Shannon J. Halkyard
SED 720 Cooks
Curriculum Guide
December 5, 2002
Content Area: Mathematics
I. Current Research *
Ia. Huntington, Linda. (2000). Focus on Teaching: Beginning Math for Beginning Readers. Focus On Basics. *
Ib. Pugalee, David K. (2001) Using Communication to Develop Studentsí Mathematical Literacy. Mathmatics Teaching in the Middle School, 6, 296-299. *
Ic. Strutchens, Marilyn E. (2002). Multicultural Literature as a Context for Problem Solving: Children and Parents Learning Together. Teaching Children Mathematics, 8 , 448-454. *
Id. MacGregor, Mollie, and Price, Elizabeth. (1999). An Exploration of Aspects of Language Proficiency and Algebra Learning. Journal for Research in Mathematics Education, 30, 449-467. *
Ie. Siegel, Marjorie; Borasi, Raffaella; and Fronzi, Judith. (1998). Supporting Studentsí Mathematical Inquiries Through Reading. Journal for Research in Mathematics Education, 29, 378-413. *
II. Lesson Plan Critiques *
IIa. Glazer, Evan. Bon Voyage! *
IIb. Colson, Bill. The Cuisenaire Four-Pan Algebra Balance. *
IIc. Burdette, Rose; Shipley, Lisa; and Thomas, Sheila. (1995). Fashion Sense and Dollar Wise. *
IId. Crecelius, Elinor H. Bean Toss. *
IIe. Smith, Margaret V. World Population Study. *
III. Individual Curriculum Activities *
IIIa. Perpendicular Slopes *
IIIb. Intro to Integers and Tile Spacer Manipulatives (Addition) *
IIIc. Subtraction with Tile Spacer Manipulatives *
IIId. The Music Industry *
IV. Resources in Content Area (Mathematics) *
IVa. King, Julie, and Rasmussen, Peter. (1992). Key to Algebra 8: Graphs. Emeryville, CA: Key Curriculum Press. *
IVb. Gilkey, Susan N., and Hunt, Carol H. (1998). Teaching Mathematics in the Block. Larchmont, NY: Eye On Education. *
IVc. Jenkins, Robert H. (1997). 61 Cooperative Learning Activities in Algebra 1. Portland, Maine: J. Weston Walch. *
IVd. Winter, Mary Jean, and Carlson, Ronald J. (1993). Algebra Experiments I. White Plains, NY: Dale Seymour Publications. *
IVe. Amdahl, Kenn and Loats, Jim. (1995). Algebra Unplugged. Broomfield, CO: Clearwater Publishing. *
Current Research
http://www.gse.harvard.edu/ncsall/fob/2000/hunting.html
Summary:
Mathematics involves substantial amounts of reading, but little guidance is usually given for instruction of mathematics to beginning readers. This is important not only for native speakers with limited reading proficiency, but also for English language learners. The author presents a framework for one hour lessons that can be used to address the needs of learners who are beginning readers of English. The primary context of the framework is an adult education program with students from the United States, the Caribbean, and Ethiopia. Principles employed in the framework include strict routine, pairs work, drills, problem solving sessions, and a large amount of talking about numbers.
Connection to Literacy:
Often students who are low-achieving in mathematics are also low-achieving in other areas, such as reading, a key component of literacy. For students who are begiinning level readers, the mathematics curriculum cannot be taught as a disjoint subject without linking it to reading skills. Rather, numeracy and math skills must be linked to basic reading and both skills taught together. Examples are presented in the article of ways to incorporate basic reading and math, such as constructing budgets and shopping lists from store circulars. Also, these reading and mathematical texts are talked about extensively in order to promote reading and to connect developing skills in mathematics and reading to more advanced speaking skills possessed by the students.
Significance of the Information:
Mathematics teacher training often neglects the role of reading skills and literacy in mathematical ability. In order for students to address word problems and be able to transfer problem solving skills, they must have adequately developed reading skills. Methods for developing reading skills in the mathematics classroom have not been sufficiently developed or promulgated through teacher training programs. This article beings to address these insufficiencies in the curricular and instructional materials available to instructors of mathematics.
EBSCOHOST: http://0-search.epnet.com.opac.sfsu.edu:80/direct.asp?an=3958349&db=afh
NCTM: http://my.nctm.org/eresources/article_summary.asp?URI=MTMS2001-01-296a&from=B
Summary:
The author discusses the National Council of Teachers of Mathematics (NCTM) 2000 Principals and Standards for School Mathematics, in particular the Communication Standard. He provides examples of ways to use the standard in instruction and how to develop students progress with respect to the standard. He also presents and details four focus areas for communication:
Connection to Literacy:
A key component of literacy is communication, both oral and written. The NCTM Communication Standard provides a goal and incentive for developing these skills. Developing students ability to organize and consolidate though and to communicate those thoughts are indispensable parts of literacy. Beyond this, however, students can critically engage this communication to analyze and evaluate the communication and the information communicated. These levels of engagement are commonly described as critical thinking and are generally highly desired levels of thinking in mathematics, literacy, and across the other content areas.
Significance of the Information:
The NCTM Communication Standard on its own only provides a limited amount of guidance and does not provide sufficient examples and information for successful implementation of itself. The authorís explication of the standard and provision of examples of how to structure classroom discussions and activities to foster communication and criticism are necessary for understanding and implementation of the standard.
EBSCOHOST: http://0-search.epnet.com.opac.sfsu.edu:80/direct.asp?an=6947557&db=afh
Summary:
The author describes the Literature/Mathematics Program, which is part of the Mathematics: Applications and Reasoning Skills (MAPS) project of the Baltimore City Public School System. The program uses childrenís literature from various cultures to foster mathematics learning. Mathematics learned this way can be a bridge to other forms of mathematics and mathematics in this context can be a tool for examining social and cultural environments. The program is composed of a read-aloud portion, with facilitators reading and asking questions, and a problem-solving session with problems that build on the context of the story.
Connection to Literacy:
The article and program address literacy on many levels. First, there is the reading of literature, which is accompanied by extracting information to answer the facilitatorís questions. Beyond this, students have to discuss the content, especially the mathematical content, in order to solve the problems that build on the story context.
Significance of the Information:
There is a dearth of multicultural materials for mathematics instruction. The inclusion of multicultural literature, especially genuine literature, is a beginning in addressing this problem. As well, the involvement of parents and community in mathematics instruction can do much to address the problem of math-phobia, which often undercuts the mathematical achievement and persistence of students in pursuing mathematical studies.
EBSCOHOST: http://0-search.epnet.com.opac.sfsu.edu:80/direct.asp?an=2166435&db=afh
Summary:
The authors describe a research project where the metalinguistic awareness of symbol, syntax, and ambiguity, or lack thereof, was correlated with student success in learning the notation of algebra. Few students who scored poorly in metalinguistic awareness scored well in algebra. The correlations between symbolism, syntax, and ambiguity in algebra and language are described. One important distinction made is that meaning in algebra generally cannot be determined from context as is often the case in language.
Connection to Literacy:
The study shows how low levels of understanding how certain elements of language and writing work hinders student understanding and mastery of algebraic notation, an important element in traditional algebra courses. Algebra and advanced mathematics rely on highly specific syntax and symbols, and ambiguity is generally minimized. Students need to master these elements in language literacy to help them in mastering them in mathematical contexts.
Significance of the Information:
The information highlights the need to improve linguistic awareness as part of addressing the high failure rates in algebra. As well, the need to develop ways of communicating important parts of algebraic thought without the traditional notation may help to develop mathematical understanding for students with weaker linguistic skills. These ways may also present a bridge for understanding the notation, instead of allowing the notation to function as a barrier to understanding algebraic concepts. The article does not state this, but this student wonders whether understanding of algebraic notation and more explicit teaching of algebraic symbolism and syntax can impact and improve linguistic awareness and performance.
EBSCOHOST: http://0-search.epnet.com.opac.sfsu.edu:80/direct.asp?an=1090774&db=afh
Summary:
The authors describe a research project where specific reading functions, in combination with writing and talking, were identified as contributory to student understanding of algebra. The researchers identified 30 functions and made specific recommendations on the roles that reading can serve in inquiry-based mathematics classes. Inquiry cycles are described and their theoretical foundations elucidated. Examples are given of inquiry and reading in mathematics instruction at a secondary school.
Connection to Literacy:
The authors detail the use of literacy (reading, writing, discussion, critical thinking, and more) in mathematics instruction, especially instruction involving inquiry-based learning. The use of literacy goes beyond the more common mathematical examples of word problems to include texts that describe mathematical inquiry and the exploration of mathematical ideas. Students are encouraged to engage in discussions where the synthesize and present ideas and strategies and then also critique those ideas and strategies.
Significance of the Information:
Often attempts to include literacy in mathematics instruction are limited to activities like journal writing or "math-writes." These activities are fairly limited compared to the range of reading materials and opportunities available. Inquiry-based learning is one method where a greater range of these materials and opportunities can be exploited to develop students mathematical understanding and communications skills. Beyond this, the employment of mathematics and reading in these different ways promotes the transferability of both sets of skills.
IIa. Glazer, Evan. Bon Voyage!
URL: http://www.glenbrook.k12.il.us/gbs/Academics/gbsmat/Internet%20Projects/travel/bonvoyage.html (downloaded November 24, 2002)
Summary:
Students use function notation in developing formulas for currency conversions for a trip to two foreign countries. They are instructed to plan a trip and the items they will buy in each country. They are instructed to make a record of how much money they would have after each purchase and after traveling to each country.
Positive aspects:
Development areas:
Adaptations for the classroom:
IIb. Colson, Bill. The Cuisenaire Four-Pan Algebra Balance.
URL: http://www.iit.edu/~smile/phma0200.htm (downloaded November 24, 2002)
Summary:
The page describes a lesson using a specialized balance to introduce basic concepts of solving algebraic equations. The balance provides a physical representation of the balance analogy often used in introducing algebraic equations. The addition of pans three and four allows for physical representation of negative quantities.
Positive aspects:
The pan provides a readily accessible physical means of modeling equations. If there are enough balances, students can learn kinesthetically as well as by hearing and seeing. Students also become more involved in learning the material and have a useful prompt for discussing how to solve problems.
Development areas:
The balance is not useful for any advanced problem solving since it is limited to equations with small integer numbers. Many schools would not be able to purchase the balances in large quantities, so they would have to be shared and used for group activities. There is no reasonable way to provide students with home versions of this manipulative.
Adaptations for the classroom:
The scale can be used for demonstrating the concepts of basic algebraic equations and for explaining solutions to simple equations. It can also be used as a tool for students presenting or explaining problems of their own. For students who need extra help, especially those having trouble with concepts, the scales can be used to model equations, especially for work outside of class where a student can use the scales individually.
IIc. Burdette, Rose; Shipley, Lisa; and Thomas, Sheila. (1995). Fashion Sense and Dollar Wise.
URL: http://www.nsa.gov/programs/mepp/ms/prealg01.pdf (downloaded November 24, 2002)
Summary: The lesson involves the use of fractions, ratios, equations, and statistics via the Consumer Price Index (CPI) and spans 3-5 days. Students are to collect clothing advertisements and examine the various ways used to describe savings or sales. They work with decimals, percents, and fractions to evaluate the dollar value and checkout prices for various items and compare them. Then they examine how inflation has theoretically affected the valuation of items by using the CPI.
Positive aspects: The use of the CPI is great. I personally did not know how the index worked, but only had an idea of its use. As well, relating percents, decimals, and fractions to something they are interested in (clothes) and to something important in studentsí everyday life increases interest in the material. Then linking to a more abstract idea, the CPI, and incorporating ratios and equations in applying CPI, involves students in using many skills that they should become fluent in during their mathematical education.
Development areas: The lessons state that the lesson involves cooperative learning, but there are never any guidelines given for how to apply the lesson in a cooperative group context. The instructions for each day are minimal and leave out many needed details. The worksheets are short and do not focus on skill development, but on fluency and application of skills. Many students need skill practice as well, so the worksheets would need to be expanded for classroom use.
Adaptations for the classroom: The worksheets can be expanded to include practice in using the given skills (percents, decimals, fractions, et al). Also, prompts or questions for students to answer given the inserts, mailers, flyers, etc. that they have collected are needed. Without these, the students could become misdirected and the teacher would not have a clear rubric for evaluation what students have or have not done. By expanding the worksheets and creating clear questions to answer and a rubric to go with the questions and worksheets, students and teachers can more successfully employ the great ideas in this series of lessons.
IId. Crecelius, Elinor H. Bean Toss.
URL: http://ofcn.org/cyber.serv/academy/ace/math/cecmath/cecmath047.html (downloaded November 6, 2002)
Summary: Students use colored lima beans to represent positive and negative numbers. Each bean has a white side and a red side, corresponding to positive and negative. Students toss the beans and add to find the net number of positives and negatives. The problems and solutions are shared at the board and students describe rules for adding the positive and negative numbers.
Positive aspects: Having students explore adding integers and then coming up with generalizations or rules for adding them helps students to remember the rules better and develops their critical thinking skills. Having the students share the problems they create with the beans helps them with communication skills.
Development areas: The lesson does not provide much structure and assumes that students will create the structure themselves. While some students do fine with this, many need more guidance, such as worksheet questions or a clear rubric with defined products. The lesson needs such a worksheet or rubric. As well, a sample product could be presented as a model, such as a sheet or table listing the problems they created, how they solved those problems, and what generalizations or rules each group agreed upon.
Adaptations for the classroom: Using colored beans to represent positive and negative could be confusing for some students. Labeling each side of a bean with a plus or minus sign can help limit this potential confusion. Also, having students share their problems on the board themselves, and then writing the generalizations (i.e. rules) for adding integers in their own words would involve them more in the activity. If possible a student or some students should lead the discussion of how to state the generalizations about adding integers.
IIe. Smith, Margaret V. World Population Study.
URL: http://ofcn.org/cyber.serv/academy/ace/math/cecmath/cecmath051.html (downloaded November 6, 2002)
Summary: The lesson focuses on two problems: the first is comparing linear growth to exponential growth using money while the second focuses on world population growth. Students use graphs and calculations to work on both problems. Students are given chances to speculate on the meanings of their findings with respect to each problem.
Positive aspects: The first problem catches their attention by focusing the problem on the students, using data (their age) and money. The second problem expands the graphing and comparison of exponential growth with linear growth to the more socially significant issue of world population growth. Students get to examine different family scenarios (how many children are born to each person) as part of examining population growth rates.
Development areas: There is a great opportunity here to also include functions and to relate equations with graphs in examining the data. The first problem could be developed more fully, especially for a full-length class. The two activities presented might not take a full class period to finish. Also, there is no attention to skill development (i.e. no homework or practice on graphing and exponents).
Adaptations for the classroom: I would have students include functions with the graphs that they make for the two problems. I would extend the world population problem by having students create graphs showing how populations grow based on different numbers of offspring (i.e. children) per adult human (i.e. parent). Students can also examine what would happen under strict enforcement of the one child for every two parents policy in China. I would be likely to make an overhead or worksheet with these extensions and possibly more for homework.
III. Individual Curriculum Activities
Algebra 9
32 Students
75-90 minutes
Partner Lesson
Objective:
Students will find slopes and then compare and contrast the slopes of perpendicular and parallel lines. Students also gain practice in making scale drawings.
Materials:
Graph Paper
Rulers
Colored Pencils or Markers
Chart Paper
Notes:
The first time I had students do this lesson, they found drawing the rectangles to be difficult. Do not skip the part where this is addressed for their benefit.
Steps:
Assessment:
By listening to students and reading the posters they prepare. Reading through answers for what students learned and communicate parallel and perpendicular slopes. Content from the lesson can also be assessed in a later test on slopes and graphing.
Literacy Aspect:
Literacy Aspects of the lesson include:
Reflection/Response: What do you think will happen?
I have done this lesson once in my class. Students had some trouble with making the rectangles, but once they had that done, they were usually able to do the rest. They had a little trouble articulating that perpendicular lines have reciprocal and opposite slopes. Looking closely at the rectangles helped them to understand how and why this isówe looked at rise and run for each side of the rectangle and they saw how these have to be opposite and reciprocal when the lines make 90 degree angles.
Worksheet Questions:
Directions for Partner Rectangles:
IIIb. Intro to Integers and Tile Spacer Manipulatives (Addition)
Pre-Algebra 9
32 Students
75-90 minutes
Partner Lesson (see notes)
Objective:
Students learn how to represent positive and negative numbers using tile spacers in the shapes of plus and minus signs. They learn how to use this representation to show zero in different ways (nothing, balance of negative and positive, et al) and to use the manipulatives for adding integers. They learn or devise ways to record the use of the manipulatives on paper.
Materials:
Tile Spacers Manipulatives are large plastic plus and minus signs. Hardware stores carry tile spacers in plus shapes and other shapes. Student assistants can cut the tiles into minus signs to match the plus signs. Tile spacers are really cheap! Teachers can use these directly on overhead projectors and students can view the shadows projected onto a screen.
Notes:
This lesson can be done individually, in pairs, or in small groups, depending on the availability of supplies and the teacherís preference.
Steps:
Assessment:
Review student problems from the class. Listening to students working during class. Viewing presentations by students on how to record manipulative activity. Reading journal entries.
Literacy Aspect:
Literacy Aspects of the lesson include:
Reflection/Response: What do you think will happen?
I have done a variation of this lesson before. Many students were not receptive to re-learning integers and a fellow teacher recommended adding the pre-quiz. This should help with getting more students on board. Several students told me after the lesson that it really helped them to understand how integers and integer operations work.
Sample Quiz on Integers
IIIc. Subtraction with Tile Spacer Manipulatives
Pre-Algebra 9
32 Students
75-90 minutes
Partner Lesson (see notes)
Objective:
Students continue learning how to use tile spacer manipulatives. They learn how to use these to subtract integers. They learn or devise ways to record subtraction with the manipulatives on paper.
Materials:
Tile Spacers Manipulatives.
Thermometer poster showing different temperature scales (this can be used for subtracting integers and for using formulas).
Notes:
This lesson can be done individually, in pairs, or in small groups, depending on the availability of supplies and the teacherís preference.
Steps:
Use a large thermometer poster and have students find the difference in some temperature pairs:
15° C and 35° C
-15° C and 35° C
-15° C and -35° C
Assessment:
Review student work from class. Listen to students working during class. Have students informally show how they record manipulative activity. Have students write solutions to problems at the board. Allow students to present problems using manipulatives on the overhead projector. Read journal entries.
Literacy Aspect:
Literacy Aspects of the lesson include:
Reflection/Response: What do you think will happen?
Students should gain a deeper understanding of how integers and integer operations work. They should also be prepared for using the integers to multiply and divide integers. They should be able to articulate their own procedures for adding and subtracting integers by the end of the lesson.
Pre-Algebra or Algebra 9
32 Students
75-90 minutes
Small group work and Presentations
Objective:
Students will read articles from various perspectives on the music industry. They will take the data from the articles and explain it using posters, charts, and graphs.
Materials:
Graph Paper
Rulers
Colored Pencils & Markers
Chart Paper
Notes:
The first time I had students do this lesson, they found drawing the rectangles to be difficult. Do not skip the part where this is addressed for their benefit.
Steps:
Assessment:
By listening to students and inspecting the graphical aids and posters they prepare. Reading through the homework assignments to see what they got from the classroom discussion and presentations..
Literacy Aspect:
Literacy Aspects of the lesson include:
Reflection/Response: What do you think will happen?
I would hope that some of the more informed students would be aware of the issues that music artists they listen to have raised about how they are paid and how much they are paid. Many of the students may find a new appreciation for why math is useful and how it can be used to persuade audiences and make arguments.
Handout and articles references and notes:
http://dir.salon.com/tech/feature/2000/06/14/love/index.htmlCourtney Love Does the Math
The controversial singer takes on record label profits, Napster and "sucka VCs."
http://www.bricklin.com/recordsales.htm
The Recording Industry is Trying to Kill the Goose That Lays the Golden Egg
Given the slight dip in CD sales despite so many reasons for there to be a much larger drop, it seems that the effect of downloading, burning, and sharing is one of the few bright lights helping the music industry with their most loyal customers.
http://events.calendarlive.com/top/1,1419,L-LATimes-Search-X!ArticleDetail-34670,00.html
Record Label Chorus: High Risk, Low Margin
With stars questioning their deals, the big companies make their case with numbers
http://www.help-finance.com/download/0478-Eng.doc
EXECUTIVE SUMMARY, Music & Entertainment,478, ACE-Independent Record Label, Startup, USA VA,$15
Detailed marketing and venture capital proposal for a startup independent record label. Students can choose to present this article as a pitch for raising money from potential sponsors.
IIIe. Basketball
Pre-Algebra or Algebra 9
32 Students
One hour
Small group work and Presentations
Objective:
Students learn about the meaning of averages, how to convert totals into averages, how to analyze statistical data. and how to then make interpretations and assumptions based on the data.
Materials:
Graph Paper
Rulers
Colored Pencils & Markers
Chart Paper
Calculators
Notes:
This is a hypothetical untested lesson. Read with care and proceed with due caution.
Steps:
Assessment:
By listening to students and inspecting the posters they prepare. Reading through the homework assignments to see what they got from the classroom discussion and presentations.
Literacy Aspect:
Literacy Aspects of the lesson include:
Reflection/Response: What do you think will happen?
Students might already know some of these rules, but not have had practice in implementing them. Also, showing how an outlier can affect real-life data and outcomes may elicit better recall and transferability of the idea.
Handout #1:
Two Rules of Statistics:
Rule #1: Take averages, not totals.
Rule #2: The more data you have, the more accurate the results.
Example #1 Jordan and Shaq
Using the rating system below, Michael Jordan (Chicago Bulls) has a rating of 33.4. Shaquille O'Neal (LA Lakers) has a rating of 42.2. Most people would agree that Shaquille O'Neal is not better than Michael Jordan, and even those who believe that he is better agree that he is not better by that much. A closer look at the statistics reminds us of several things. Below is a table of some important totals for these players during the 96-97 NBA regular season.
| Name |
Games |
Points |
Rebounds |
Assists |
|
Jordan, Michael |
82 |
2431 |
482 |
352 |
|
O'Neal, Shaquille |
51 |
1336 |
640 |
159 |
Obviously, since O'Neal played fewer games, his totals are less. However, if you find the averages for the players, a different picture forms. Below are the same statistics, except that instead of totals, there are season averages in the points, rebounds, and assists column.
| Name |
Games |
Points per game |
Rebounds per game |
Assists per game |
|
Jordan, Michael |
82 |
29.6 |
5.9 |
4.3 |
|
O'Neal Shaquille |
51 |
26.1 |
12.5 |
3.1 |
These statistics show that the two players are nearly equal in points and assists per game, but Jordan has a huge disadvantage in the rebounds column. Most basketball fans would notice that something is wrong. Shaquille O'Neal's scoring average (26.1) was very much affected by the several good games he had after his return. In this manner, his averages were affected more than they should have been.
Example #2: An Imaginary Scenario
For example, in an NBA season our imaginary player Milton has a scoring average of 20.0 points per game (ppg) after playing in 81 of the 82 games of the regular season. That means that he scored a total of 1620 points this season. Our second imaginary player Bradley also has an average of 20.0 ppg, but he was injured half of the season and only played 40 games, which means that he has a total of 800 points.
In the last (82nd) game of the season, the two players meet in a game and each one scores an incredible 60 points. After such a performance, Milton's average rises to 20.5 points. Bradley's average, however, rises to 21.0 points. This gives the impression that Bradley is much better than Milton, although they are almost exactly equal in ability. This shows that a good performance benefits a player who has played less games more than a player who has played more games, and very well illustrates the second rule of statistics: the more data you have, the more accurate the results.
At first, it seems that this rule goes against rule #1 (take averages, not totals), but that is untrue. The best solution is to find the averages of Milton and Bradley over the past several years. That way, you will have an average representation, and you will receive the benefit of having more accurate data because it's "evened out" by the amount of data.
Data and text from the following website:
http://library.thinkquest.org/12006/S-S-1.shtml
Handout #2:
Here is a sample of player statistics from the following website:
http://library.thinkquest.org/12006/gather/tmpages/teampages.shtml
| Name |
Games Played |
Points |
Rebounds |
Assists |
Steals |
Rating |
|
Artis,Katasha |
20 |
16 |
16 |
8 |
6 |
0.6 |
|
Bullett,Vicky |
28 |
359 |
178 |
65 |
54 |
20.1428571428571 |
|
Congreaves,Andrea |
28 |
187 |
133 |
41 |
16 |
11.75 |
|
Hopson-Shelton,Susie |
6 |
16 |
5 |
1 |
1 |
2.5 |
|
Levesque,Nicole |
27 |
109 |
47 |
75 |
21 |
4.05555555555556 |
|
Manning,Sharon |
28 |
137 |
98 |
13 |
25 |
8.10714285714286 |
|
Mapp,Rhonda |
28 |
326 |
154 |
64 |
21 |
12.8392857142857 |
|
Moore,Penny |
28 |
135 |
72 |
28 |
16 |
4.35714285714286 |
|
Stinson,Andrea |
28 |
439 |
155 |
124 |
43 |
21.3035714285714 |
|
Suber,Tora |
28 |
131 |
42 |
56 |
13 |
4.57142857142857 |
|
Vukadinovic,Milica |
1 |
3 |
1 |
1 |
1 |
3.5 |
|
Williams,Debra |
10 |
27 |
13 |
9 |
2 |
1.15 |
IV. Resources in Content Area (Mathematics)
Summary of Resource
The Key to Algebra series covers algebra topics using ten small workbooks. There are also Key book series for fractions, decimals, percents, geometry, measurement, and the metric system. Key to Algebra 8: Graphs is a 37-page workbook that focuses on graphing skills.
Positive Aspects
Students like the activities from this book because they have clear explanations on how to do the problems. Most of my students are also happy because the book provides just the right amount of scaffolding for them to learn without getting bored from rote repetition. They develop their skills and are able to build upon them at a good solid pace.
Development Areas
This book unfortunately focuses only on skills, so it is not useful for me as a stand-alone resource on graphing. It can augment a curriculum, but since it does not put graphing into context nor does it apply graphing to other areas or other types of problems, its use is limited.
How would you use this resource your classroom?
I use this book as a source for worksheets that I give out for students to develop their skills, especially when we are learning new skills. I also use it for students who need extra help because they can often re-do some of the pages or do the ones I omit for the whole class to develop their skills.
Summary of Resource
This 186-page book covers a large amount of material. Chapters address NCTM standards, curriculum planning, instructional design, lesson planning, instructional strategies, use of technology, evaluation and assessment, sample lessons and labs, and further resources. There are in-depth discussions and descriptions of ideas and their implementation. The sample lessons and labs illustrate many of the ideas presented in the text.
Positive Aspects
This book covers everything. For math teachers, it is a virtual encyclopedia of techniques, sample lessons, and ways to arrange lessons, chapters, and units. There seems to be little left out. The sample lessons and labs are included in Appendix A and Appendix B provides an extensive annotated bibliography, with many of the resources evaluated by students as well as teachers.
Development Areas
This book is quite comprehensive, but daunting to read and then to put into practice. It requires a large investment of time to be useful and many beginning teachers do not have the time to invest in it. It is probably more useful for teachers after their first year or two, and also for teachers who are faced with changing from a traditional school schedule to a block schedule. The book could be rearranged so that it can be read in small portions that can be implemented in daily teaching without having to read or sort through the whole book. The book also does not address some areas, such as culturally sensitive pedagogy.
How would you use this resource your classroom?
The simplest way to use it is to include sample lessons and activities in my teaching. The book also provides many ideas on how to structure my lessons and curriculum that I plan to use in planning my courses for next semester. There is a section on teaching AP classes that will be important for the students who will be with me for only three months before the AP exam is administered in May.
Summary of Resource
This 150-page books contains 61 activities suitable for first year algebra and pre-algebra classes. The activities are all designed for small groups and cover a variety of topics. All of the activities can be completed in a one-hour class period. There is a range of difficulty in the activities and a range in the amount of prep time required. The activities can stand alone or can be incorporated into a large lesson plan. Some of the activities are designed as units.
Positive Aspects
The activities do not require a lot of special materials or preparation. Handouts are ready for copying from the book. I have tried two of the activities in my classroom. One did not go wellóprimarily because my studentsí skills were not as well developed as I thought they were. The other went quite well and my students exceeded my expectations.
Development Areas
Each activity needs to be tested in the individual teacherís classroom. Some may require tweaking, or students may need additional training and skill development to perform them. Some of the activities seem rather simple and trivial, but the one trivial one I tried ended up being more successful.
How would you use this resource your classroom?
I have included the activities in my classroom lessons. I try to pair exploratory and discovery activities with skill development and problem solving. This develops the two primary areas of mathematical thinking and skill. As well, it provides some variety of activity for the long 90-minute classes at my school. Since the time estimates are usually on target, the activities can be planned into lessons fairly precisely.
Summary of Resource
This resource includes 17 experiments for exploring linear relationships in algebra one. For the experiments there are lesson plans with introductions, equipment, procedures, extensions, and student worksheets. The experiment activities include individual work, pairs work, and small group activities.
Positive Aspects
The experiments provide an alternative to traditional algebra teaching methods, which can be very important for students who have not learned algebra from traditional methods of instruction. The lesson plans provide a base from which to tailor the lessons for given student populations and teachers. The activities get students involved in math in a kinesthetic way.
Development Areas
The lessons need to be adapted to specific student populations, as do the worksheets. It would be useful to have more experiments to choose from. Some of the experiments are not always practical; especially those that require a lot of prep time. Some of the lessons require exceptional classroom management capabilities.
How would you use this resource your classroom?
I have used this resource to supplement the textbook, which was written from a skills-based approach with lots of drills and skills practice. The exercises in this book allow for variations on the lessons and get more students involved. As well, they present the material in a different way and allow for more student-centered learning and teaching.
IVe. Amdahl, Kenn and Loats, Jim. (1995). Algebra Unplugged. Broomfield, CO: Clearwater Publishing.
Summary of Resource
This book is designed for beginning students of algebra. It includes a review of basic concepts, including fractions, and develops other mathematical ideas. Itís full of good explanations, using examples and situations that kids can relate to. The book does not contain problems or lessons, but it is full of ideas on how to approach algebra generally as well as specific algebraic concepts.
Positive Aspects
The explanations and examples are the best part of this book. It helps teachers get in touch with how students are thinking and provides bridges for reaching students. For students it provides an alternative explanation of concepts from what they get in the classroom. It also provides strategies on how to approach algebra (for one thing, itís a game with rules to learn and follow) and master it.
Development Areas
There should be another volume to cover the areas that are left untouched. The book is only 260 pages long and canít cover all of algebra. It would also be nice to have problems similar to those in textbooks as examples with strategies for decoding, understanding, and solving them.
How would you use this resource your classroom?
This book is full of ideas for lectures and presentations for material. The analogies are good resources for explanations and for structuring problems. It is also a great resource for students who are oriented more towards English and reading than mathóthey can use those skills with this book, which then can help them with algebra ability.