Hi, I'm Robert!
For my fellow teachers, I've constructed a model of teaching that I've summarized as the puncturing of space with pedagogical objects. . . The term "objects which puncture space" may help solidified one's sense of how pedagogy can be described within its new conceptual framework. Teachers who see the world in this manner should become more fully invested in the enterprise of teaching and learning.
Teaching Methematics
S.T.O.R.E.S.
for teachers
S.T.O.R.E.S.
for students
Handbook
The Euclid Project
Teacher's Manual
The Euclid Project
Student's Manual
An Introduction
to Geometer's Sketchpad
The Euclid Project
Pre-Algebra
Teaching Mathematics
"Teaching Mathematics Puncturing Space: A Developing Pedagogical Tool" uses a diverse
body of research to clearly introduce important ideas related to learning. Theories from
the fields of neurology and cognitive development about how students obtain, synthesize
and retain information are examined and cohesively presented.

With an in-depth discussion of how educators compete with predictable outside stimuli
as well as with the internal life of the student mind, Dr. Mason explains the idea of
using a combination of objects as pedagogical tools to 'puncture' the learning space to
re-engage the student and to re-establish attentive behavior.

This readable book is valuable to educators in all fields not just to those teaching
Mathematics, and not just to those teaching in lower and secondary schools. Educators
will think carefully and differently about how information is delivered and processed
in the classroom, after reading this book.
S.T.O.R.E.S.
(for teachers)
Structured Teaching of Research and Experimentation
Skills (S.T.O.R.E.S.) science curriculum for elementary
school and middle school students is a process oriented
approach, focusing on classical principles of induction
and deduction, evidence gathering, and hypothesis
building, and empirical testing and refinement of
hypotheses that highlights scientific procedures.
S.T.O.R.E.S.
(for students)
Structured Teaching of Research and Experimentation
Skills (S.T.O.R.E.S.) science curriculum for elementary
school and middle school students is a process oriented
approach, focusing on classical principles of induction
and deduction, evidence gathering, and hypothesis
building, and empirical testing and refinement of
hypotheses that highlights scientific procedures.
Sketchpad Basics
Handbook
Sketchpad Basics Handbook is designed to introduce elementary school and middle school students
and teacher to Geometer’s Sketchpad. The Sketchpad, is a construction tablet on which one draws models of geometric shapes, transforms them, colors them, measures them, and animates them. The models invite students to explore, represent, solve problems, construct, discuss, investigate, describe, and predict. Implicit to these functions is the ability to build mathematical models of simple and complex ideas. The Sketchpad allows students to engage in “doing mathematics,” which is emphasized in the National Council of Teachers of Mathematics (NCTM) Standards.

The investigations encourage students to work together in pairs and small groups, and to build on their knowledge by applying their knowledge to new information.

Sketchpad introduced through a series of explorations. All of the explorations are designed specifically to teach how to use the “tool box.” They represent technical exercises. That is, they teach how to use the drawing tools, and how to use the command menus to accomplish specific task. In some investigations students will replicate as set of instructions and then evaluate their findings. In other activities students are free to create their own investigation.
The Euclid Project
Teacher's Manual
The Euclid Project computer-based geometry program uses a scientific-experimentation approach to
providing middle school students with an intuitive un?derstanding of geometry as a precursor to the formal study of geometry later (e.g., in the 10th grade) and as a mediator for application of geometric understanding in a variety of contexts.

This scientific-experimentation approach to teaching geometry involves pre?senting the students with a mathematical hypothesis
(e.g., a line drawn across two sides of a triangle parallel to the third side divides the first two sides proportionally),
then having them use a “construction tablet” (Logo, Geometer Supposer, Geometer’s Sketchpad computer programs) to systematically
generate a series of cases to test the validity of the hypothesis (e.g., create a triangle and line parallel to a side,
then use animation to gener?ate a series of such triangles to see if the hypothesis holds for all of them).
The Euclid Project
Student's Manual
The Euclid Project computer-based geometry program uses a scientific-experimentation approach to
providing middle school students with an intuitive un?derstanding of geometry as a precursor to the formal study of geometry later (e.g., in the 10th grade) and as a mediator for application of geometric understanding in a variety of contexts.

This scientific-experimentation approach to teaching geometry involves pre?senting the students with a mathematical hypothesis
(e.g., a line drawn across two sides of a triangle parallel to the third side divides the first two sides proportionally),
then having them use a “construction tablet” (Logo, Geometer Supposer, Geometer’s Sketchpad computer programs) to systematically
generate a series of cases to test the validity of the hypothesis (e.g., create a triangle and line parallel to a side,
then use animation to gener?ate a series of such triangles to see if the hypothesis holds for all of them).
An Introduction to
Geometer's Sketchpad
This workbook is designed to introduce elementary school and middle school teachers to Geometer’s Sketchpad.

The Sketchpad, is a construction tablet on which one draws models of geometric shapes, transforms them, colors them, measures them, and animates them. The models invite students to explore, represent, solve problems, construct, discuss, investigate, describe, and predict.

Implicit to these functions is the ability to build mathematical models of simple and complex ideas.
The Sketchpad allows students to engage in “doing mathematics,” which is emphasized in the National Council of Teachers of Mathematics (NCTM) Standards.
The Euclid
Pre-Algebra
description

STORES and STEM for students Phase 3

A Phase III Example of a controlled experiment and statistical analysis to test their hypothesis about Mealworms preference Bran Flakes by Two Sixth Graders.

 

Do Mealworms (Tenebrio Molitor) Really Prefer Bran Flakes?

 

Rachel Ambats, Hunter College Elementary School, 1977
Elizabeth Taxin, Hunter College Elementary School, 1977

Abstract

This paper is about the mealworm, scientifically categorized as the Tenebrio Molitor. This beetle belongs to the Tenebrionidae family containing more than 10,000 species. The mealworm, a black or dark reddish brown thirteen to seventeen mm. animal, is the larvae stage of the Darkling Beetle. This beetle developed its name on account of its nocturnal habits. When the larva is fully grown, it is about one and a quarter inches long, and is yellow and distinctly segmented. After the larva has developed in to a full grown beetle, it is one and half inches in length and its color has changed to black.

Taste and smell sense organs include a great amount of hair-type receptors with other types of receptors such as pegs, which are found on the antennae, plaps and legs; they aren't sensitive to touch, but by responding to dissolved substances, they produce the chemical senses of taste and smell.

Smell receptors are often found on the mealworms antennae, although some are found on the palps. In many beetles, smell is useful in locating food. It also may bring the beetles of opposite sex together. The intensity of smell is important, especially that of water. Humidity receptors are found on the antennae. It is not known how these work, although they seem to respond to the drying power of air. Mealworms prefer fairly low humidities, but after being dried, their preference is reversed. We explore the search behavior of Tenebrio Molitor given the choice between food and an ideal temperature.

BACKGROUND

We read three articles concerning the mealworm species. We agree with some of the authors points and have some question with others. The author of the first two articles is anonymous; we do know, however, that this author is one of the author's of the Teachers Guide For Behavior Of Mealworms. In the first article, this author thinks that disputes will arise about where a mealworm travels in his exploration of a exploratory box. The author also says that it is necessary to record the time the mealworm spends in different parts of the box. The article also suggests that one might use a metronome's ticks to time how long the mealworm stays in each part of the box. He tested his theory and recorded the time the mealworm was stationary in all of the five specified parts of the box (see Chart A)

In this article, a more simplistic procedure is suggested in which one measures the mealworm's position in the box at regular specified intervals; i.e 1 minute.

By this same author another experiment was posed. The question for this experiment was how does a mealworm know that it is under bran? He thinks that there is a difficulty. This difficulty is that there is more than one stimulus involved in the mealworm's ability to stay underneath bran. The amount of variables is so numerous that it is impossible to control them sufficiently.

The author leaves certain question unanswered; "Do mealworms stay under bran because they eat it? Will the mealworms show a preference for bran as opposed to other materials such as pencil shaving or chalk dust?"

Professor Blaustein, of Hunter College of the City University of New York, asks the readers in his her article why the mealworms enjoys staying under cereal; i.e. bran? She posed five hypotheses; 1) because it is the mealworms food supply; 2) because it is dark; 3) because they like weight on their back; 4) because it is quiet; 5) because it has an odor which is pleasing to them.

After researching these three experiments, we have analyzed them and will state our opinions on them.

For the first experiment, we agree with the author that there will be disagreement about where a mealworm travels in his exploration of a box. We also agree with the author in that it is necessary to note the time a mealworm spends in each part of the exploratory box in a specific manner. The author suggests that one uses a more simplistic way to record the mealworm's positions in various parts of the box at certain intervals. However, we feel that this is not necessary and that the technique of timing the mealworms with a metronome's ticks is quicker and more precise.

We also agree with the author of the second article that there is more than one stimulus involved in the mealworm's ability to stay under bran. We believe that the two questions posed in the second article are important. We also think that that latter of the two questions can indeed be answered by performing an experiment which has bran one time and other materials the other time.

We agree with Professor Blaustein in her five hypotheses about why mealworms prefer the bran environment.

We found separate experiments done using bran, mealworms, and smell but few done on observing the effects of the three variables acting together. For some reason, we feel the most things happen together with other things and that we would get a more accurate picture if we study them together.

DESIGN

After reading about the experiments done by other students and discussing what Professor Blaustein's hypotheses we decided to study the following

question. Given the choice between two environments would mealworms choose the environment that contains bran? We thought that the mealworms would gravitate to the bran. The independent variables are moist bran and a wet sponge. The dependent variable is the chose behavior of the mealworms defined as how long the stay in the area as measured by the number of ticks on the metronome.

Apparatus

The laws of probability suggest that 50% of the mealworms will go to the bran and 50% of the mealworms will go to the wet sponge. We think the there is something special about bran flakes that will attract the mealworm therefore more mealworms will travel to the bran.

We placed ten untrained mealworms into a 2.5' long, 7'' high box. This box will have ten small ventilation holes on the left and right sides of it, and will also have a five inch peep hole on the top so that we can observe the mealworms while we conduct our experiment. In the interior of the box there will be a vertical line exactly down the middle.

On one side of the box will is a box of moist bran, and on the other side well be a moist clean sponge of the same height (7 in.) and width (7 in.) as the box of moist bran. The side on which the moist bran and the moist clean sponges are placed on will vary. The reason for this variation is so that we can make sure that the mealworms do not prefer right or left.

Experiment

Ten mealworms were placed on the center line of the main box. Each of these mealworms will be labeled with a piece of scotch tape with a randomly chosen number written on it. Which mealworm gets which number will be randomly assigned as well. We will allow forty minutes for the mealworms to move to either side of the box.

We recorded the number of mealworms with move towards the moist bran and the number that moved towards the moist clean sponge. (Chart not include)

Data Analysis

We wanted to know if given the choice between to condition would the mealworms show a preference for one of them. As mentioned before the laws of probability would suggest that half of the mealworms should go the bran and half of them should go the moist sponge. We then expect five/tenths (.50) of them to go to bran and five/tenths (.50) to go to the moist sponge. But, we really feel that there is something special about the bran that will cause the mealworms to be attracted to it, therefore, we hope to observe more worms on the bran side. After we do the experiment and collect the data we will compare what we observed to what we expected to see by computing Chi Squared probabilities.

X(squared) = Sum of the [(observed results - what we expected to see)(squared) / expected]

We changed the method of analyzing the raw data because we forgot to consider the sample size. Instead, we used the T-test to see if the difference between the means were caused because we did something wrong or because bran is really preferred by the mealworms.

DISCUSSION

In doing our experiment we altered a few conditions;

1. We transformed our question into a hypothesis: Given the choice between two environments, mealworms would choose the environment that contains Bran.
2. We altered the amount of time that the mealworms spent in the experimental box during testing. The new time was four and a half hours.
3. We changed the way in which we recorded our raw data. The new procedure was: # of mealworms near bran, # of mealworms near sponge, # of mealworms in middle.
4. We had to redesign the box because it was too big.
5. Before we started our experimentation, we conducted an experiment using a control group; which was a group of ten mealworms put in the experimental box with neither bran nor sponge on either side. The purpose of this was to make sure that the mealworms did not simply "prefer" the left or right sides of the experimental box. We found out that the group of mealworms did not have a preference.

 

 

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