. Children use a variety of math tools. “My Reference Book” or “Student Reference Book” contains information related to the lesson content and game rules.

9 En Matemáticas Diarias, puede esperar:
solucionar problemas basados en situaciones diarias Un acercamiento en instrucción que revisa conceptos regularmente Practicas frecuentemente en habilidades básicas, normalmente con juegos Lecciones basadas en actividades y discusiones, no un libro de texto Contenido en Matemáticas que va mas allá de la aritmética básica Children receive instruction in all major areas of math: number sense, data analysis, geometry, measurement, algebra, and probability. Strands are not taught in isolation. They are interwoven with other strands in a real-world way. For example, children may graph the weight of different animals and find the difference in weight between the most and least heavy.

10 Los Estudios han Encontrado
Los currículos tipicos son: aritmética guiada Instrucción lenta con ayuda Con una idea amplia y sin un contenido profundo Los niños aprenderán mas matemáticas con un currículo mas completo Todos los niños pueden ser buenos matemáticos Matemáticas tienen sentido cuando es variada completa Y basada en problemas y aplicaciones reales

11 Matemáticas Dot tiene dos monedas de $.25 centavos (Quarters).
Jim tiene tres monedas de $.10 centavos (dimes). Hank tiene una moneda de $.05 centavos (nickel). Cuanto dinero tienen entre todos?

12 Matemáticas Tengo monedas que valen 42 centavos.
Que son dos posibilidades de monedas que yo pudiera tener?

13 Matemáticas 9 2 5 3 6 15

14 Matemáticas Dibuja un polígono de 6 lados irregulares con un perímetro de 40 unidades.

15 Lo que se Espera solucionar problemas basados en situaciones diarias
Un acercamiento en instrucción que revisa conceptos regularmente Practicas frecuentemente en habilidades básicas, normalmente con juegos Lecciones basadas en actividades y discusiones, no un libro de texto

16 Rutinas del Programa de Matemáticas Diarias
Marcos y Flechas Triangulo de Factor Cual es mi Regla? Cajas de Colección de Nombres Juegos Everyday Math relies on a number of routines. A routine, of course, is a familiar, predictable activity that provides ongoing practice in a skill or content area. Some examples of routines in Everyday Math that we’ll explain today include: Frames and Arrows Fact Triangles What’s My Rule? Games Name-Collection Boxes

17 +2 3 5 7 9 13 11 Marcos y Flechas Regla
Frames-and-Arrows diagrams are one of many routines children work with regularly in Everyday Math. Also called “chains,” it helps children think and record their work with patterned numbers sequences, or a list of numbers. Identifying patterns and the rules that create them is an activity that prepares children for success with algebra. Every Frames-and-Arrows diagram has three parts: a rule box, frames and arrows. The frames in this example are circles, but they can be squares, triangles, hexagons, and so on. The rule tells how to get to the next number in the sequence. So, in this example, the rule is to add two. Each arrow stands for the rule. Apply the rule to one number to get the next number. Here, we have: = 5; = 7; and so forth. In Frames-and-Arrows problems, some information is missing. The missing information can be found by using the information that IS given. 13 11

18 Marcos y Flechas - 2 Reglas
*5 3 15 5 25 Here’s another example, where we combine applications. 65 75 15 REGLA RULE -10 -10

19 Entra Sale REGLA? 4 19 63 14 9 73 +10 Maquina de Funciones ENTRA SALE
15 25 4 19 63 REGLA? 14 +10 9 The “Function Machine” or “What’s My Rule?” activity is another routine common in Everyday Math. In “What’s My Rule?,” there is a diagram that represents the imaginary “function machine.” The machine takes in a number, applies a rule, and puts out a new number. A table is used to track the “in” and “out” numbers. To solve a “What’s My Rule?” problem, some missing information must be found by using the information that is given. Here’s an example. The red numbers and the rule would be the missing information, the white is what is provided. Your child would ask, how can you get from 15 to 25? And then determine answers for the others in the table. Sale 73

20 Triangulo de Factor *9 6 + 3 = 9 3 + 6 = 9 9 - 6 = 3 9 - 3 = 6 +, - Being able to recall basic number facts, such as or 8 x 8, with speed and accuracy is called fact power. Fact power is an important part of learning math, and it involves frequent practice. In addition to the games and short exercises children do in class, they also use Fact Triangles to practice and master basic number facts. Fact Triangles are the Everyday Math version of flash cards. Because Fact Triangles are based on fact families, they help children memorize facts more effectively than flash cards. Fact families are sets of related facts that link either addition and subtraction or multiplication and division. Here’s an example. Fact family: 6 + 3 = 9 9 - 3 = 6 Etc. It is best to practice Fact Triangles with a partner. One person covers one corner with a finger, and the person practicing gives a number fact that has the covered number as the answer. This is a simple game that is easy for children to play at home, and Fact Triangles are often recommended in Everyday Math’s Home Links. 6 3

21 Caja de Colección de Nombres
12 Otras? una docena XXXX XXXX XXXX 6 * 2 Children use name-collection boxes to develop the idea that there are many equivalent names for one number. Arithmetic, for the most part, involves replacing numbers or expressions with equivalent numbers or explanations. For example, we replace with 12 or 1/2 with 1/4 + 1/4. Because of this, it’s an important concept for children to understand. All name-collection boxes features a label attached to a box with an open space for writing. The idea is to fill up the box with different names for the number on the label. Numbers can be named using operations, words in any language, tally marks, Roman numerals, and so one. Here’s an example for the number 12. We can say 24 minus 12, a dozen, 6 times 2, etc. 9 + 3

22 Juegos de Matemáticas Diarias
Proveer practica frecuentemente Divertido y flexible Jugar regularmente Students need frequent practice to master a skill. Unfortunately, drills become monotonous and lose effectiveness over time. Games, however, relieve the tedium of rote repetition, reduce the need for worksheets, and offer an almost unlimited source of problem material because, in most cases, numbers are generated randomly. Many parents and educators make a sharp distinction between work and play. However, students naturally carry their playfulness into all activities. This is why games are an integral part of Everyday Math.

23 Algunas Soluciones Incluyen
Nombra ese Numero! Numero a Solucionar Algunas Soluciones Incluyen 8 x 2 = 16 – 2 = 16 7 x – 8 = 16 8 / – 5 = 16

24 Múltiples Algoritmos Un algoritmo es una serie de pasos específicos le darán la respuesta correcta todo el tiempo. Hay mas de un algoritmo correcto. Dejando que los estudiantes desarrollen sus propios procedimientos para trabajar, prueba que entienden el concepto detrás de la solución. In addition to games, something you’ll see different in Everyday Math is that we use multiple algorithms. An algorithm is a well-defined procedure or set of rules guaranteed to achieve a certain objective. You use an algorithm every time you follow the directions to put together a new toy, use a recipe to make cookies, or defrost something in the microwave. In math, an algorithm is a specific series of steps that will give you the correct answer every time. For example, in grade school, you and your classmates probably learned and memorized a certain algorithm for multiplying. Chances are, no one new why it worked, but it did! In Everyday Mathematics, children first learn to understand the math behind the problems they solve. Then, quite often, they come up with their own unique working algorithms that prove that they “get it.” Through this process, they discover that there is more than one algorithm for computing answers to addition, subtraction, multiplication and division problems. Ideally, children should develop a variety of computational methods and the flexibility to choose the procedure that is most appropriate in a given situation. Everyday Mathematics includes a variety of standard computational algorithms as well as children’s invented procedures. The program leads children through three phases as they learn each mathematical operation.

25 Múltiples Algoritmos Algoritmos Inventados Algoritmos Alternativos
Algoritmos para Enfocarse In the early phases of learning an operation, children are encourage to invent their own methods for solving problems. This approach requires children to focus on the meaning of the operation. They learn to think and use their common sense, as well as new skills and knowledge. Children who invent their own procedures: learn that their intuitive methods are valid and that math makes sense. Become more proficient with mental arithmetic. Are motivated because they understand their own methods. Become skilled at representing ideas with objects, words, pictures and symbols. Develop persistence and confidence in dealing with challenging problems. After children have had many opportunities to experiment with their own computational strategies, they are introduced to several algorithms for each operation. Some of these algorithms may be the same or similar to the methods children have invented on their won. Others are traditional algorithms, which have commonly been taught in the United States. Others are entirely new algorithms that have significant advantages in today’s technological world. Children are encouraged to experiment with various algorithms and to become proficient with at least one. For each operation, Everyday Math designates one algorithm as a “focus” algorithm. Focus algorithms are powerful, efficient, and easy to understand and learn. They also provide a common and consistant language for classroom use. All children are expected to learn and demonstrate proficiency with the focus algorithm. Once they can reliably use the focus algorithm, children may use it or any alternative they prefer. The aim of this approach is to promote flexibility while ensuring all children know at least one reliable method for each operation.

26 Participación de Padres de Familia
Ser Voluntario en los Salones Cartas de Padres de Familia Ayudar con Tareas en casa y Estudiar Juegos en la casa Practicar con factores de triángulos Leer libros de matemáticas To continue this success, parental involvement is crucial. Here are some ideas of what you can do. First, visit your child’s classroom. When you volunteer to help with activities in Everyday Math, you also learn a great deal. Don’t worry if you’re not a math expert - teachers always appreciate an extra hand and will find ways to use your skills. Read the parent letters provided. These pages describe what your child is learning so that you can help. They also suggest fun and easy math activities you can do at home. Consider keeping all these pages in a special folder to refer to later. Assist with Home Links and Study Links. For example, create a homework routine - decide on a time and place to do homework. Also, encourage your child to teach you the day’s math lesson using the problems in Home Links. Ask questions about the steps your child uses to solve a problem. Remember, although it’s tempting to give the children answers when they’re confused, they learn more if you help them discover the answers themselves. The games - such as fact triangles - that your child brings home from school or store-bought games that involve mathematical thinking will help your child master skills. Your child’s teacher can give you a list of popular commercial games to try at home as well as a literature list.

27 Visite www.WrightGroup.com
Muchas Gracias! Visite Para mas información. For more information about Everyday Math, please feel free to visit WrightGroup.com. And, to register for an all new Everyday Math parent network, X [MELINA? OR LOCAL REP?]