Happy holidays, Merry Christmas, Happy New Year, all the greetings of the season to everyone. I will post again when Garfield is back in session on January 2.
Jeff Combe
Monday, December 17, 2007
Friday, December 14, 2007
More on Rigor
Hello everyone,
Happy winter break to all the middle school teachers. I'll see you sometime when you get back in January.
Good luck on finals to the high schoolers.
You will all forgive me for creating a non-sequitur with today's subject. It's just that it's been on my mind lately, for a variety of reasons.
When I first started teaching, I was given the warning, "Just remember, these are junior high school students, not college students. Don't try to give them college level work." That was good advice, and I commend it to all of you.
But I got other advice, both spoken and implied, that has troubled me.
I was taught that the students in East LA were not up to the sort of rigor I had been accustomed to when I was growing up. It was taught that I should not expect too much from them, and that it was unfair for me to demand things from them that were "beyond" them. I even had a teacher suggest to me once--suggest? nay, I was forcefully told--that it was racist to expect very much from the students of East LA.
I shake with anger as I write this.
I had a student in my honors English class at Belvedere who was accepted to a very prestigious university after high school graduation. The student failed out of the university because, I learned to my shame, my colleagues and I had not provided an education that was adequate preparation for the post-high school experience. (I have many students, by the way, who went on to fine universities and succeeded. I can't help but feel that many of them succeeded despite me. They would have succeeded anywhere.)
In post-year interviews with my students (something I always did, and something I recommend), after grades were in and there were no consequences for telling the truth, many of my early students confessed to me that I was too easy and my class was too light.
I resolved that I would never allow those things to happen again.
And in response to the teacher (long gone, by the way) that it is racist to demand too much, I say that it is racist to demand too little. I grew up in a state that was notoriously underfunded, and I believed that my education was inferior, yet I cannot in good conscience give an education that is less than I received without being able to answer for it before a fair tribunal.
I am not advocating a return to all the practices of the 1960s and 1970s, by any means. Still, I can't help but feel that, if I learned so much in classes that were not designated honors or gifted or AP, my students can learn as least as much in their regular classes if I commit myself to teach them.
And we all know that this generation of student is different from the generations before. They have more tools and information available to them than we ever dreamed. They are wealthier and better protected than we ever were. They are able to gain more with less effort than we could ever imagine.
And we all know that there were things that the previous generation was taught that are not important now. No one needs to waste time teaching slide rules. Key punch operators are a trove of useless knowledge. Communism is not a serious threat.
And we know that they are inclined to give more than their share of adolescent resistance to work.
But it is wrong to be anything less than rigorous.
We should not teach honors and AP classes as if they were well behaved regular classes. We should not teach our regular classes as if they needed to repeat elementary school. We should not waste their time. They are college bound middle and high school students. They must be ready or we condemn them to lives of poverty and difficulty.
Resolve to do it. For the New Year, resolve to teach them.
Jeff Combe
Thursday, December 13, 2007
CAHSEE, part 2 (English)
Hello everyone,
Yesterday I mailed the math blueprint for the California High School Exit Exam. Today, I'm including the English portion.
English takes a different approach to testing than math does. Students must be able to read and understand selections from fiction, non-fiction, poetry, or drama. They must also be able to write well organized, well thought out, well constructed, coherent essays.
There is no way to suddenly teach students to read and write. Those things require practice over a period of time. Furthermore, the sorts of essays that students write on tests like the CAHSEE (not to mention the AP exams) are not the sorts of essays that allow them to edit and be edited. These are supposed to be excellent first drafts, not carefully edited final drafts.
If I were teaching 9th or 10th grade English (I have, by the way), and I wanted to help my students pass the CAHSEE, I would require them to read and write more than they wanted to. Because students are reluctant to read independently, we would read together in class. Because writing can be done at home without supervision, I would frequently assign editable essays for homework. There would also be frequent in-class quickwrites and essay tests. I know from experience that the students don't always like to do that much reading and writing; but I also know from experience that they need it, and there's no other way to perfect the skills than to practice them frequently.
You will note from the blueprint I include below that students must be able to interact with a variety of texts. You will not be able to predict which texts they will be tested on, so you must present that variety in class. You will also note that students must have a good grasp of grammar and usage.
You may see the entire blueprint by clicking on the link:
http://www.cde.ca.gov/ta/tg/hs/documents/bplangarts03.pdf
I include which standards are tested and how many objective questions or essays are required. If a standard is not listed, it isn't tested.
THE BLUEPRINT IS BELOW.
45 Multiple-choice Items Total
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
7 Multiple Choice Items
1.1 Identify and use the literal and figurative meanings of words and understand word derivations.
(5)
1.2 Distinguish between the denotative and connotative meanings of words and interpret the connotative power of words.
(2)
2.0 Reading Comprehension
18 Multiple-choice Items
Structural Features of Informational Materials
†2.1 Compare and contrast the features and elements of consumer materials to gain meaning from documents (e.g., warranties, contracts, product information, instruction manuals).
(3 questions; 8th grade standard)
2.1 Analyze the structure and format of functional workplace documents, including the graphics and headers, and explain how authors use the features to achieve their purposes.
(1)
Comprehension and Analysis of Grade-Level-Appropriate Text
2.4
Synthesize the content from several sources or works by a single author dealing with a single issue; paraphrase the ideas and connect them to other sources and related topics to demonstrate
comprehension.
(3)
2.5
Extend ideas presented in primary or secondary sources through original analysis, evaluation, and elaboration.
(3)
Expository Critique
2.7 Critique the logic of functional documents by examining the sequence of information and procedures in anticipation of possible reader misunderstandings.
(3)
2.8
Evaluate the credibility of an author’s argument or defense of a claim by critiquing the relationship between generalizations and evidence, the comprehensiveness of evidence, and the way in which the author’s intent affects the structure and tone of the text (e.g., in
professional journals, editorials, political speeches, primary source material).
(5)
3.0
Literary Response and Analysis
20 Multiple-choice Items
Structural Features of Literature
3.1
Articulate the relationship between the expressed purposes and the characteristics of different forms of dramatic literature (e.g., comedy, tragedy, drama, dramatic monologue).
(2)
Narrative Analysis of Grade-Level-Appropriate Text
3.3
Analyze interactions between main and subordinate characters in a literary text (e.g., internal and external conflicts, motivations, relationships, influences) and explain the way those interactions affect the plot.
(2)
3.4
Determine characters’ traits by what the characters say aboutthemselves in narration, dialogue, dramatic monologue, and soliloquy.
(2)
3.5
Compare works that express a universal theme and provide evidence to support the ideas expressed in each work.
(2)
3.6
Analyze and trace an author’s development of time and sequence, including the use of complex literary devices (e.g., foreshadowing, flashbacks).
(2)
3.7
Recognize and understand the significance of various literary devices, including figurative language, imagery, allegory, and symbolism, and explain their appeal.
(2)
3.8 Interpret and evaluate the impact of ambiguities, subtleties, contradictions, ironies, and incongruities in a text.
(2)
3.9 Explain how voice, persona, and the choice of a narrator affect characterization and the tone, plot, and credibility of a text.
(2)
3.10 Identify and describe the function of dialogue, scene designs, soliloquies, asides, and character foils in dramatic literature.
(1)
Literary Criticism
(3) (Tasks that assess the three different approaches will be rotated across test forms.)
†8.3.7 Analyze a work of literature, showing how it reflects the heritage, traditions, attitudes, and beliefs of its author. (Biographical approach--8th grade standard)
3.11 Evaluate the aesthetic qualities of style, including the impact of diction and figurative language on tone, mood, and theme, using the terminology of literary criticism. (Aesthetic approach)
3.12 Analyze the way in which a work of literature is related to the themes and issues of its historical period. (Historical approach)
Writing (Grades Nine and Ten)
27 Multiple-choice Items
1.0
Writing Strategies
12 Multiple-choice Items
Organization and Focus
1.1 Establish a controlling impression or coherent thesis that conveys a clear and distinctive perspective on the subject and maintain a consistent tone and focus throughout the piece of writing.
(3)
1.2 Use precise language, action verbs, sensory details, appropriate modifiers, and the active rather than the passive voice.
(3)
1.4 Develop the main ideas within the body of the composition through supporting evidence (e.g., scenarios, commonly held beliefs, hypotheses, definitions).
(2)
1.5 Synthesize information from multiple sources and identify complexities and discrepancies in the information and the different perspectives found in each medium (e.g., almanacs, microfiche, news sources, in-depth field studies, speeches, journals, technical documents).
(1)
Evaluation and Revision
1.9 Revise writing to improve the logic and coherence of the organization and controlling perspective, the precision of word choice, and the tone by taking into consideration the audience, purpose, and formality of the context.
(3)
2.0
Writing Applications (Genres and Their Characteristics)
Essay Item
Students combine the rhetorical strategies of narration, exposition, persuasion, and description to produce texts of at least 1,500 words each. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in Writing Standard 1.0.
THESE ARE THE POSSIBLE ESSAYS THAT MIGHT BE INCLUDED ON THE TEST:
Students:
2.1
Write biographical narratives:
a. Relate a sequence of events and communicate the significance of the events to the audience.
b. Locate scenes and incidents in specific places.
c. Describe with concrete sensory details the sights, sounds, and smells of a scene and the specific actions, movements, gestures, and feelings of the characters; use interior monologue to depict the characters’ feelings.
d. Pace the presentation of actions to accommodate changes in time and mood.
e. Make effective use of descriptions of appearance, images, shifting perspectives, and sensory details.
2.2
Write responses to literature:
a. Demonstrate a comprehensive grasp of the significant ideas of literary works.
b. Support important ideas and viewpoints through accurate and detailed references to the text or to other works.
c. Demonstrate awareness of the author’s use of stylistic devices and an appreciation of the effects created.
d. Identify and assess the impact of perceived ambiguities, nuances, and complexities within the text.
2.3
Write expository compositions, including analytical essays and research reports:
a. Marshal evidence in support of a thesis and related claims, including information on all relevant perspectives.
b. Convey information and ideas from primary and secondary sources accurately and coherently.
c. Make distinctions between the relative value and significance of specific data, facts, and ideas.
d. (Deleted)
e. Anticipate and address readers’ potential misunderstandings, biases, and expectations.
f. Use technical terms and notations accurately.
2.4
Write persuasive compositions:
a. Structure ideas and arguments in a sustained and logical fashion.
b. Use specific rhetorical devices to support assertions (e.g., appeal to logic through reasoning; appeal to emotion or ethical belief; relate a personal anecdote, case study, or analogy).
c. Clarify and defend positions with precise and relevant evidence, including facts, expert opinions, quotations, and expressions of commonly accepted beliefs and logical reasoning.
d. Address readers’ concerns, counterclaims, biases, and expectations.
2.5 Write business letters:
a. Provide clear and purposeful information and address the intended audience appropriately.
b. Use appropriate vocabulary, tone, and style to take into account the nature of the relationship with, and the knowledge and interests of, the recipients.
c. Highlight central ideas or images.
d. Follow a conventional style with page formats, fonts, and spacing that contribute to the documents’ readability and impact.
2.6 Write technical documents (e.g., a manual on rules of behavior for conflict resolution, procedures for conducting a meeting, minutes of a meeting):
a. Report information and convey ideas logically and correctly.
b. Offer detailed and accurate specifications.
c. Include scenarios, definitions, and examples to aid comprehension (e.g., troubleshooting guide).
d. Anticipate readers’ problems, mistakes, and misunderstandings.
1.0
Written and Oral English Language Conventions
15 Multiple Choice Items
1.1 Identify and correctly use clauses (e.g., main and subordinate), phrases (e.g., gerund, infinitive, and participial), and mechanics of punctuation (e.g., semicolons, colons, ellipses, hyphens).
(5)
1.2 Understand sentence construction (e.g., parallel structure, subordination, proper placement of modifiers) and proper English usage (e.g., consistency of verb tenses).
(5)
1.3 Demonstrate an understanding of proper English usage and control of grammar, paragraph and sentence structure, diction, and syntax.
(5)
Use your breaks
Hello everyone,
Lengthy breaks in the school year, such as the sort that happen during winter break, are an ideal opportunity to make mid-year corrections in your policies and practices.
When I was first teaching, I discovered (well, someone suggested it to me and I used it; I'm not the discoverer) that changes were best made after a break. Weekends are good; three day weekends are better. Lengthy breaks are ideal.
You may spend the next few weeks before schools re-open in January, thinking about what is working and what is not working in your classes. When students return, you might say something like, "I've been thinking that these things aren't working very well in the class." (Be honest, but be careful about not getting into accusation/counter-accusation with the students; and don't undermine your own authority or credibility by emphasizing your faults.) "Because of that, I've decided to [tell them what you're going to do]."
Some things I recommend.
Many of you will want to reconsider the seating chart in the class. All sorts of bad things happen when students move around and sit in irregular spots. (It's true that some classes function well enough without a seating chart, but they are frankly the exception, not the rule--especially for new teachers.) I think it's not a bad thing to have students begin in strictly alphabetical patterns. This will account for the changes that many of you will have at the semester, and it will give the middle school students the feelings that they may begin the New Year with no previous marks on their character. (If they mess around, then change their seat later, but start them off in alphabetical order.)
Take this opportunity to get out of the habit of giving multiple warnings and chances for misbehavior. Resolve to tell your students what you expect of their behavior and what the consequences are, then give the consequences immediately--not after repeated warnings. "I'm not going to tell you again," is more a joke than a warning. "If you do that one more time...," is more an invitation than a threat.
Resolve to learn again to laugh and find humor. A good joke is a good joke, even if you are the brunt of it. Seeing the humor in situations is a healthy way to live. In the middle of a pitched battle between a teacher and a mis-behaving kid, it's easy to lose perspective, so take the time off to try to rebuild it.
Come back on the first day and begin working. Establish in your students the expectation of work, and keep building on that expectation. They're too far behind for you to waste time--especially after they just had time off. (If you're in a class that justifies it, by all means give work during the break.) They'll buck you at first, but they'll come around.
Whatever you do, work toward simplifying your routine. Don't plot ways to make things difficult. Plot ways to make things better. Then carry out your plot.
Jeff Combe
Tuesday, December 11, 2007
California High School Exit Exam, part 1 (Math)
Hello everyone,
Garfield met today to discuss the California High School Exit Exam and how to help students to pass it (consequently helping our API--if I may paraphrase the classic film "Miracle on 34th Street"). The California Department of Education publishes their blueprint for the CAHSEE, telling exactly which standards will be tested, and how many questions are devoted to each standard.
If I were a math teacher, in middle or high school, and I were trying to help students pass the CAHSEE, I would focus on the standards that have the most questions, or the standards that provide the best foundation for answering the most questions correctly. Some of the standards are never covered on the CAHSEE, and ought not be emphasized unless they provide foundational material.
If I were an English teacher, I would wait until tomorrow when I publish the same blueprint for English.
If I were teaching an elective or a core academic subject (like science) that utilized math extensively, I would focus on the math concepts that my students needed to pass the CAHSEE.
If my students had all passed the CAHSEE, I would focus all my attention on getting them ready for college, which involves much higher skill and content levels than the CAHSEE.
If I were uncertain about what Combe is writing about, or if there were questions I had, I would go to the California Department of Education website and look at the blueprint for the CAHSEE. It's aligned with the California standards. Here is the link:
http://www.cde.ca.gov/ta/tg/hs/documents/bpmath03.pdf
BELOW, YOU WILL FIND THE MATH STANDARDS THAT ARE TESTED ON THE CAHSEE. THE NUMBER IN PARENTHESES IS THE NUMBER OF QUESTIONS FROM EACH GIVEN STANDARD THAT ARE FOUND ON THE TEST. IF WORDS ARE STRICKEN OUT WITH A LINE, THEY ARE NO LONGER TESTED. IF A STANDARD IS NOT LISTED, IT'S NOT TESTED.
Grade 6—Statistics, Data Analysis, and Probability
8 Items Total
1.1 Compute the range, mean, median, and mode of data sets.
(3)
2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
(1)
3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
(1)
3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if Pis the probability of an event, 1-Pis the probability of an event not occurring.
(2)
3.5 Understand the difference between independent and dependent events. (1)
Grade 7—Number Sense
14 Items Total
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
(1)
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
(3)
1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
(2)
1.6 Calculate the percentage of increases and decreases of a quantity.
(1)
1.7 Solve problems that involve discounts, markups, commissions, and profit, and compute simple and compound interest.
(2)
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
(1)
2.2 Add and subtract fractions by using factoring to find common denominators.
(1)
2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
(1)
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
(1)
2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
(1)
Grade 7—Algebra and Functions
17 Items Total
1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
(2)
1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2 .
(1)
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
(3)
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
(1)
2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
(1)
3.1 Graph functions of the form y=nx2 and y=nx3 and use in solving problems.
(1)
3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.
(2)
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of a line equals the quantities.
(1)
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
(3)
4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
(2)
Grade 7—Measurement and Geometry
17 Items Total
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
(2)
1.2 Construct and read drawings and models made to scale.
(1)
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
(2)
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
(3)
2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.
(2)
2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and volume is multiplied by the cube of the scale factor.
(1)
2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).
(1)
3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
(2)
3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.
(2)
3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
(1)
Grade 7—Statistics, Data Analysis, and Probability
4 Items Total
1.1 Know various forms of display for data sets, including a stem-and-leaf
plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.
(2)
1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).
(2)
Grade 7—Mathematical Reasoning
8 Item Total
Plus Integrated
into Other Strands
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
(2)
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
(1)
2.1 Use estimation to verify the reasonableness of calculated results.
(2)
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
(1)
2.4 Make and test conjectures by using both inductive and deductive reasoning.
(1)
3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
(1)
Algebra I
12 Items Total
2.0
Students understand and use such operations as taking the opposite, finding
the reciprocal, and taking a root, and raising to a fractional power. They
understand and use the rules of exponents.
(1)
3.0
Students solve equations and inequalities involving absolute values.
(1)
4.0
Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
(1)
5.0
Students solve multistep problems, including word problems, involving linear
equations and linear inequalities in one variable and provide justification for
each step.
(1)
6.0
Students graph a linear equation and compute the x- and y-intercepts (e.g.,
graph 2x+ 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x+ 6y< 4).
(1 graphing item; 1 computing item)
(2)
7.0
Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations. by using the point-slope formula.
(1)
8.0
Students understand the concepts of parallel lines and perpendicular lines
and how their slopes are related. Students are able to find the equation of a
line perpendicular to a given line that passes through a given point.
(1)
9.0 Students solve a system of two linear equations in two variables
algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
(1)
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
(1)
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
(1)
Garfield met today to discuss the California High School Exit Exam and how to help students to pass it (consequently helping our API--if I may paraphrase the classic film "Miracle on 34th Street"). The California Department of Education publishes their blueprint for the CAHSEE, telling exactly which standards will be tested, and how many questions are devoted to each standard.
If I were a math teacher, in middle or high school, and I were trying to help students pass the CAHSEE, I would focus on the standards that have the most questions, or the standards that provide the best foundation for answering the most questions correctly. Some of the standards are never covered on the CAHSEE, and ought not be emphasized unless they provide foundational material.
If I were an English teacher, I would wait until tomorrow when I publish the same blueprint for English.
If I were teaching an elective or a core academic subject (like science) that utilized math extensively, I would focus on the math concepts that my students needed to pass the CAHSEE.
If my students had all passed the CAHSEE, I would focus all my attention on getting them ready for college, which involves much higher skill and content levels than the CAHSEE.
If I were uncertain about what Combe is writing about, or if there were questions I had, I would go to the California Department of Education website and look at the blueprint for the CAHSEE. It's aligned with the California standards. Here is the link:
http://www.cde.ca.gov/ta/tg/hs/documents/bpmath03.pdf
BELOW, YOU WILL FIND THE MATH STANDARDS THAT ARE TESTED ON THE CAHSEE. THE NUMBER IN PARENTHESES IS THE NUMBER OF QUESTIONS FROM EACH GIVEN STANDARD THAT ARE FOUND ON THE TEST. IF WORDS ARE STRICKEN OUT WITH A LINE, THEY ARE NO LONGER TESTED. IF A STANDARD IS NOT LISTED, IT'S NOT TESTED.
Grade 6—Statistics, Data Analysis, and Probability
8 Items Total
1.1 Compute the range, mean, median, and mode of data sets.
(3)
2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
(1)
3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
(1)
3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if Pis the probability of an event, 1-Pis the probability of an event not occurring.
(2)
3.5 Understand the difference between independent and dependent events. (1)
Grade 7—Number Sense
14 Items Total
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
(1)
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
(3)
1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
(2)
1.6 Calculate the percentage of increases and decreases of a quantity.
(1)
1.7 Solve problems that involve discounts, markups, commissions, and profit, and compute simple and compound interest.
(2)
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
(1)
2.2 Add and subtract fractions by using factoring to find common denominators.
(1)
2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
(1)
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
(1)
2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
(1)
Grade 7—Algebra and Functions
17 Items Total
1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
(2)
1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2 .
(1)
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
(3)
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
(1)
2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
(1)
3.1 Graph functions of the form y=nx2 and y=nx3 and use in solving problems.
(1)
3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.
(2)
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of a line equals the quantities.
(1)
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
(3)
4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
(2)
Grade 7—Measurement and Geometry
17 Items Total
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
(2)
1.2 Construct and read drawings and models made to scale.
(1)
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
(2)
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
(3)
2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.
(2)
2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and volume is multiplied by the cube of the scale factor.
(1)
2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).
(1)
3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
(2)
3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.
(2)
3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
(1)
Grade 7—Statistics, Data Analysis, and Probability
4 Items Total
1.1 Know various forms of display for data sets, including a stem-and-leaf
plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.
(2)
1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).
(2)
Grade 7—Mathematical Reasoning
8 Item Total
Plus Integrated
into Other Strands
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
(2)
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
(1)
2.1 Use estimation to verify the reasonableness of calculated results.
(2)
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
(1)
2.4 Make and test conjectures by using both inductive and deductive reasoning.
(1)
3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
(1)
Algebra I
12 Items Total
2.0
Students understand and use such operations as taking the opposite, finding
the reciprocal, and taking a root, and raising to a fractional power. They
understand and use the rules of exponents.
(1)
3.0
Students solve equations and inequalities involving absolute values.
(1)
4.0
Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
(1)
5.0
Students solve multistep problems, including word problems, involving linear
equations and linear inequalities in one variable and provide justification for
each step.
(1)
6.0
Students graph a linear equation and compute the x- and y-intercepts (e.g.,
graph 2x+ 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x+ 6y< 4).
(1 graphing item; 1 computing item)
(2)
7.0
Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations. by using the point-slope formula.
(1)
8.0
Students understand the concepts of parallel lines and perpendicular lines
and how their slopes are related. Students are able to find the equation of a
line perpendicular to a given line that passes through a given point.
(1)
9.0 Students solve a system of two linear equations in two variables
algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
(1)
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
(1)
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
(1)
Monday, December 10, 2007
Formative assessment
Hello everyone,
The whole point of assessment is to know how well your students have understood what you've been teaching them. Formative assessment is a critical kind.
Formative assessment is what you use to check on their understanding daily. You adjust your teaching--don't you?--to make sure they've understood.
By the way, things like asking them, "Are there any questions?" or "Did you get it?" or--worse--"Why didn't you get that? I told you three times!" are not assessments. Homework is not usually a good assessment because it's so easy to cheat. (Correcting the homework, however, can serve as an assessment.)
I liked to use a variety of formative assessments in the classroom.
Here's an assessment I would use in my classroom: "Hold your hands in front of your body so no-one but me can see you. Put your thumbs up if 'walks the dog' is the subject; thumbs down if it is the predicate." I wouldn't tell them which it was if most of them got it wrong; I would just know how extensively I needed to reteach.
Here's a tricky sort of assessment to keep them on their toes: "Raise your hand if you don't know which punctuation to put here." Then I call on someone without a hand raised to explain the answer. If the student knows, then I know I have a reasonably accurate assessment going, and I can force participation. The lazy ones who don't like to raise their hands are faced with the problem of whether to take a chance of being called on or having to raise their hands. If everyone raises a hand, then I will reteach as if they are all telling the truth about what they don't know.
Here's something to keep in mind: NEVER CRITICIZE A STUDENT FOR NOT GETTING IT, FOR NOT UNDERSTANDING, OR FOR ASKING YOU TO EXPLAIN. The most accurate assessment you can probably get is in the questions students will ask, not the answers they give. If you allow them to ask questions, then you know exactly what to reteach, and they will direct how you will reteach. If you kill the questions, you kill the assessment. Remember, if they tell you they "don't get it," they are not attacking you personally. Help them "get it."
A quickwrite is an excellent assessment. "Write everything you know about mitosis in 10 minutes." (Try giving open-ended points for everything correct.) You must be willing to read beyond their spelling and grammar to see what they really know about mitosis, but you will have a pretty good assessment of what they know. (These are harder to correct than objective quizzes, but they are excellent assessments.)
Try using games as assessments. Adapt a game to fit what you have just taught, then let the students play. It will give a good overall idea of what the class remembers. I had a white-board version of football and baseball that I used as "review." I also used it as an opportunity to assess the students and reteach difficult concepts. (They were anxious to learn when points were on the line.)
Find ways to assess the full range of thinking in Bloom's taxonomy. Don't just test their knowledge; assess their ability to think critically. Don't just test for synthesis; make sure they understand the vocabulary. Test the full range, and reteach when necessary.
You're getting close to summative assessment (the final, the last hurrah, the ultimate test, the summation, make or break). Use formative assessments to fill in the gaps that they haven't gotten yet.
Next semester, try starting with the assessment. If you know what you're going to test on, you will teach to your own test. Work backward from the summative exam in all your planning, and your planning will go easier. Constantly use formative assessment to make sure they're on track.
Jeff Combe
The whole point of assessment is to know how well your students have understood what you've been teaching them. Formative assessment is a critical kind.
Formative assessment is what you use to check on their understanding daily. You adjust your teaching--don't you?--to make sure they've understood.
By the way, things like asking them, "Are there any questions?" or "Did you get it?" or--worse--"Why didn't you get that? I told you three times!" are not assessments. Homework is not usually a good assessment because it's so easy to cheat. (Correcting the homework, however, can serve as an assessment.)
I liked to use a variety of formative assessments in the classroom.
Here's an assessment I would use in my classroom: "Hold your hands in front of your body so no-one but me can see you. Put your thumbs up if 'walks the dog' is the subject; thumbs down if it is the predicate." I wouldn't tell them which it was if most of them got it wrong; I would just know how extensively I needed to reteach.
Here's a tricky sort of assessment to keep them on their toes: "Raise your hand if you don't know which punctuation to put here." Then I call on someone without a hand raised to explain the answer. If the student knows, then I know I have a reasonably accurate assessment going, and I can force participation. The lazy ones who don't like to raise their hands are faced with the problem of whether to take a chance of being called on or having to raise their hands. If everyone raises a hand, then I will reteach as if they are all telling the truth about what they don't know.
Here's something to keep in mind: NEVER CRITICIZE A STUDENT FOR NOT GETTING IT, FOR NOT UNDERSTANDING, OR FOR ASKING YOU TO EXPLAIN. The most accurate assessment you can probably get is in the questions students will ask, not the answers they give. If you allow them to ask questions, then you know exactly what to reteach, and they will direct how you will reteach. If you kill the questions, you kill the assessment. Remember, if they tell you they "don't get it," they are not attacking you personally. Help them "get it."
A quickwrite is an excellent assessment. "Write everything you know about mitosis in 10 minutes." (Try giving open-ended points for everything correct.) You must be willing to read beyond their spelling and grammar to see what they really know about mitosis, but you will have a pretty good assessment of what they know. (These are harder to correct than objective quizzes, but they are excellent assessments.)
Try using games as assessments. Adapt a game to fit what you have just taught, then let the students play. It will give a good overall idea of what the class remembers. I had a white-board version of football and baseball that I used as "review." I also used it as an opportunity to assess the students and reteach difficult concepts. (They were anxious to learn when points were on the line.)
Find ways to assess the full range of thinking in Bloom's taxonomy. Don't just test their knowledge; assess their ability to think critically. Don't just test for synthesis; make sure they understand the vocabulary. Test the full range, and reteach when necessary.
You're getting close to summative assessment (the final, the last hurrah, the ultimate test, the summation, make or break). Use formative assessments to fill in the gaps that they haven't gotten yet.
Next semester, try starting with the assessment. If you know what you're going to test on, you will teach to your own test. Work backward from the summative exam in all your planning, and your planning will go easier. Constantly use formative assessment to make sure they're on track.
Jeff Combe
Friday, December 7, 2007
Practical advice on writing objective exams
Hello everyone,
As the semester comes to a close at
Generally, final exams are summative assessments, though first semester finals can be used to guide instruction in many of your classes' second semesters. I want to think in summative terms, however, and I want to consider only written exams.
Let's put grading aside, and consider only how to write a final exam as a summative assessment. There are a few rules that you MUST keep in mind:
1. You cannot hold students accountable for something they haven't been required to learn. Avoid including questions on your final that reference anything that wasn't covered in some explicit way in class.
2. Your questions must be clear, understandable, and unambiguous. Do not use trick questions; do not hold students fully accountable for ambiguous questions.
3. Written exams used as summative assessments cannot measure everything a student has learned if your subject teaches both skills and concepts, unless the skills you are testing are reading, writing, or calculation. Practical skills like performing music, playing a sport, or using equipment must be assessed using another kind of test.
Keep in mind the general rule that essay tests are easy to write but hard to correct. Objective tests (multiple choice, true and false, matching) are easy to correct but hard to write. As a former English teacher, I prefer essay tests, but there is rarely time to correct them (unless you're very fast) at the end of the semester. Having said all that, I want to give a few suggestions on objective tests.
MULTIPLE CHOICE
I think this is the best objective method for measuring knowledge, but you need to be careful how you write them or your assessment will be skewed.
You should give students four or five choices. Make sure that the possible answers are spread randomly over the full range of possibilities. (Letter "B" is the most commonly used answer slot; consciously make sure that "A," "C," and "D" are used equally as much.
Make sure that the answers are unambiguous. There should only be one correct answer. If a student points out that you've mis-written a question or the answers, be prepared to give credit for multiple answers.
Most students can easily answer 100 questions in an hour.
TRUE OR FALSE
These are easy to write and correct, but do not give a very good assessment because they are so easy to guess on. I don't think it's fair to make the questions hard to understand to compensate for the ease of answering them. Mixing a few true/false questions in a lengthy test, however, is like giving the kids a break.
100 questions in 1/2 hour.
CLOZE
This is the sort of question that makes a statement, leaving out a key vocabulary word. Students must be able to put the correct word in a blank. It is very easy to get too ambiguous with Close tests. Make sure that only one word could possibly go in the blank. "Marie Curie is credited with the discovery of the radioactive substance named ______." This sort of test is good for cold recall, but teachers often get caught up in what they WANT to go in the blank, and forget what COULD go in the blank, which is frustrating for students.
100 questions in 75 minutes.
MATCHING
This requires students to match one thing in one column, with a similar thing in another column. Having students match more than ten pairs of words or concepts is usually difficult and confusing, while matching five pairs gives just as fair an assessment, if they really know the material. Having words that could be the answers for more than one question, or having words that don't match with anything provides a more accurate assessment than having matchups that allow the process of elimination to dictate thinking.
100 questions in 50-90 minutes.
I hope this is useful. Remember, you're trying to assess them, not stump them. It's a test, not a trick.
Jeff Combe
Tuesday, December 4, 2007
Tribute to a Garfield alum
Hello everyone,
I had an experience today that gives perspective to our jobs.
Raymond Emil (Mike) Wolohen's funeral was today. Mike was 81 years old, and he died of cancer.
He was a graduate of Garfield High School, class of Winter 1943.
When he was a boy, he lived across the street from the high school, and as an adult he would regale me with stories of how his brother could sleep in until the last possible minute, then jump into his PE clothes, and be on campus before his name was called in roll call. Mike could do the same thing with his shop classes. (I thought that he said that he lived on Fraser Street, which meant that the shop building used to be on the west end of campus. Otherwise he would have had to sprint a couple of blocks to get to where his class was.)
In Mike's school years, Garfield had classes on staggered schedules, and students graduated in both the summer and the winter.
Mike joined the Navy right out of high school, and he was buried with full military honors as a veteran of the Pacific Theater of World War II. He met his wife when he was in Seattle as the war was ending, and they remained married for 61 years.
Mike's family was hard working Irish/Germans. He was short and stout, and he would tell the most outrageous stories with a completely straight face.
He lived among hard working people of a wide variety of backgrounds. They all got along--at least as well as high school students normally get along--and they kept in contact with each other over the years.
His memories are fond of Garfield. He was a prankster, and I suspect he played pranks on both his teachers and his classmates. He never spoke of himself as a particularly distinguished student, and I suspect that may have been true.
But he was a good man--as good as they come.
He used to keep a cup of spare change in his car to give to the homeless. He lived modestly, but he had sufficient wealth to help many people when they needed it. He often did anonymous acts of service in his church and community.
He faced death head on with no apologies or fears. "How are you doing?" I asked him when he was in the hospital just before he died. "Well, I'm dying," he answered. Then he told me a joke and a series of funny stories. "Come and see me again before I go," he said, but he died too quickly for me to see him again.
I tell people, "I want to go like Mike." He died with courage, panache, and humor. He left his family well provided for, though not wealthy. He made all the funeral and death arrangements himself before he died. No one ever met him who didn't love him.
Mike is what our students will be in 60 years or more. At least, I hope so.
Jeff Combe
I had an experience today that gives perspective to our jobs.
Raymond Emil (Mike) Wolohen's funeral was today. Mike was 81 years old, and he died of cancer.
He was a graduate of Garfield High School, class of Winter 1943.
When he was a boy, he lived across the street from the high school, and as an adult he would regale me with stories of how his brother could sleep in until the last possible minute, then jump into his PE clothes, and be on campus before his name was called in roll call. Mike could do the same thing with his shop classes. (I thought that he said that he lived on Fraser Street, which meant that the shop building used to be on the west end of campus. Otherwise he would have had to sprint a couple of blocks to get to where his class was.)
In Mike's school years, Garfield had classes on staggered schedules, and students graduated in both the summer and the winter.
Mike joined the Navy right out of high school, and he was buried with full military honors as a veteran of the Pacific Theater of World War II. He met his wife when he was in Seattle as the war was ending, and they remained married for 61 years.
Mike's family was hard working Irish/Germans. He was short and stout, and he would tell the most outrageous stories with a completely straight face.
He lived among hard working people of a wide variety of backgrounds. They all got along--at least as well as high school students normally get along--and they kept in contact with each other over the years.
His memories are fond of Garfield. He was a prankster, and I suspect he played pranks on both his teachers and his classmates. He never spoke of himself as a particularly distinguished student, and I suspect that may have been true.
But he was a good man--as good as they come.
He used to keep a cup of spare change in his car to give to the homeless. He lived modestly, but he had sufficient wealth to help many people when they needed it. He often did anonymous acts of service in his church and community.
He faced death head on with no apologies or fears. "How are you doing?" I asked him when he was in the hospital just before he died. "Well, I'm dying," he answered. Then he told me a joke and a series of funny stories. "Come and see me again before I go," he said, but he died too quickly for me to see him again.
I tell people, "I want to go like Mike." He died with courage, panache, and humor. He left his family well provided for, though not wealthy. He made all the funeral and death arrangements himself before he died. No one ever met him who didn't love him.
Mike is what our students will be in 60 years or more. At least, I hope so.
Jeff Combe
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