Keywords: Geometry, ,
Ref: Peterson1
Author(s): Galindo, Enrique
Date: Jan. 1998
Title: Assessing Justification and Proof in Geometry classes
taught using dynamic software
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: v91 n1 p76(7)
Reviewer: Peterson
Date of Review: 3/13/00
This article was mainly focused on the assessment of justification and proof in geometry classes taught using dynamic software. It is exclaimed that Mathematics teachers and their students may utilize dynamic geometry software such as "Cabri Geometry II," "The Geometer's Sketchpad" and "Geometry Inventor" in designing innovative approaches to proof and justification in geometry. Such software may encourage students to conduct meaningful justification of ideas, create simple geometric figures and explore the figures' relationships. The software may also promote better understanding of geometric problems. It makes for better understanding, both visual and conceptual, of the many postulates and axioms of geometry.
So often are students hindered in their understanding of and
motivation toward geometry based on their lack of allowance to
work with material objects, or creation programs. Geometry is the
study of shapes and their properties. Hence, the students should
be able to both see and use these shapes to model their
understanding and appreciation of this complex world of points,
lines, and angles. Such software as stated above is the next step
toward assessing these kinds of goals.
Keywords: Technology, ,
Ref: Peterson2
Author(s): Blume, Glendon W.
Date: Summer 1991
Title: Preparing Mathematics Teachers to use Computers:
shifting the Focus from Teaching to Learning
Journal or Publisher: Education
Volume, Issue, Pages: V111 n4 p538(4)
Reviewer: Peterson
Date of Review: 3/14/00
As this article suggests, a variety of recent reports have recommended substantial changes in precollege mathematics curricula and instructional methods. Included in these recommendations is more substantial use of technology and, consequently, a focus on outcomes different from those currently emphasized. Models for educational change emphasize the importance of motivating individuals so they recognize the need for the potential of proposed changes.
Teacher's own experiences in learning mathematics in a
technology-rich environment can have a powerful influence on their
acceptance of technology intensive curricular and instructional
changes. Attention needs to be shifted from efforts to
familiarize mathematics teachers with new materials and
instructional methods incorporating technology to efforts that
emphasize teachers' new materials and instructional methods
incorporating technology to efforts and emphasize teachers'
understanding of how individuals learn mathematics when computers
and calculators are available as tools. The later suggests a much
less intuitive notion of the advantage of technology and
mathematics. It is one thing to know how to use and apply
something, but another to know why it is such an effective tool.
Keywords: Assessment, ,
Ref: Peterson3
Author(s): Cornell, Charles
Date: Summer 1999
Title: "I hate math! I couldn't learn it, and I can't teach
it!". (effective math instruction)
Journal or Publisher: Childhood Education
Volume, Issue, Pages: V75 i4 p225(6)
Reviewer: Peterson
Date of Review: 3/14/00
This article exclaims that success in learning and teaching mathematics is substantially conditioned by the student's or teacher's attitude. Fears of and actual frustration and failure have been identified with false assumptions of students' knowledge , incomplete instruction, and inadequate real-world applications. Effective math instruction can be enhanced by increasing real-world applications, integrating projects and contests to generate greater interest, and immediate correction of student errors to ensure continuous learning.
This article also goes on to suggest what some sources of
frustration and failure are with mathematics courses. Teachers'
assumptions of their students' knowledge is a major problem area.
Many students believe that their math teachers act as if
computational procedures and processes are simple and
self-explanatory; even worse, students say, their teachers have
little sympathy for students who do not understand the concepts.
Indeed, it may be difficult for one whose interests naturally
gravitate to things mathematical to recognize that seemingly
simple, self-explanatory processes may be complicated to others.
This is why teachers must strive toward excellence within the
classroom, but must be careful not to leave their students behind
in the process. Sometimes a step backward is necessary to take
a step or two forward. Full assessment involves teacher, as well
as student, achievement and success.
Keywords: Standards, ,
Ref: Peterson10
Author(s): Vacc, Nancy Nesbitt
Date: Oct. 1993
Title: Implementing the 'Professional Standards for Teaching
Mathematics': Questioning in the Mathematics Classroom
Journal or Publisher: Arithmetic Teacher
Volume, Issue, Pages: v41 n2 p88(4)
Reviewer: Peterson
Date of Review: 3/14/00
In this article, the focus is on the implementation of professional standards for teaching mathematics. It is suggested that mathematical teaching should encourage creative thinking in students, and the traditional system in which teachers teach what they feel is necessary, should be changed. Furthermore, the questioning attitude of students should be fostered. It is estimated that traditionally, teachers used to ask 50,000 questions for every 10 questions from students. The questions of the teacher, which were factual, open-ended and reasoning, only permitted labeling phenomenon, and were also guided by the teacher's attitude toward classroom activity.
For many, implementing the Professional Standards for Teaching Mathematics (NCTM 1991) in the classrooms makes great sense. The article implies that it is clearly reasonable that if students are to develop and understanding of and an ability to use mathemati8cal applications in a variety of contexts, they should have meaningful and relevant experiences that will actively engage them in constructing their own knowledge. Also, that active engagement needs to be accompanied by opportunities for students to talk about what they already know and don't know and what they are doing as they strive to extend or change their current level of understanding.
Concerning questions that teachers should ask, Barnes (1990) identifies three categories of teacher questioning that relate directly to classroom instruction; factual, reasoning, and open. Factual questions seek factual answers such as a name or specific information. Reasoning questions require students to construct, or reconstruct from memory, logically organized information. Open questions could be considered factual because they elicit previously learned knowledge. However, they are deemed open questions because a wide range of acceptable answers exists.
In summary, the learning is affected by the opportunities students have to relate incoming information to what they already know and then restructure their existing knowledge or construct new ideas when appropriate. As the FPS (Professional Teaching Standards) indicates, the ways of representing, thinking, talking, agreeing, and disagreeing is central to helping students develop mathematical understanding and skills. This development, however, cannot be achieved without teachers' asking a variety of questions that challenge students' thinking--questions that require much more than factual recall.
Therefore, a place for us to begin as we strive to
implement the standards is with a self-evaluation of the types
of questions we ask our students, as the article suggests.
Furthermore, comparing the types of questions we ask with those
presented in the foregoing is a way to initiate this analysis.
The results should form a basis for modifying or changing our
day-to-day practices so that our students talk about what they
know and think; we listen to what they are telling us; and we
plan instruction based on what we are hearing from, and learning
about, our students.
Keywords: Issues, ,
Ref: Peterson9
Author(s): Adams, Paul E.; Krockover, Gerald H.
Date: Jan. 1997
Title: Concerns and Perceptions of Beginning Secondary
Science and Mathematics Teachers
Journal or Publisher: Science Education
Volume, Issue, Pages: v81 n1 p29(22)
Reviewer: Peterson
Date of Review: 3/14/00
This article discusses the various concerns associated with
beginning secondary science and mathematics teachers. The
concerns and perceptions of beginning secondary school science
and mathematics teachers about teaching and efficacy of their
preservice training program have implications for improving the
preservice programs. In a nut shell, the article goes on to
highlight some of the major concerns about being a new teacher,
such as time management, content presentation, curriculum
formation, and class assignments. It turns out that teachers
believe, in general, that their training is too specific, has
limited utility, needs more field work, and fails to ease the
transition from student to teacher. Furthermore, one may be
safe to conject that concerns and perceptions are present, to a
certain extent, with every beginning secondary science and
mathematics teacher.
Keywords: Connections, Issues,
Ref: Peterson8
Author(s): Masingila, Joanna O.
Date: Oct. 1998
Title: Thinking Deeply About Knowing Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: v91 n7 p610(5)
Reviewer: Peterson
Date of Review: 3/14/00
The notion that "teaching" is different from "knowing" is the focus of this article. Mathematics teachers often "erroneously" equate the ability to teach mathematics with knowing mathematics. However, teaching is different from knowing. Teachers who know the procedures involved with certain mathematical concepts are able to teach them. However, knowing the concept is different from knowing the procedure. An example the article provides is that of the ellipse where the equation of the ellipse is often presented. It is often forgotten that an ellipse can be generated just by specifying the two foci and a constant distance.
Mathematics teachers often get so caught up in the procedures
and the "how to" of a problem situation, that they often forget
to acknowledge or assess the "why" associated with the same
problem. The article goes on the suggest that it is the "why"
of a problem situation that allows us to not only solve the
problem, but appreciate it's origin as well. Often times, we
can look at the insides of a problem and recognize all kinds of
fundamental properties, which if acknowledged ahead of time,
would open up a much more efficient and manageable door for us
to pass through in our attempt to find the ideal solution. This
is something that must be assessed by mathematics teachers in
order for their to exist a glimmer of hope for their students in
their attempt to "get to the bottom of things" with what they
are doing.
Keywords: Curriculum, ,
Ref: Peterson7
Author(s): Barnett, Carne
Date: Sept-Oct 1991
Title: Building a Case-Based Curriculum to Enhance the
Pedagogical Content Knowledge of Mathematics Teachers
Journal or Publisher: Journal of Teacher Education
Volume, Issue, Pages: v42 n4 p263(10)
Reviewer: Peterson
Date of Review: 3/14/00
Along the lines of "Case-Based Curriculum," this article exclaims
that very little attention has been given to research on cases
in specific disciplines or on the development of an integrated
case-based curriculum. In the article, it is discussed how the
cognitive flexibility and knowledge transfer theory, proposed by
Rand Spiro and his colleagues, frames the design of a case-based
curriculum for use in mathematics teacher education. The paper
includes a sample mathematics teaching case and presents an
analysis of four discussions based on that case. In the analyses,
the dominant themes of those case discussions are identified and
a framework for selecting and sequencing cases for an integrated
curriculum is discussed. The analysis also shows the potential
of subject-specific cases for enhancing mathematics teachers'
pedagogical thinking and reasoning.
Keywords: Tests, ,
Ref: Peterson6
Author(s): Weber, William B. Jr.; Somers, Laurie; Wurzbach,
Linda
Date: Dec. 1998
Title: Inproving the Teaching and Learning of Mathematics;
Performance-Based Assessment of Beginning Mathematics Teachers.
Journal or Publisher: School Science and Mathematics
Volume, Issue, Pages: p 430(7)
Reviewer: Peterson
Date of Review: 3/14/00
The focus of this article is on the means by which beginning
mathematics teachers are evaluated with respect to the way that
they teach, and the content that their students are learning.
The teaching body Interstate New Teacher and Support Consortium
has established standards designed for novice mathematics teachers
through performance evaluation. The teacher's work is assessed
through a number of routes, including such things as portfolio
documentation and classroom technique appraisal. Each portfolio
represents ten hours work, and comprises teaching plans,
videotapes, work samples and written reports. All in all, this
form of evaluation hopes to produce optimal achievement and
assessment within the realm of mathematics educators.
Keywords: Connections, ,
Ref: Peterson5
Author(s): Quaal, Debbie
Date: Sept. 1993
Title: Mathematics Teaching - A Student's View
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: v86 n6 p441(1)
Reviewer: Peterson
Date of Review: 3/14/00
This article generally implies that teachers instruct students in mathematics as a part of their routine, with a complete lack of interest and involvement. These are cases where the teacher is teaching, not to teach, but to "earn a paycheck" so to speak. The education system does not necessitate the students' comprehension of the concepts that they are introduced to. Consequently, teachers must analyze the individual capacity of each student and instruct the student accordingly.
It is also stated that questions must be encouraged; each
concept must be clearly understood by every student in the class
before the teacher can proceed to the next one. By encouraging
questions or asking the students if they have any, the teacher
is already making a stride toward developing a more personal
and conceptual relationship with his/her students. This is the
ultimate goal.
Keywords: Teaching Strategies, Assessment,
Ref: Peterson4
Author(s): Tate, William
Date: Feb. 1995
Title: Mathematics Communication: Creating Opportunities to
Learn
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: V1 n6 p334(7)
Reviewer: Peterson
Date of Review: 3/14/00
The importance of mathematics communication that builds on the lives and experiences of African American students in urban schools, thereby creating additional opportunities to learn and explore mathematics, is the focus of this article. The development of mathematics communication among African-Americans is stunted because teaching techniques that focus on an African-American's life experiences have only just been implemented. Mathematics communication is a necessary part of democratic life and prepares children to understand their surroundings. Thus, mathematics teachers should acquaint themselves with a student's background, which influences learning, and provide realistic applications of mathematics.
Carter G. Woodson (1993) argued that mathematics pedagogy built on the African American students' experiences fostered two mathematics learning environments within the school and outside of school. However, two disciplines with great influence on mathematics education - mathematics and psychology - place significant stress on objectivity and neutrality (Kilpatrick 1992). As a result, school mathematics has been tacitly constructed as a "color-blind" body of knowledge. It seems that often, little consideration is given to the cultural appropriateness of mathematics pedagogy and communication.
More recently, mathematics textbooks have included
pictures of African Americans, and some mathematics textbooks
include stories about Africans and African Americans who have
contributed to the growth and development of mathematical
knowledge. These efforts represent progress and should be
encouraged and expanded. Yet these efforts are unlikely to
prove sufficient to empower African American students to
communicate with mathematics. Connecting the pedagogy of
mathematics to the lived realities of African American students
is essential to creating optimal opportunities to learn
mathematics.
Keywords: Connections, ,
Ref: Peterson11
Author(s): Jones, Doug
Date: Oct. 1993
Title: Teacher's View of the Mathematical World Through a
Student's Perspective
Journal or Publisher: Arithmetic Teacher
Volume, Issue, Pages: v41 n2 p73(3)
Reviewer: Peterson
Date of Review: 4/2/00
It is the purpose of this article to suggest that arithmetic teachers can motivate students' interest in solving mathematical problems and enhance the development of their mathematical skills by approaching mathematical problems from their point of view. Furthermore, mathematics teachers need to refrain from adopting a biased stand by imposing their ideas on students and altogether rejecting the students' approach to problem solving. They have to avoid being "over accomodative" of students' ideas and have to maintain a specific standard of evaluation. Mathematicians, while formulating theories and algorithms, always take into account previous research work conducted in that particular field. This is an unbiased approach to mathematical problems.
Teachers are asked to help students develop their mathematical power--their abilities to explore, conjecture, and reason logically, as well as to use a variety of mathematical methods effectively to solve non-routine problems (NCTM 1989, 1991). Their role is to be more of a facilitator of learning and less a dispenser of facts and skills--to get students involved in doing Mathematics. But by itself, getting students to "do" mathematics is not enough. Teachers and their students need to make sense of their mathematical activity.
Helping students appreciate different perspectives and different
ways of doing mathematics may help them to deepen their
understanding. Indeed, one theme of this article is that
teachers need to emphasize the search for, and purposeful use of,
different perspectives by students. The second theme is the
teachers need to expand their own perspectives to include those
of their students.
Keywords: History, ,
Ref: Peterson12
Author(s): Van Voorhis, Judith L.; Anglin, Jacqueline M.
Date: Dec. 1994
Title: Teachers Share Their Mathematics Backgrounds: Telling
It Like It Was
Journal or Publisher: School Science and Mathematics
Volume, Issue, Pages: v94 n8 p407(6)
Reviewer: Peterson
Date of Review: 4/2/00
A study was conducted on 45 mathematics teachers to analyze their
backgrounds and the help and confidence they received from their
family while choosing a career in math teaching. In short,
stemming from the experiences described by the teachers in this
article, data collected for the survey, both quantitative and
qualitative, generally revealed that family support, the practical
uses of math, and an enthusiasm for math in school were positive
influences, while rote drilling and grouping students according
to their ability proved to be negative influences. Most teachers
expressed confidence in their ability to teach math overall.
Keywords: Research, ,
Ref: Peterson13
Author(s): Usiskin, Zalman
Date: Nov. 1997
Title: Application in the Secondary School Mathematics
Curriculum: A Generation of Change
Journal or Publisher: American Journal of Education
Volume, Issue, Pages: v106 n1 p62(17)
Reviewer: Peterson
Date of Review: 4/2/00
As this article describes, in the 1960's, the ideal curriculum, as seen from recommendations in journals and reports, and the implemented curriculum, as viewed from textbooks, referred very little to applications of mathematics outside the subject. Yet today the teaching of real-world applications of mathematics is seen as a necessary component of a good mathematics education. A number of factors responsible for this change include: changing enrollment trends, changing theories toward how students learn and what they can learn, the arrivals of computers and calculators in schools, the public perception of performance of students on standardized tests, and recommendations of business and industry regarding what they would like to see in the people they hire. The change is manifested in various ways beyond the inclusion of problems that relate mathematics to the world outside the classroom.
The most widely used of the newer curricula develops important
application ideas from basic principles over many years. Newer
influences on the thinking of mathematics educators come from
advances in applied mathematics that have resulted in major
changes in the workplace and a corresponding desire that no
students be excluded from significant applied mathematics. As a
result, some of the more recent curricula include entire courses
based on units, each with a particular application theme, with
the expectation that students will work both individually and in
groups.
Keywords: Curriculum, ,
Ref: Peterson14
Author(s): Alper, Lynne; Fendel, Dan; Fraser, Sherry;
Resek, Diane
Date: Nov. 1997
Title: Designing a High School Mathematics Curriculum for
all Students
Journal or Publisher: American Journal of Education
Volume, Issue, Pages: v106 n1 p148(31)
Reviewer: Peterson
Date of Review: 4/2/00
The Interactive Mathematics Program has created a four-year secondary-school curriculum designed to provide a sound mathematics background for all secondary students. This article describes various characteristics that must go into such a curriculum in order for it to be successful with all students and discusses crucial elements that are needed for its successful implementation. Furthermore, it discusses the principles that went into the design and development of the curriculum. They are as follows: 1. Students must feel at home in the curriculum. 2. Students must feel personally validated as they learn. 3. Students must be actively involved in their learning. 4. Students need a reason for doing problems. These principles have been implicit in many projects that have worked to provide more students with successful experiences in mathematics.
Many mathematics educators agree that in order to develop "mathematical power" in our students, the primary focus of mathematics education must shift from the learning of procedures to the solving of complex problems. The goal in this shift is not simply to develop mathematical power in a few students, but to develop it in all students. The need for such a shift in educational direction has been prompted in part by changing needs in the workforce.
The National Research Council recommended that the United States
adopt as a national goal the development of "new curricula
appropriate to the mathematical needs of the twenty-first
century"(National Research Council 1989, p.88). Also in 1989,
the National Council of Teachers of Mathematics (NCTM) set forth
new goals for mathematics education, which are based on the
changing needs of society.
Keywords: Technology, ,
Ref: Peterson15
Author(s): Scott, Brenda H.
Date: July-August 1996
Title: Are We Teaching the Mathematics Skills Students Will
Need for Work in the Twenty-first Century
Journal or Publisher: The Clearing House
Volume, Issue, Pages: v69 n6 p354(4)
Reviewer: Peterson
Date of Review: 4/2/00
The substance of this article implies that high school mathematics should be made relevant by infusing present technology in problem solving. Students should be motivated to learn mathematics by showing the link between mathematical skills and real life. This relevance may be associated with such things as computer programs/software, calculators, concrete objects, etc. It is with the use of these kinds of technological, educational tools that students will grasp the link between this new way they are expressing what they have learned, and problem solving situations present in the real world.
The use of these forms of technology in the classroom allows
students to look at mathematics in a new light of modernism.
It is not a "new rule system" that these students will
encounter in terms of what now applies and what doesn't, but
rather it is a different system by which mathematics students
will learn to look at math as it pertains to the lives they
live.
Keywords: Teaching Strategies, ,
Ref: Peterson16
Author(s): Daisey, Peggy
Date: April 1994
Title: The Use of Trade books in Secondary Science and
Mathematics Instruction: Classroom Strategies
Journal or Publisher: School Science and Mathematics
Volume, Issue, Pages: v94 n4 p170(6)
Reviewer: Peterson
Date of Review: 4/2/00
This article expands on the notion that trade books, which include boigraphies, fiction, autobiographies, discoveries, poetry and non-fiction, can be used for secondary science and mathematics teaching in schools. They include various activities such as projects, song and poem compositions, journal writing and plays. Trade books enable a quick understanding of science and mathematics by promoting literacy and a positive attitude toward the science.
It is the intention of these books to expand the students'
understanding of what exactly they are trying to learn.
Furthermore, the students will be able to better apply or
associate what they are learning to/with ideas or notions
suggested by a source outside of their texts. Learning with
the use of a wide variety of sources develops an optimal
understanding of the ideas and concepts associated with what
is being taught. This approach seems ideal, and promotes a
well-rounded educational experience in the math and sciences.
Keywords: Tests, ,
Ref: Peterson17
Author(s): Brody, Linda E.; Benbow, Camilla Persson
Date: Dex. 1990
Title: Effects of High School Coursework and Time on SAT
Scores
Journal or Publisher: Journal of Educational Psychology
Volume, Issue, Pages: v82 n4 p866(10)
Reviewer: Peterson
Date of Review: 4/2/00
Two studies were conducted to determine (a) whether differential educational experiences contribute to differential growth on Scholastic Aptitude Test (SAT) scores and (b) whether such experiences must occur over a long rather than a short duration to have impact. Specific content knowledge in mathematics/science and verbal areas taught during a short time interval did not increase SAT-M and SAT-V scores even when the content was of the type required to solve SAT problems.
Exposure to academically rigorous educational experiences over
a long time period (5 years) did relate to the development of
abilities measured by SAT. In addition, students who experienced
very large gains on SAT over this 5-year period, in comparison
with students with small gains, were achieving better in a more
rigorous program of high school courses in mathematics and
science for the SAT-M and in verbal areas for the SAT-V.
Results support the position that educational experiences over
time influence SAT scores.
Keywords: Assessment, ,
Ref: Peterson18
Author(s): Bohrnstedt, George W.
Date: Fall 1997
Title: U.S. Mathematics and Science Achievement; How are we
doing?
Journal or Publisher: Teachers College Record
Volume, Issue, Pages: v99 n1 p19(4)
Reviewer: Peterson
Date of Review: 4/2/00
This article exclaims that the negative feedbacks of the
National Commission on Excellence in Education have prompted
policymakers, practitioners and parents to come out with an
improved American elementary and secondary education. It is
necessary to use international standards as a way to determine
the performance of US students. The Third International of
Mathematics and Science Study is a carefully constructed
assessment, which provides useful information about how American
fourth and eighth graders are performing relative to other
nations. It is the findings of such a study that give us an
interpretation suggesting whether or not we need to implement
a universal/particular set of standards to be assessed by every
nation.
Keywords: Geometry, Teaching Strategies,
Ref: Peterson19
Author(s): Richardson, Judy S.; Gross, Ena
Date: March 1997
Title: A Read-Aloud for Mathematics
Journal or Publisher: Journal of Adolescent & Adult
Literacy
Volume, Issue, Pages: v40 n6 p492(3)
Reviewer: Peterson
Date of Review: 4/2/00
This article generally suggests that fictional reading materials
can be integrated in a Math class. It is believed, that through
these texts, a class can discuss terms that are related to math
and discuss the epistemology of those terms. An example is the
text 'The Color of Magic.' Apparently after reading the text,
the students easily understand the term like 'circumference' and
picture it out, because they usually encounter it in geometry
class. They also performed inferential reading, thus enhancing
their reading comprehension skills. Therefore, it is possible
that fictional reading texts can be applied in other subjects as
well.
Keywords: Research, ,
Ref: Peterson20
Author(s): Lee, Valerie E.
Date: Oct. 1998
Title: Sector Differences in High School Course Taking;A
Private School or Catholic School Effect?
Journal or Publisher: Sociology of Education
Volume, Issue, Pages: v71 i4 p314(2)
Reviewer: Peterson
Date of Review: 4/2/00
In this article, we are introduced to this study, which investigated the influence of attending public, Catholic, or independent secondary schools on students' course taking in mathematics, using data on 3,374 high school graduates of 184 urban and suburban high schools from the High School Effectiveness Supplement to the National Education Longitudinal Study of 1988.
With hierarchical linear modeling methods and accounting for factors associated with selection into schools in different sectors, in a nut-shell, the authors found that the private school students took more advanced mathematics courses than did the public school students. However, after controlling for additional differences in selectivity between the two types of private schools, they found that Catholic schools influence their students' course-taking behaviors especially strongly and that the social distribution of course taking is especially equitable in Catholic schools.