<p> PERCEPTIONS OF TEACHERS ON THE USE OF HISTORY IN TEACHING MATHEMATICS</p><p>Engr. Maria Cristina Agustin-Sicat Holy Angel University Angeles City, Pampanga, Phils. [email protected] </p><p>Ms. Angela Faith B. Daguman Ateneo de Manila High School Quezon City, Philippines [email protected] </p><p>Ms. Ivy Gay O. Salvador Pampanga State Agricultural University Magalang, Pampanga, Phils. [email protected]</p><p>ABSTRACT In this study, the researchers sought to investigate the perceptions of teachers on the use and the extent of utilization of mathematics history in teaching mathematics. A total of 72 teachers across the three levels- primary, secondary, and tertiary, from both public and private schools participated in the study. It was found out that there was no significant difference in the perceptions on the use of history of teachers across level but there was a significant difference in the perceptions of teachers depending on whether they came from a private or public school. In terms of the extent of use, teachers, regardless of the level and type of school in which they came from, sometimes use teaching methods which incorporate the history of mathematics. Categories and Subject Descriptors: A.1 Introductory and Survey General Terms: Documentation, Human Factors, Management Keywords: History of mathematics, mathematics education, perceptions of teachers, teaching methods 1. INTRODUCTION students to outstanding mathematicians, History of mathematics has always been according to their level of understanding. The a special branch of mathematics that actually all same situation remains nowadays. Lectures and those concerned with the process of learning and seminars in which mathematical discoveries, even teaching mathematics demonstrated their local and insignificant, could be traced with interest to. That interest was from primary school analysis of historical information about them,</p><p>[1] provide for students better understanding for decades. Nevertheless, before taking as different ideas and theories, motivation for viewpoint that history must be integrated in further learning, and show brilliant richness of mathematics, an obvious question is, “why should human activities in mathematics. It is therefore the history of mathematics have a place in fitting on us, educators, to keep the narrative mathematics education?” Addressing this alive and never let the history of mathematics question is difficult, since the answer is subject to becomes just a myth of antiquity and, thereby, one’s personal definition of teaching and is also help perpetrate its fall into disuse. bound up with one’s perspective of mathematics. It is in this regard that the researchers embarked in a study aiming to find out the extent The role of using the history of of utilization of the history of mathematics in mathematics in the teaching and learning of teaching mathematics. Particularly, the research mathematics is a major area of research which task attempted to pinpoint worthwhile has made important contributions to the field of considerations to help teachers from primary to mathematics education (Fauvel & Maanen, 2000). tertiary level, in both public and private schools, For example, the use of the history of to think about what history can really do for the mathematics in instruction provides opportunities curriculum and for their teaching. for students to deepen their mathematical understanding and can help students gain a better Statement of the Problem understanding of the meaning of mathematical concepts, methods, theories, and proofs (Tzanakis This research was designed to determine & Arcavi, 2000). In most institutions of higher the different perceptions of teachers on the use education, mathematics is taught as an abstract of history in mathematics education. Specifically, science without much attention given to teaching it focused on the viewpoint of mathematics what mathematics is about and how teachers, from primary to tertiary levels, in both mathematical ideas developed. In order to bridge public and private schools regarding the extent of this gap, the history of mathematics can serve as a utilization of the history of mathematics in major pedagogical tool for the teaching of higher teaching mathematics. mathematics. Concerning the use of the history of Thus, the research aimed to look into mathematics as a pedagogical tool, there exists a the following questions: plethora of classroom resources for teachers 1. How did teachers perceive the meaning of (Swetz, Fauvel, Bekken, Johansson, & Katz, 1995). the following: However, there is currently a limited amount of a. History research focused on how the historical b. Mathematics development of mathematics contributes to 2. To what extent did teachers make use of students’ growth of mathematical understanding. history in teaching mathematics? The virtues of incorporating history into 3. How did teachers perceive the use of history mathematics education have received in teaching mathematics? considerable attention and have been discussed 4. Is there a significant difference on the perceptions of teachers in utilizing history in teaching mathematics across levels? 5. Is there a significant difference between the Permission to make digital or hard copies of all or part of perceptions of teachers in the public and this work for personal or classroom use is granted private schools regarding the use of history in without fee provided that copies are not made or teaching mathematics? distributed for profit or commercial advantage and that 6. Is there an interaction effect between the copies bear this notice and the full citation on the first type of school and the different educational page. To copy otherwise, or republish, to post on servers levels? or to redistribute to lists, requires prior specific permission and/or a fee. [2] Research participants were teachers Significance of the Study from primary to tertiary levels, in both public and The result of this study will be useful to private schools where the researchers are the following: currently connected with. It cannot be interpreted as extending to other populations. This The Curriculum Experts. This will provide necessitates the researchers to make use of empirical data which will be utilized in curriculum purposeful sampling technique in selecting their planning as well as in the development of lessons respondents. that match the desired teaching strategy to make teaching-learning more effective and meaningful. . Results of the study can serve as bases for 2. REVIEW OF RELATED LITERATURE redesigning the curriculum and can be used in The history of mathematics and its short and long term plans in education. implications in mathematics education had been The School Administrators. The findings studied by different kinds of researchers of the study may serve as the baseline empirical (historians, mathematicians and educators) from data for planning quality education that will different dimensions. The following are results satisfactorily meet the program of activities in from some of these studies. mathematics and other developmental needs of Lahoylahoy (2003) looked into the students related to mathematics instruction and relative effects of integrating history of in recommending to evolve innovations for a mathematics in the teaching of algebra and mathematics curriculum, if necessary. In their trigonometry on the cognitive and affective capacity as administrators, they can promote the learning. In the study both qualitative and results of this study and encourage teachers from quantitative method of collecting data were other subject areas to also test similar techniques employed. The quantitative data gathered from in their fields of specialization. the experimental method that was implemented The Teachers. This study can be utilized indicated that integration of history had no effect to help teachers modify their teaching practices on the cognitive learning of the students but it not only to improve students’ mathematics had a positive effect on their affective learning. achievement but also to facilitate the appreciation On the other hand, the qualitative data gathered of history in teaching mathematics. This will also from classroom observations, journals of students serve as a guide in developing other lessons with and interviews indicated effectiveness of the the integration of history in them. They can then integration of mathematics history in both the attend to the broader spectrum of individual cognitive and affective aspects. needs of each student, thereby enabling them to Farmaki and Paschos (2007) conducted a think of some other ways to improve their study employing an experimental design on the teaching skills. use of genetic ‘moments’ in the history of mathematics in the classroom. They developed The Students. The lessons will definitely self-contained courses on the topic linear motion arouse student’s motivation for further inquiry using an approach that takes into account the and investigation. This will challenge them to historical origins of the concept under engage in meaningful learning that could be a consideration and administered them to fifteen transformative experience and will, somehow, year-old students. Although, the use of enable them to improve their achievement in mathematics history was not the main flavor of mathematics. the courses they developed, they concluded that history of mathematics can inspire a chain of Scope and Delimitation of the Study teaching activities that will lead to the attainment of the goals of mathematics education. </p><p>[3] Katz (2007) zoomed in on the history of the “hows” of using history of mathematics In algebra and reflected on the role of this history in particular, he suggested two sets of categories, the teaching of algebra in the secondary or one for the “whys” and another one for the university level. A widely accepted summary of “hows”. He proposed dividing the “whys” or the the development of the history of algebra is its arguments for using history of mathematics into progress into three stages of expressing algebraic the two groups: history-as-a- tool and history-as- ideas: the rhetorical stage, the syncopated stage a-goal. On the other hand, he recommended and the symbolic stage. Katz offered an categorizing the “hows” or the different alternative view of the development of algebra as techniques of using history of mathematics into a four-stage conceptual development: geometric the three groups: the illuminations, the modules stage, static equation-solving stage, dynamic and the history based. He then exemplifies these function stage and abstract stage. He discussed categorizations using the results from a number of important development in the history of algebra study and papers on the use of history of in the context of these four stages and their use in mathematics in mathematics education. He also the teaching of algebra and concluded that discussed the interrelationships between these attention to the history of algebra can be a categories and discussed criticism on the different valuable guide in the teaching and learning of “whys” and “hows” of using history of algebra. mathematics in the classroom in the context of Otte (2007), believing in the important these categorizations. roles of mathematical history and philosophy of Similarly, Gulikers and Blom presented a mathematics within the educational context, survey of literature on the use and value of the offered some methodological reflections on them. history of geometry in mathematics education Case studies from nineteenth century history of and offered a way of categorizing the arguments arithmetic and integration theory were they were able to collect as conceptual, cultural considered from which he concluded that some and motivational. They also provided details and mathematical ideas that may first appear abstract contents of the article surveyed for further can become comprehensible if viewed from their studies of those interested to pursue the topic historical angle. history of geometry in mathematics education. Fried (2007) changed his original belief of Some studies looked into the history of the separation between mathematics and history mathematics in relation to the development of of mathematics. He now maintains the position teacher education programs. One is Furinghetti that the historian’s and the mathematician’s way (2007) who conducted a study to determine the of knowing are complementary and thus accepts affect of history in the construction of lesson the essential role of the history of mathematics in plans by prospective teachers. He found out that mathematics education. An important discussion history affected their output in two ways. Some of in his article is a comparison between a historical the outputs considered looking at the evolution of and non-historical view of mathematics which he a given concept through the centuries. Other later exemplifies using a particular case of outputs considered recovering the cognitive roots teaching and looking at the topic “Conics” in of a given concept. analytic geometry using these two points of view. The study by Charalambos et. al. (2009) Some studies provided a survey of the on the effects of using history of mathematics to myriad literatures on history of mathematics in influence the beliefs and attitudes towards mathematics education and proposed a way of mathematics of prospective teachers traced categorizing these literatures. Examples are the through questionnaires that were administered papers by Jankvist (2009) and Gulikers and four times, the beliefs and attitudes of preservice Blom(2001). teachers over a period of two years. The analysis Jankvist proposed a way of organizing of the data collected indicated changes in some and structuring the discussion of the “whys” and dimensions of the preservice teacher’s beliefs and</p><p>[4] attitudes. From their analysis, they offered Table 1 implications for the design of teacher education Distribution of Respondents According to Level programs that take into account history of and Type of School mathematics. Type of School Percentag These are just a few of the results related Level Private Public Total to history of mathematics in mathematics e education and most of them indicated agreement F % F % on the positive effect of history of mathematics. Primary 11 100 0 0 11 15.3 But this is not the real picture for there are also a Secondar 11 35. 20 64. 31 43.0 number of criticisms on the use of history of y 5 5 mathematics in mathematics education. In fact, Jankvist (2009) discusses some of these criticisms. Tertiary 20 66. 10 33. 30 41.7 Unfortunately, we, the authors of this study, were 7 3 not able to get hold of actual studies criticizing Total 42 58. 30 41. 72 100 the use of history of mathematics in teaching for 3 7 review. Nonetheless, these criticisms exist and are indications that the research of applying history of Legend: F – Frequency % - Percentage mathematics in teaching can still be enriched. Research Instrument 3. METHODOLOGY The researchers utilized a self-made This chapter presents the research questionnaire to answer the objectives of the design, respondents of the study, local of the study. Part A in the questionnaire asked the study, research instruments, data gathering respondents five words they can associate with procedures, and the statistical tools employed. the word “history” while part B asked them to write five words they can associate with the word “mathematics”. The questionnaire used a 3-point Research Design scale for part C to determine the extent of use of The descriptive survey method was used the teachers on teaching methods involving in this study in identifying the profile of the history of mathematics. The respondents rated teacher-respondents as well as in the determining the given 11 items as always, sometimes, or never the extent of utilization of the history of used in their mathematics teachings. In part D, mathematics in the mathematics teachings of the researchers used a 4-point scale to measure if primary, secondary, and tertiary teachers. the respondents strongly disagree, disagree, agree, or strongly agree on the given 16 Respondents of the Study statements regarding the use of history in Research participants were teachers teaching mathematics. There were 8 positive (3, from primary secondary and tertiary levels, in 5, 8, 10, 13, 14, 15, and 16) and 8 negative (1, 2, 4, both public and private schools where the 6, 7, 9, 11, and 12) statements. researchers were connected with at the time this study was conducted. Table 1 presents the distribution of the respondents according to level Data Gathering Procedure and Analysis and type of school. As seen from the table, most The questionnaires were administered of the respondents except in the secondary levels personally to the respondents. The data gathered are from private schools. The secondary level also were arranged, tabulated, and analyzed. To got the highest number of respondents. address the objectives of the study, frequency count, mean, rank and percentage were used.</p><p>[5] To interpret the answers of the 1 – 1.49 Strongly respondents on their extent of use on the given Disagree teaching methods in the questionnaire, the following numerical ratings with their descriptive ratings were employed. Factor analysis was employed to reduce the vast number of variables used in the Numerical Rating Descriptive Rating instrument for determining the extent of use of 2 Always history in teaching mathematics to a meaningful, 1 Sometimes interpretable, and manageable set of factors. This enabled the researchers to identify relevant 0 Never constructs in the instrument based on the To interpret the mean scores, the obtained information from the respondents. The following numerical ratings with their verbal analysis involved two stages: factor extraction and interpretations were used. rotation. Moreover, the Multivariate Tests were run to determine if there exists a significant difference on the perceptions of the respondents Numerical Rating Verbal on the use of history in teaching mathematics Interpretation across levels, and between the perceptions of 1.50 – 2.00 Always these teachers in the public and private schools. 0.50 – 1.49 Sometimes SPSS 16.0 Statistical Software and 0 – 0.49 Never Microsoft Excel were utilized in all the computations and processing of data.</p><p>To interpret the answers of the respondents on their perceptions on the use of 4. RESULTS AND DISCUSSIONS history in teaching mathematics, the following numerical ratings with their verbal interpretations Perceptions of Teachers on the Meaning of were used for both positive and negative History and Mathematics statements. When teachers were asked on what words they can associate with the meaning of Numerical Rating Descriptive history, most common words listed were “past”, Rating 4 Strongly Agree “events”, “origin”, “dates”, “background”, and 3 Agree “record”. When asked on the words they 2 associate with the meaning of mathematics, most Disagree 1 of them wrote “numbers”, “problem solving”, Strongly Disagree “operation”, “symbols”, “analysis”, and To interpret the mean scores, the “variables”. following numerical ratings with their verbal interpretations were used.</p><p>Numerical Rating Extent of Use of History in Teaching Mathematics Verbal Interpretation Teacher respondents rated the listed 3.50 – 4.0 Strongly Agree methods in the questionnaire as to “always”, 2.50 – 3.49 Agree “sometimes”, or “never” used in teaching 1.50 – 2.49 Disagree mathematics. Their responses are summarized in tables 2 and 3.</p><p>[6] As seen in tables 2 and 3, most of the or ancient methods which incorporate the use of history in instruments teaching mathematics are “sometimes” used by of teachers regardless of the level and type of school calculation they are teaching. Among all methods, “internet and resources” obtained the highest mean score, measureme followed by “experimental mathematical nt activities”. “Role playing” and “worksheets 8. 1.2 S 1.0 S 1.3 S 1.1 S 2 involving history of concepts” got the lowest Experimenta 7 3 0 8 mean scores among the given methods. l mathematic al activities Table 2 9. Role 1.4 S 0.6 S 0.4 N 0.6 S 10. Extent of Use of History in Teaching Mathematics playing 5 5 7 9 5 of Teachers from Different Levels 10. Films 0.8 S 0.7 S 0.7 S 0.7 S 9 Method Level Gra D and other 2 1 0 2 Primar Second Tertiar nd R visual means y ary y Me showing the an history of mathematics 1. Historical 0.8 S 0.8 S 1.0 S 0.9 S snippets or 2 4 3 2 11. Internet 1.2 S 1.1 S 1.4 S 1.3 S 1 anecdotes resources 7 9 7 2 2. Student’s 0.3 N 0.8 S 0.9 S 0.8 S Legend: research 6 7 0 1 A – Always N – Never project R - rank based on S – Sometimes DR – Descriptive Rating history texts</p><p>3.Worksheet 0.8 S 0.7 S 0.5 S 0.6 S It is shown in table 2 that teachers in the s involving 2 4 9 9 primary level never used student’s research history of project based on history text and historical concepts packages on mathematics in teaching. Meanwhile, 4. Historical 0.4 N 0.8 S 0.8 S 0.8 S in this level, “role playing” obtained the highest packages on 5 7 7 1 mean score among all the methods listed. math However this method obtained the lowest mean 5. Taking 1.0 S 0.9 S 1.2 S 1.0 S score in the secondary and tertiary level. It can advantage of 9 3 3 8 also be seen in the table that it is “never” used by errors or teachers in the tertiary level. “Internet resources”, alternative on the other hand obtained the highest mean concepts score in both secondary and tertiary level. 6. Historical 1.2 S 0.9 S 0.9 S 0.9 S problems 7 0 0 6 Table 3 Extent of Use of History in Teaching Mathematics 7. 0.9 S 0.9 S 0.8 S 0.8 S of Public and Private School Teachers Mechanical 1 0 3 8 Method Type of School Gran DR R instruments</p><p>[7] 5 Public Private d playing 7 Sco Mea 10. Films 0.81 S 0.6 S 0.72 S 9 Score DR DR re n and other 0 1. Historical 0.93 S 0.9 S 0.92 S visual snippets or 0 means anecdotes showing the history 2. Student’s 0.79 S 0.8 S 0.81 S of research 3 mathemati project cs based on history 11. Internet 1.26 S 1.4 S 1.32 S 1 texts resources 0 3.Workshe 0.79 S 0.5 S 0.69 S Legend:S ets 5 A – Always N – Never involving R - rank history of S – Sometimes DR – Descriptive Rating concepts 4. Historical 0.76 S 0.8 S 0.81 S Table 3 also shows that “internet packages in 7 resources” obtained the highest mean score from math teachers both in the private and public schools. “Historical packages in math” and “worksheets 5. Taking 1.17 S 0.9 S 1.08 S involving history of concepts” obtained the lowest advantage 7 mean scores from the teachers in the public and of errors or private schools respectively. alternative concepts Perceptions of Teachers on the Use of History in 6. Historical 1.07 S 0.8 S 0.96 S Teaching Mathematics problems 0 7. 0.88 S 0.8 S 0.88 S Tables 4 and 5 show how teacher- Mechanical 7 respondents perceive the use of history in instrument teaching mathematics. In table 4, teachers’ s or ancient perceptions are compared according to the instrument education level they are teaching while in table 5, s of comparison of perceptions was based on the type calculation of school. and It can be seen in table 4 that teachers in measureme different levels almost have the same perceptions nt on the use of history in teaching mathematics 8. 1.24 S 1.1 S 1.18 S except in statement 3. Teachers in the primary Experiment 0 and secondary levels believe that “teachers have al sufficient time to include history in teaching mathemati mathematics”, while teachers in the tertiary level cal do not agree in this statement. In table 5, it can activities also be seen that it is only in statement 3 that 9. Role 0.79 S 0.5 S 0.69 S teachers in the private and public schools differ in their perceptions. Teachers from private schools</p><p>[8] agree that “teachers have sufficient time to  The utilization of the history of math in include history in teaching mathematics, while teaching math is not sufficient enough to teachers from public schools disagree in this improve Mathematics education. statement.  This could be an avenue for other Meanwhile, teachers in general agree on strategies like role playing, puppet show, the positive effect of incorporating history in among others. However, discussion of teaching and learning of mathematics and history is sometimes pretty boring disagree on the negative statements. Statements especially when the class is used to which obtain the highest mean scores were problem solving. “History in mathematics class can increase  Most students are not aware about the teachers’ and students’ appreciation of the history of mathematics. evolution mathematics” and “History can help  Sometimes, it would be better if the roots learning mathematics.” Statements which of a certain tree are being appreciated obtained the lowest mean score is “History is not first before its fully grown leaves and mathematics” followed by the statement “History fruits. History is more on appreciation. is tortuous and confusing rather than  DepEd should give teachers enlightening.” seminars/trainings on how to include However, despite the belief that Mathematics history in their teachings. incorporating history has a positive effect in  Mathematics has a very rich history. It is teaching mathematics, teachers also believe that just waiting for us to learn from it. they “lack training and expertise in using history  For college students majoring in of mathematics as well as historical resources and mathematics, a Mathematics history appropriate assessment rubrics in mathematics subject can be part of the curriculum but involving history”. They all believe that “chief for high school students, the teacher emphasis should be on equipping students with should have a creative way of injecting it routine skills rather than on historical context of so that students would not find that mathematics”. Some of the unedited comments boring. of the teachers are the following:  Curriculum planners should include the  History can be a helpful tool in injecting subject “History of Mathematics” in the this “real life situations” but not the sole undergraduate course of BSE Math. key in making pupils learn Math concepts. It may only be one of the various ingredients in making Math concepts tastier to children.</p><p>Table 4</p><p>[9] Perceptions of Teachers from Different Levels on the Use of History in Teaching Mathematics Level Gra DR nd Statement Primary Second Tertiary ary Me an 1. Teachers lack training and expertise in using history of 2.73 A 2.9 A 2.9 A 2.9 A mathematics. 7 3 2 2. Teachers lack historical resources. 3.00 A 2.7 A 2.8 A 2.8 A 4 7 3 3. Teachers have sufficient time to include history in teaching 2.73 A 2.6 A 2.3 D 2.5 A mathematics. 1 3 A 1</p><p>[10] 2. DA History is not mathematics. 2.00 D 1.9 D 2.1 D 2.0 A 4 A 7 A 4 5. Using historical projects in mathematics class increase my knowledge 3.18 A 2.9 A 3.0 A 3.0 A of mathematics. 3 0 0 6. History is tortuous and confusing rather than enlightening. 2.09 D 2.1 D 2.0 D 2.0 DA A 0 A 0 A 6 3. It is hard to make any connection of history with the present day 2.18 D 2.4 D 1.9 D 2.2 DA context and present topics in mathematics. A 7 A 7 A 1 8. Historical projects in mathematics class increase teachers’ and 2.91 A 3.1 A 3.2 A 3.1 A students’ knowledge of different ways of thinking. 0 1 1 9. Involving history in mathematics is only time consuming and 2.18 D 2.2 D 2.0 D 2.1 DA inappropriate for most topics in mathematics. A 9 A 7 A 8 10. History in mathematics class can increase teachers’ and students’ 3.18 A 3.1 A 3.2 A 3.1 A appreciation of the evolution mathematics 7 1 9 11. Chief emphasis should be on equipping students with routine skills 2.55 A 2.8 A 2.5 A 2.6 A rather than on historical context of mathematics. 1 0 4 12. Teachers lack appropriate assessment rubrics in mathematics 2.91 A 3.0 A 2.7 A 2.8 A involving history. 0 6 9 13. Using history in mathematics can develop students’ creativity and 3.00 A 3.0 A 3.0 A 3.0 A critical thinking. 0 7 3 14. Using historical projects in mathematics class can make me a more 3.18 A 2.9 A 3.0 A 3.0 A versatile teacher. 0 7 1 15. History can help learning mathematics. 3.27 A 3.1 A 3.2 A 3.1 A 3 3 9 16. Using historical projects in mathematics class can make me a more 2.91 A 2.8 A 3.0 A 2.9 A effective teacher. 4 7 4 Sco Scor D DR re e R Me 1. Teachers 2.7 A 3.10 A 2.9an A lack training and 9 2 expertise in using history of Legend: mathematics. SA – Strongly Agree D – Disagree DR – Descriptive Rating 2. Teachers lack 2.8 A 2.77 A 2.8 A A - Agree SD – Strongly Disagree historical 8 3 resources. Table 5 3. Teachers have 2.6 A 2.37 D 2.5 A Perceptions of Public and Private School Teachers sufficient time to 2 A 1 on the Use of History in Teaching Mathematics include history in Statement Type of School Gra teaching mathematics. Public Private nd</p><p>[11] 2. History is 2.1 D 1.87 D 2.0 D 4. Involving 2.1 D 2.27 D 2.1 D not mathematics. 7 A A 4 A history in 2 A A 8 A 5. Using historical 2.9 A 3.03 A 3.0 A mathematics is projects in 8 0 only time mathematics class consuming and increase my inappropriate for knowledge of most topics in mathematics. mathematics. 6. History is 2.1 D 2.00 D 2.0 D 5. History in 3.1 A 3.29 A 3.1 A tortuous and 0 A A 6 A mathematics class 2 9 confusing rather can increase than enlightening. teachers’ and 3. It is hard 2.1 D 2.36 D 2.2 D students’ to make any 2 A A 1 A appreciation of connection of the evolution history with the mathematics. present day 6. Chief 2.5 A 2.80 A 2.6 A context and emphasis should 2 4 present topics in be on equipping mathematics. students with 8. Historical 3.0 A 3.27 A 3.1 A routine skills projects in 0 1 rather than on mathematics class historical context increase teachers’ of mathematics. and students’ 7. Teachers 2.8 A 2.90 A 2.8 A knowledge of lack appropriate 8 9 different ways of assessment thinking. rubrics in mathematics involving history. 8. Using 3.0 A 3.07 A 3.0 A history in 0 3 mathematics can develop students’ creativity and critical thinking. 9. Using 3.0 A 2.97 A 3.0 A historical projects 5 1 in mathematics class can make me a more versatile teacher. 10. History 3.1 A 3.30 A 3.1 A can help learning 2 9 mathematics. 11. Using 3.0 A 2.87 A 2.9 A 0 4</p><p>[12] historical projects 6-HISTORY IS TORTUOUS . in mathematics 7-HARD TO CONNECT . class can make me 11-EMPHASIZE ON ROUTINE .606 a more effective teacher. 2-TEACHERSSKILLS LACK .592 Legend: 5-HISTORYHISTORICAL INCREASES RESOURCES 654 . SA – Strongly Agree D – Disagree DR – Descriptive Rating 9-TIMEKNOWLEDGE CONSUMING OMATH . .769 A - Agree SD – Strongly Disagree 8-HISTORY PROJECTS 446 .712 12-TEACHERSINCREASE TEACHER LACK AND 519 . The sixteen (16) items pertaining to the 16-MAKEASSESSMENT A MORE RUBRIC EFFECTIVE .589 perceptions of the respondents on the use of 3-TEACHERSTEACHER HAVE .567 history in teaching mathematics were then processed using exploratory factor analysis to SUFFICIENT TIME 525 identify four relevant constructs. These constructs Extraction Method: Principal Component Analysis. were formed using an eigenvalue of 1. These four Rotation Method: Varimax with Kaiser constructs have 53.58% variance explained. Five Normalization. items (1, 10, 13. 14, 15) belong to the first factor; a. Rotation converged in 7 iterations. another five items (2, 4, 6, 7, 11) comprise the second factor, and three items each for the third (5, 9, 8) and fourth (3, 12, 16) factors. Table 6 shows these results of the rotated component matrix done under factor analysis. On the other hand, the outcome of the multivariate tests on Table 7 shows that the level effect on the perspectives of teachers on the use of history in teaching mathematics is not significant, Wilks’ Lambda (8, 118) = 1.201, p < . 304. That is, there is no significant difference in the perception of teachers on the use of history on math teaching across all educational levels. On the contrary, the effect of the type of school on Table 6 the perception of these teachers on utilizing Rotated Component Matrix history in teaching mathematics is significant Component (Wilk’s Lamba (4,59) = 3.309, p = .016. Thus, in terms of public and private school teachers, the Perceptions 1 2 3 4 perceptions are significantly different. The tests (Note: Only keywords are also reveal that there is no interaction effect used) 14-VERSATILE TEACHER . between the type of school and the different educational levels (Wilk’s Lamba (4,59) = .402, p 779 15-HELP LEARNING MATH . < .806. This indicates that the perceptions of the 1-TEACHERS LACK TRAINING .718 teachers across all educational levels on the use of history in teaching mathematics do not depend IHISTORY 672 13-HISTORY CAN DEVELOP . on the type of school where these respondents 10-INCREASECRITICAL THINKING TEACHER .658 are coming from. 4-HISTORYAPPRECIATION IS NOT OF MATH 469 . Table 7 406 MATHEMATICS</p><p>[13] 2. Methods that involve history of mathematics were not popular Hypothes Error Effect Value F Sig. among all the respondents is df df Interce Pillai's .996 4.134E 4.000 59.000 .000 regardless of the level and type of school in which they came from. pt Trace 3a Wilks' .004 4.134E 4.000 59.000 .000 They sometimes use those methods Lambda 3a but they prefer using internet Hotelling' 280.2 4.134E 4.000 59.000 .000 resources and experimental s Trace 43 3a mathematical activities. Teachers in Roy's 280.2 4.134E 4.000 59.000 .000 the primary level that were asked Largest 43 3a ELEM1 Pillai's .147 1.187 8.000 120.00 .312 never assigned research project based on history texts to their HS2COL Trace 0 Wilks' .855 1.201a 8.000 118.00 .304 students and never used historical 3 Lambda 0 packages in teaching mathematics. Hotelling' .168 1.215 8.000 116.00 .297 Role playing was the method preferred by them. On the other s Trace b 0 Roy's .154 2.317 4.000 60.000 .067 hand, role playing was the least Largest popular among the teachers from PUBLIC Pillai's .183 3.309a 4.000 59.000 .016 the secondary and tertiary level 2PRIVA Trace Wilks' .817 3.309a 4.000 59.000 .016 while the use of internet resources is TE1 the most popular among them. Lambda a Hotelling' .224 3.309 4.000 59.000 .016 3. In general, all the teachers s Trace have the same perceptions on the Roy's .224 3.309a 4.000 59.000 .016 use of history in teaching Largest ELEM1 Pillai's .027 .402a 4.000 59.000 .806 mathematics. They agree on all the enumerated statements regarding HS2COL Trace Wilks' .973 .402a 4.000 59.000 .806 the positive implication of using 3 * history in mathematics educations Lambda a PUBLIC Hotelling' .027 .402 4.000 59.000 .806 except for the item stating that s Trace teachers have sufficient time to 2PRIVA Roy's .027 .402a 4.000 59.000 .806 include history in teaching TE1 Largest a. Exact mathematics. Those in the primary and secondary levels agree that they b. The statistic is an upper bound on F that yields a have sufficient time to include c. Design: Intercept + ELEM1HS2COL3 + PUBLIC2PRIVATE1 history while the teachers in the tertiary level disagree. Teachers 12. CONCLUSIONS from private schools maintain that they have sufficient time while teachers from the public schools say Based on the findings of this study, the they do not. All the teachers are also following conclusions were drawn: in agreement with the statement 1. History as perceived by the that they lack training and expertise respondents is a record of past in using history of mathematics, events detailing the origin or historical resources and appropriate background of things while assessment rubrics in mathematics mathematics is something that involving history. They all agree that involves numbers, symbols, problem the chief emphasis of teaching solving and analysis. should be on equipping students</p><p>[14] with routine skills rather than on the mathematics education, just as mathematics, historical context of mathematics. though important, is not the only subject worth 4. There is no significant studying. It is the harmony of mathematics with difference in the perception of other intellectual and cultural pursuits that makes teachers on the use of history on the subject even more worth studying. In this math teaching across all educational wider context, the history of mathematics has yet levels. a more important role to play in providing a fuller education of a person. 5. In terms of public and private school teachers, the perceptions are significantly different. 13. ACKNOWLEDGMENTS We would like to express our sincerest 6. However, the perceptions of gratitude to the faculty members of LPU, HAU, the teachers across all educational PSAU for sparing their time to answer the levels on the use of history in questionnaires for this study. We are also grateful teaching mathematics do not to Dr. Amelia Punzalan, our faculty-in-charge, for depend on the type of school where validating the questionnaire. Her valuable these respondents are coming from. corrections and inputs on the earlier version of the instrument inspired the authors to pursue this The teachers agree on the positive effect study. Above all, we praise and thank the of using history in teaching mathematics and yet Almighty God for His goodness, for the countless they don’t usually employ methods that will blessings that He has showered upon us and for incorporate history. This can be attributed to their having paved the way, using institutions and perceived lack of time and their perceived lack of people, to enable us to finish this paper. Laus Deo confidence to integrate history. The uniform stand Semper! Praise be to God always! of the teachers on the lack of training and expertise, historical resources and appropriate assessment rubrics indicates that they may not be 14. 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