This action research began with the definition of the problem to be studied and the formulation of the research questions.
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The problem statement focused on the analysis of the extent to which an authentic Montessori mathematics environment is compatible with the regular mathematics classes in order to fulfill the needs of all students.
In this regard, the research involved comparing the Montessori system with the conventional education system in order to identify the model that best suits learners’ needs.
The research was done in a privately owned Catholic school in Campbell, California. The school’s learning program promotes intellectual, emotional, and physical development of students. Thus, it provided the best setting for conducting an action research in Montessori education.
The participants were recruited from a class that consisted of 12-year-old students. They were mainly from middle and upper upper-middle class families.
Even though, most of them came from families with relatively stable financial backgrounds, nearly 5% of them depended on financial aid. Overall, fourteen students participated in the study.
Several methods were used to collect data concerning learning activities in the class. The methods include the following.
First, I used the results of formative assessments to collect data concerning students’ performance. The assessment results were retrieved from mathematics worksheets and students’ homework.
Second, formal and informal observations were used to collect data. This method was used to collect data concerning students’ participation in class activities, as well as, the suitability of my instructional methods. In particular, is used videotaping to observe my performance in various lessons.
The aim of these observations was to enable me to identify the strengths and weaknesses of my instructional methods. The observations concerning students’ performance were recorded in teaching journals.
Consequently, it was possible to evaluate students’ performance and the suitability of my instructional methods.
Third, focus group discussions were used to collect data from the participants. The participants in these discussions included teachers and students. Through the focus group discussions, I was able to collect data concerning students’ knowledge, opinions, and class experiences.
Concisely, the discussions gave the opportunity to collect data concerning the instructional methods that the students were familiar with, as well as, the challenges that they faced in the process of learning. Furthermore, the discussions enabled me to obtain feedback concerning my teaching methods.
The data collection methods that have been described in the foregoing paragraph were used to collect information through learning activities that took place in the class. Verbally administered questionnaires and interviews were also used to collect data.
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Concisely, the questionnaires and interviews were used in the evaluation of students’ understanding and performance in each activity. This involved asking students questions that were related to the learning activities.
The learning activities or the lessons that have been completed and from which data has been collected include the following.
The first, exercise involved evaluating the students’ knowledge and skills in mathematics. The tests focused on skills such as ability to write numbers from 0 to 9, applying, and number concepts. The evaluations were conducted through written tests and the scores are indicated in appendix A.
Having tested the students’ math skills, I proceeded to the next exercise, which involved evaluating the learners’ sensorial skills. The evaluation was done with the aid of Montessori sensorial items such as flowers. The students were expected to classify the flowers into different categories.
The assessment for this exercise was done through verbally administered questionnaires. Each questionnaire had ten questions with 10 points each. Red and blue Montessori rods were used to assess the students’ ability to apply the concept of more than and fewer than.
The students were assessed individually using 10 questions, which focused on testing their ability to compare numbers between 1 and 10. Numeral counters were used to demonstrate the concept of odd and even numbers.
The evaluation involved asking the students to place the counters under each number in order to illustrate the odd and even arrangement, as well as, to demonstrate the concept of less than or more than. Students’ scores in these activities are recorded in appendix B.
The students’ ability to apply the concept of addition and subtraction was tested using California state standard curriculum content and Montessori materials. Colorful illustrations are often used to attract students’ attention.
Even though the pictures distracted students from their work, they were able to visualize math concepts after the Montessori addition and subtraction materials were presented to them. Appendix C shows the students’ performance in this assessment.
Students’ mathematical skills were also evaluated through positive sake games, the hundred board, the hundred chains, and teen board. The test strategy and questions that were used for this assignment are listed in appendix E. These assessments were done in the first and second quarter of the year.
The second phase of classifying objects involved the use of drawings, photographs, graphic organizers among others. These items usually motivate students to learn. The exercise involved a problem solving process in which the students asked themselves questions regarding the things they did and how they did them.
The students’ performance was reviewed on a weekly basis. The conclusion on these activities is that Montessori sensorial materials enable children to understand fine details.
Additional lessons included the study of fractions, money, and clock (time). The faction lesson began with an explanation of the importance of studying fractions. The students were provided with pieces of paper, which they were required to fold into half in order to understand the concept of dividing things equally.
They were also expected to identify the shapes that they created by folding the papers. Additionally, the students completed the dotted paper and shape-drawing exercises, as well as, dividing shapes equally. The evaluations were done using 10 questions with 10 marks each.
Using Montessori material involved dividing an apple into smaller parts in order to demonstrate the concept of the whole, half and quarter. I also made various shapes and divided them into equal parts.
The students were expected to explain why they thought the parts were equal or unequal. Evaluations for this assignment were based on a standard formative matrix plan and rubrics.
Using money to teach number concepts improves students’ understanding. The money lesson was meant to enable students to use their math skills to count coins. The concept of one cent was presented with the aid of red and blue number rods, as well as, number cards.
The classroom was setup as a shop so that children could practice the concept of buying. I dollar, half a dollar, and a quarter dollar were used to represent the concept of one whole, half and quarter.
In the clock lesson, the concept of one whole was used to explain the rotation of the minute hand from 12 to 12. Assessments were done using scoring rubrics. Additionally, anecdotal evidence was measured using a scale of 1 to 4.
Having completed these exercises, the next stage will involve using Montessori materials to evaluate students’ ability to apply concepts such as the decimal system, addition, subtraction, division, and geometry.
The materials that will be used to demonstrate the decimal system include introduction tray, building tray, large numerical cards, 45-tray, nine-tray, and the change game. The concept of addition will be illustrated using bank materials, stamp game materials, and bead frame.
The materials will be used to create and solve mathematical problems by the students. Subtraction exercises will also involve the use of bank materials, stamp materials, and bead frame. These materials will be used to construct subtraction problems and answers.
Multiplication exercises will be presented with the aid of bank game, multiplication board, and bead box. Bank materials will be used to illustrate multiplication operations. The concept of division, will be illustrated with the aid of bank game, division board, stamp game, bead frame and dot board.
Bank materials will help in illustrating division operations. Students will slide down their fingers until they meet the answers in the division board. Finally, geometry exercises will be demonstrated using cylinder grid, geometric solids, and cards, as well as, constructive triangles and other shapes.
California State Board of Education Sacramento. (1999). Mathematcis Content Standard for California Public Schools. California: California State Board of Education.
Har, Y., Segaran, N., & Aziz, D. (2008). Early Bird Kindergarten Mathematics. New York: McGraw-Hill.
McDonelle, R., Tourneau, C., Ackler, K., & Ford, E. (2001). Progess in Mathematics. New York: McGraw-Hill.