G IFTED AND T ALENTED M ATHEMATICS 6 An Introduction to the Program for Parents
W HAT IS THE P HILOSOPHY OF THE PROGRAM ? Why has this course always been relevant? What are the skills and habits of mind necessary to succeed in the 21 st century?
C ONSTRUCTIVE STRUGGLING, NOT POINTLESS FRUSTRATION An important element of this kind of education is a commitment to go beyond teaching basic skills, beyond requiring students to know how to perform procedures, and beyond offering recipes for solving problems that look alike. Teachers are beginning to realize that they can guide students learning without doing all the work for them. They are beginning to see the power of letting students struggle a bit to determine how to solve a problem before helping them find the best or most efficient approaches to the problem. How Can a Parent Help with Homework? Assure your student that the pre- reading is an introduction to what will be taught in class. Assure your student the lesson will provide activities to help them understand the content. Look at your students notes after the lesson is taught for evidence that their questions were answered.
W HAT SKILLS DO STUDENTS NEED TO FUNCTION IN THE 21 ST C ENTURY ? Core Subjects Learning & Innovation Skills Information, Media, & Technology Skills Life & Career Skills Mathematics is one of the core subjects Critical Thinking & Problem Solving Communication & Collaboration Information Literacy Media Literacy Flexibility & Adaptability Initiative & Self- Direction http://www.p21.org
W HY D O T HE S TUDENTS READ THEIR TEXTBOOKS ? What is the expectation as they pre-read a lesson?
C OMMON C ORE S TATE S TANDARDS FOR L ITERACY Read closely to determine what the text says explicitly & to make logical inferences from it; cite specific evidence to support conclusions. Interpret words & phrases as they are used in a text, including determining technical meaning. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text relate to each other and the whole. Read & comprehend complex literary and informational texts independently & proficiently. Write arguments to support claims, using valid reasoning and relevant & sufficient evidence. Produce clear and coherent writing. Draw evidence from informational texts to support analysis, reflection, and research. Anchor Standards for Reading Anchor Standards for Writing http://www.corestandards.org
W HY ARE THE STUDENTS READING THEIR BOOK ? Some students read a math book too quickly, glossing over little words that may be crucial to understanding a mathematical statement. Time will be spent in class teaching the students how to read mathematics. There will be times when the lessons are read aloud in class to emphasize aspects that might be overlooked by the students. The communication process helps students build meaning and permanence for ideas and enables the student to make ideas public. Because mathematics is often conveyed in symbols, oral and written communication about mathematical ideas must be recognized as an important part of mathematics education. Learning the content of mathematics is as much about learning to read, write, and talk about the content as it is learning the concepts, skills, and facts. Writers learn to write many times by reading and seeing how language is formed and how ideas are brought to life with words. Reading the language of mathematics enables a student to see how the symbols and verbal descriptions work together to bring the content to life and make it clear. Every profession has a specific language that must be learned in order to truly master the demands and expectations of the job. Having the students read their textbooks and learning to use it as a valuable resource is a beginning step on the path to independence and success in mathematics.
W HAT IS THE EXPECTATION AS STUDENTS PRE - READ A LESSON ?
E XAMPLE OF C URRICULUM G UIDE Prior to presenting the lesson, read pp. 29-31 in The UCSMP Implementation Guide to understand the authors perspective and strategies for teaching the students to read their textbook. Present this Challenge problem. Have the students solve and relate the importance of reading and understanding math vocabulary to solving the Challenge. What vocabulary words do you need to know to solve the Challenge puzzle? Challenge: What number am I? Clue 1: I am a number between 100 and 500 that is divisible by 6. Clue 2: The sum of my digits is 15. Clue 3: The product of my ones and tens digits is between 25 and 35. Clue 4: All of my digits are different. Elicit specific mathematical definitions for the underlined vocabulary in the challenge. Invite volunteers to enhance the definitions or to compare the given definitions to the definitions in a dictionary. Instruct the students to turn to p. 1. Determine a strategy to have the students read pp. 12. Give the students several minutes to skim the questions on pp. 23. Have the students answer the questions orally. Guide the students through the text features. Explain that Transition Mathematics starts each chapter with an opener that lists the titles of the lessons and a short lead-in to the chapter. Prepare the students to read Lesson 1-1 Numbers in Everyday Use, pp. 6-10, by reading pp. 4-5 aloud. Ask the students what the important ideas are. Model a note-taking method, having the students write their own notes as you show the method. Assign homework: Read pp. 6-8 and take notes. Ask the students if they have any newspapers or magazines at home that can be cut up to bring them tomorrow.
A NOTHER EXAMPLE … Read Lesson 4-6 orally in class, taking notes together and discussing class definitions on the vocabulary words. Give the students ample time to draw examples in their notes. Ask various students to share the drawings and notes they are writing. Encourage the students to interject prior learning and describe how their new learning adds to what they knew. Stop after reading p. 239 Using a Protractor. Ask a volunteer to explain how the last paragraph differs from how they learned to determine which scale to use on the protractor. Distribute protractors for p. 240 Activity 1 and Activity 2. Allow a student to lead the activity by demonstrating how to measure the first angle. Circulate among the students as they measure the other angles. Provide at least one angle that the students can measure and place in their notes. Have another student demonstrate how to draw an angle of a given measure by using p. 240 Activity 2 (1). Talk to the students about a reasonable margin of error for measuring and drawing angles. Refer to TE p. 239 Notes on the Lesson for an acceptable leeway. Circulate among the students as they draw the other angles. Encourage the students to draw an angle in their notes. Continue reading aloud. Stop and have the students do p. 241 Activity 3 as a class to come up with as many possibilities as they can. Continue reading Lesson 4-6 aloud. Show the students the names for..
BCPS P OLICY 5210 Classroom learning is improved through homework by students. At times, classwork is dependent upon outside preparation. Homework may include review, reinforcement, and reading in preparation for class discussion, data gathering, analysis and synthesis, preparation of long-term projects and reports, and enrichment through the utilization of resources outside the school. Homework provides an opportunity for students to develop self-reliance and self-direction. It helps students establish habits of work which will influence their use of time throughout life. Homework requires attention in class in order to understand assignments thoroughly and to develop creative ways to follow up class activities. It also requires organization of time and materials to complete successfully the required work.
T HE H OMEWORK R OUTINE Read Take notes from the reading Complete Covering the Ideas Complete Applying the Mathematics from the previous lesson
P URPOSEFUL C ONNECTIONS … SQUARE R OOTS Section 1-7: the radical is introduced as a grouping symbol and the inverse operation of squaring a number Section 2-5: The Pythagorean Theorem is introduced; a calculator is used to find the lengths of non-perfect squares Section 3-8: the geometric origins of square roots are explored; students place irrational numbers on the number line Section 6-9: the Pythagorean Theorem is used to find the distance between oblique points on the coordinate plane
Today we need new mathematical skills to bring meaning and order to the flood of data and statistical information that hits us every day. Our definition of an educated person is now a much richer vision than in previous times, when reading, writing, and some basic arithmetic would suffice for day-to-day survival. Todays literacy means quantitative literacy, scientific literacy, and high- level critical thinking and problem-solving skills. Teachers must give students learning experiences that help students appreciate the power & precision of mathematics language.
I F YOU STILL HAVE QUESTIONS … Contact Leslie Johnson, Mathematics Resource Teacher Maria Everett, Mathematics Specialist or John Staley, Director of Mathematics The Office of Mathematics PreK12 410-887-4052