Everyday Mathematics
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Contents |
[edit] Introduction
It is not a surprising thing to see curriculum change within a school district. It happens all the time anymore. People are constantly looking at different ways to instruct students in accordance with new research and theories.
These changes in and of themselves are not bad things. In fact, they can often be great. However, frequent changes (and some with bad results) have made many instructors skeptical of such alterations and left them wondering whether they are warranted.
So, how does one know whether a new method, a new idea, or a new textbook is a good choice? Research seems to be the plausible answer. However, many relates to“…the ominous nature of the word “research” and its associated baggage. The mere inclusion of the word in the title of articles or workshop offerings often causes teachers and administrators to look for an escape route…” (Johnson 2000). What happens, also, when research is not explicit and there are varied findings and opinions from authorities reviewing the material?
This is very much the case with Everyday Mathematics. It seems there are few that take the opinionative middle ground. Researchers, professors, teachers, parents, and many others have all been asked to weigh in and the findings are not exactly clear. Depending on with whom you speak, Everyday Mathematics (EM) may appear to be a great new transition in mathematics instruction or the worse thing that has happen in mathematics instruction in recent years.
Knowing this, what are educators to do? As always, it seems they must exercise good judgment upon receiving as much information as possible. What follows is an attempt to give the information so that the reader may synthesize and it and determine what it all means.
[edit] Description of the Program
Scope and Sequence:
Surely, many can remember the traditional and seemingly generalized scope and sequence of mathematics instruction. Perhaps, you as the reader can recall being taught how to multiply in third grade and divide in fourth. It seemed that there was a flow from mastery of one topic to the next. Well, “…[t]he developers of Everyday Mathematics believe that the groundwork for mathematical literacy should begin at a much earlier age than offered by traditional mathematics programs…”(Current Curriculum 2002).
This idea of a “spiral” curriculum, where mastery is not required before the introduction of new topics, is difficult to swallow in relation to their own experience. Many feel more comfortable seeing an obvious progression of skill build-up occur (student masters one digit addition and moves on to two digit addition) In opposition to this view, however, “…Everyday Mathematics was designed to take advantage of the spacing effect…” (Braams 2003). It relies on the notion that regular reinforcement of important skills is necessary, emphasizing that skills should appear multiple times and throughout a course of study. The key principle in regards to spiraling and distributed practice is that mastery and fluency in basic skills are goals that should be achieved long after they are first introduced (Braams 2003).
In accordance with this belief, the Everyday Mathematics program is set up around seven mathematical strands. Those seven are as follows:
• Algebra and Uses of Variables
• Data and Chance
• Geometry and Spatial Sense
• Measures and Measurement
• Numeration and Order
• Patterns, Functions, and Sequences
• Operations
• Reference Frames (About Everything Mathematics 2003)
Features of the Program:
Beyond the scope and sequence, EM has several other discerning features. The following is a listing of them, as well as an explanation for how the program incorporates them.
• Real-Life Problem Solving-
As its name implies, EM places a great deal of focus on real-world problems. A great deal of instruction revolves around application of mathematical concepts in everyday situations.
• Balanced Instruction-
“…Learning is conducted in whole group, small group, and individual settings. Students experience open-ended questions, hand-on explorations, supervised practice, and long term projects…” (Current Curriculum 2003).
• Multiple Methods for Basic Skills Practice-
Students practice basic skills through daily review problems, mental math activities, flash cards, games, homework, etc.
• Emphasis on Communication-
Discussion is very important to the program. Students are asked to explain their problem solving strategies. Students are also expected to listen and learn from other students.
• Enhanced Home/School Partnerships-
Information is sent home to help parents work with their children. Homework is structured so that students are meant to rework problems from previous lessons with adults in the home.
• Appropriate Use of Technology-
Technology is used within the program in a way that is meant to instruct children when and where it is appropriate to use it. This is especially true when it comes to calculators.
[edit] Application in the Classroom
When educators, namely teachers, look at information about curriculum, descriptions are nice, but application of that curriculum is crucial. Teachers understand that theory and rationale for a program means nothing if it can not be practically applied to the classroom. Below is an outline of the components of EM as they are generally seen throughout the curriculum.
Lessons:
A typical lesson outlined in one of the teacher’s manuals includes 3 parts.
1. Teaching the Lesson- This is where the new content is introduced.
2. Ongoing Learning and Practice-In this section, material is reviewed for maintenance purposes.
3. Options for Individualizing- Here is where options for extending or reteaching concepts are presented. There are also suggestions for enrichment.
(Click link to view a sample of a lesson http://everydaymath.uchicago.edu/samplelessons/2nd/index.html)
Daily Routines:
Everyday, there are certain things that each EM lesson requires the student to do routinely. These components can be dispersed throughout the day or they can be part of the main math lesson.
• Math Messages- These are problems, displayed in a manner chosen by the teacher, that students complete before the lesson and then discuss as an opener to the main lesson.
• Mental Math and Reflexes- These are brief (no longer than 5 min) sessions “…designed to strengthen children's number sense and to review and advance essential basic skills…” (Program Components 2003).
• Math Boxes- These are pages intended to have students routinely practice problems independently.
• Home Links/Study Links- Everyday homework is sent home. Grades K-3 they are called Home Links and 4-6 they are Study Links. They are meant to reinforce instruction as well as connect home to the work at school.
Supplemental Aspects
Beyond the components already listed, there are supplemental resources to the program. The two most common are games and explorations.
• Games
• Explorations- One could, perhaps, best describe these as mini-projects completed in small groups. They are intended to extend upon concepts taught throughout the year.
General Comments about Application
Implementing all of these components is not an easy task. Time is an issue that must be considered. Attitudes, those of students and teachers, can also be a problem. “…Instead of fostering a competitive environment and teaching students through logical deduction, Everyday Mathematics uses a collaborative milieu and allows students to draw their own conclusions after seeing recurring math patterns. Teachers facilitate the process instead of teaching it… (Knight 2005). Teachers must also have faith in the spiral curriculum in order to implement and assess student work. Teachers, who are bent on grading for mastery, may become frustrated in application of EM.
[edit] Evidence of effectiveness
As mentioned earlier there has been much discussion over the effectiveness of EM. It is important to mention that “[d]espite its critics, Everyday Mathematics has 13 years of university research behind it …” (Knight 2005).
In comparison to other textbooks and programs, 13 years seems amazing. Within these years, a great deal of research has piled up. What does the research say? “The research evidence about Everyday Mathematics (EM) almost all points in the same direction: Children who use EM tend to learn more mathematics and like it better than children who use other programs.” (University of Chicago 2005).
Research was the building block for the program. It was not developed by a publishing company, but as a research project for the University of Chicago. “Each grade level of the Everyday Mathematics program went through a three-year development cycle that included a year of writing, a year of extensive field-testing in a cross-section of classrooms, and a year of revising…” (University of Chicago 2005).
No other program has been through so much testing and research. It is hard to discount a program’s effectiveness, no matter how much controversy, when it is backed by a mountain of research. Nevertheless, it has been challenged and this is the topic of the next section.
[edit] Critics and their rationale
Many look on at the EM program and have opinions to voice. Criticism of EM has come from all directions.
One direction from which criticism comes is from parents. “..[S]uch programs as Everyday Mathematics raise the eyebrows and sometimes the ire of parents simply because they don’t use the traditional methods parents are accustomed to…” (Knight 2005). It is difficult for some to trust EM because it seems to differ so much from the math they grew up with. Some professional mathematicians also fear EM. Many argue against it based on the same grounds that parents do, claiming that it overlooks the basics or does not promote the use of standard algorithms that have been tested and used for a long time.
However, Wertheimer (2002) points out that “…[t]he mathematicians are among the few survivors of the traditional mathematics program. They are trying to apply what they know to the entire population”. He also has a great deal of reservations about the ability of these mathematicians to evaluate the complexity of educational methodology that can help everyone achieve. Mathematics education should help promote the success of everyone not just those naturally successful at math. (Wertheimer 2002).
Beyond parents and professional mathematicians, even teachers have joined in the argument. I have personally seen teachers resist the methods of this program. They fear the new and unfamiliar as do most.
However, after the first year or so, I began to see an uprising of teachers, who had previously detested EM, began to support certain proponents of the program. Nevertheless, many still continue to dispel any comments of success.
In one final note about my research of the critiques of EM, I want to mention a common complaint. I was surprised to see that many argued that the program was not the problem, but implementation was. Critics claimed that the content was difficult for teachers to teach without a great deal of training. Something that I think would be advocated by people on both sides of the fence of this argument.
[edit] Signed "life experiences", testimonies and stories
I think that this is a good idea to stimulate the minds of young students with math. I've noticed during my time tutoring at Champaign-Urbana school, alot of students either have math anxiety or dislike math. This causes them to not think math is important, thus they won't even memorize the multiplication table. This makes math extremely tough for them later on in life. I think this is a problem that stems from grade schools. This is one way to reach math to them early so they believe math is important to their future. - John N. Janowiak
Using the spiral curriculum of Everyday Mathematics requires knowledge of the program prior to teaching it. I was able to use it during my student teaching experience and think that was very helpful. I was able to talk to my cooperating teacher about the pros and cons of it and how she used it effectively in her Kindergarten classroom. She incorporated it everyday in morning meeting and then again during math time. The lessons were short, but the children seemed to grasp the concepts by using the manipulatives. I think that the manipulatives or concrete objects that accompany the curriculum are key to using Everyday Mathematics effectively. -TYM
I try to always teach math as real life scenarios. I urge each student to ask me "When will we use this in real life?” if they don’t understand why we are doing something. This helps the students understand they will use many of the lessons we do later in life. If we make a real life story problem out of our lesson, the students tend to pay a little more attention and have more interest in the lesson. – D. Donner
Both of my children have had Everyday Math during their schools years. I liked the concept of making the math real - finding a real problem and solving it with the concept they were learning. The Home Links were also a positive because each night they had math homework that we completed together. The only thing I was not happy about with Everday Math was the method they use to teach multiplication and division. It seemed like a crutch and to this day still doesn't make sense to me. I went ahead and taught my children the old fashion way of doing multipliation and long division. My eldest does both the old fashion way but did tell me that the Everyday Math method helped explain "why" better then my method. ~BSmall
I taught Everyday Math in my 4th grade classroom this past year. It was my first experience with the program and, although I had my doubts, I am quite pleased with the affect it had on my students' mathematical skills. My initial apprehension was with the amount of time it would take to teach the program, as well as prepare the materials for my students. Like all teachers, I had to mold the program to work in my classroom and sometimes I had to leave some things out. It must be noted that the program works on a spiral so the fourth grade lessons are dependent upon students having prior knowledge from the previous years of Everyday Math instruction. Therefore, the first couple years of the program can be difficult. It might be necessary to take additional time to review certain skills prior to teaching a new lesson. Once I accepted that my students would not master all the skills that they are expected to because they had not had prior Everyday Math instruction, it was easier to just expose my students to new ideas and teach for mastery of the standards. Overall, I liked Everyday Math because it stressed that there is almost always more than one way to solve a problem. The program actually teaches more than one way to compute long division and multiple digit multiplication, as well as several other algorithms. It also encourages students to decide for themselves which strategy works best for them. It allows more opportunity for student success. The combination of the multiple strategies, everyday applications, and math games got my students excited about math. I am excited to see what my students will be able to do once they have had it from the beginning of first grade. --Amanda P.
Last year was my first time teaching with Everyday Mathematics in my second grade classroom. At first, I was extremely apprehensive about using this type of math program in my class. In previewing the teaching manuals and literature on the program, I knew that it would require a lot of advanced preparation on my part. Not only that, but the program would require me to let go of the idea of "direct" instruction, and instead force me to change my approach to teaching math to a more inquiry-based approach where my students would be more responsible for much of their learning. With Everyday Mathematics, the students would be exploring mathematical concepts and making sense of these concepts using their prior knowledge, hands-on manipulation of objects in mathematical situations, as well as in making connections between math and their everyday lives. Despite my initial apprehension, I found the program exciting in that it was not simply a regurgitation of facts and equations. I also found my students more excited about and engaged in mathematical thinking and activities. They were learning concepts and making connections to the concepts, not memorizing facts. It will be exciting to see how the implementation of and results of using this program change over the next few years. -D. Jacob (June 2006)
I taught this program for the first time this past year. I love it! It was difficult to plan since there are so many components to each lesson and the management of the materials was also a challenge. But, I feel that this upcoming year will be phenomenal. Furthermore, I was a little frustrated that my students were not all “getting the material” like I thought they would. I was used to teaching for mastery. But, I have learned to pull back a bit because the spiral effect does work if you give it a chance. This year’s class will have been taught from this program as well so I will be better able to see how the skills are developed. ~S. Ward
This is my first year teaching with this program and I am enjoying being able to show the students many different ways to solve problems. I also think it creates a good foundational understanding of math concepts. It is a struggle at times to not teach and reteach until the students completely understand a concept, but I am beginning to see how it continues to build throughout the year. E. Kilroy
I have been teaching Everyday mathematics for three years now. At first I struggled with the spiral effect the program uses. They will only introduce a skill to the students and later (even years) they will continue to reteach the skill. Therefore some of the skills I teach to my first graders are not expected to be "mastered" by the end of first grade. When parents see their children struggling with a math concept in first grade that is not expected to be mastered until third grade they have a hard time with it. I understand as well the frustration. I have to just tell myself that they will catch on more each time. I know that in the long run it will benefit them. When a person repeatedly sees something they remember it more. ~R.U.
I teach high school mathematics using the Saxon textbook series. It sounds as though it has the same philosophy as the Everyday Mathematics program. Students are not expected to master a topic the first time they see it. The Saxon textbook series assumes at least 4 days on a new topic before the students build on that topic. The Saxon textbook series is controversial, but my experience says that teachers who use it for a couple of years love it and teachers who have never used it or have just begun to use it don't like it. It is difficult to get used to. I feel that I teach a little and facilitate a lot. The most valuable teaching is through answering questions rather than lecture. I do think that retention is much much better with Saxon. Students are constantly reviewing through the homework and the difficult problems eventually turn into the routine problems. R. Grunloh
We use Everyday Mathematics at our school. Our kids have learned so much and enjoy all the things they get to do with the program. One of the favorite activities the kids love is the games. There are so many educational games that enhance a skill being taught in the program. Everyday Mathematics also allows the students to be able to explore all different aspects of a given skill. -RU
I believe Everyday Mathematics would be very beneficial for lower-performing students. I feel the lack of motivation and effort stems from the fact that most of these students do not understand why math is so important. EM does a wonderful job of providing real-world scenarios and problems for students to solve. It is also important for these students to practice skills over and over, which EM requires. -JB
[edit] Links of Interest
Everyday Mathematics Center Website http://everydaymath.uchicago.edu
http://www.mathematicallycorrect.com/bishop4.htm
http://www.mathematicallycorrect.com/everyday.htm
http://www.chatham.edu/PTI/2003%20Units/Looking%20at%20Everyday%20Mathematics/abstracts%20math.htm
http://www.nychold.com/let-carson-031218.html
http://www.nychold.com/em.html
http://everydaymath.uchicago.edu/educators/references.shtml
[edit] References
About Everyday Mathematics: Research & Development. (2003) http://everydaymath.uchicago.edu/about.shtml#scope. Retrieved June 27, 2006.
Bas, Braams. (2003) Spiraling Through UCSMP Everyday Mathematics. http://www.nychold.com/em-spiral.html. Retrieved June 27, 2006.
Current Curriculum: About Everyday Mathematics. (2002) http://www.ashlandhs.org/Curriculum/currprojects.html. Retrieved June 27, 2006.
Knight, Michelle. (2005) Everyday Math Has Its Proponents. http://www.toacorn.com/News/2005/0331/Community/018.html Retrieved June 27, 2006.
Johnson, Jerry. (2000) Teaching and Learning Mathematics: Using Research to Shift from “Yesterday” Mind to “Tomorrow” Mind. http://www.k12.wa.us/research/pubdocs/pdf/MathBook.pdf. Retrieved June 27, 2006.
Program Components for Grades 1-6 (2003) http://everydaymath.uchicago.edu/samplelessons/lessonbackground.html#part1. Retrieved June 27, 2006.
University of Chicago Mathematics Project. (2005) http://everydaymath.uchicago.edu/educators/em_research_summary_8.pdf. Retrieved June 29, 2006.
Wertheimer, Richard. (2002) Forum: Making It All Add Up. http://www.post-gazette.com/forum/comm/20021110edwert1110p3.asp. Retrieved June 29, 2006.
