Prospective mathematics teachers’ argumentation structure when constructing the mathematical proof: The importance of backing
Christina M. Laamena, Toto Nusantara, Makbul Muksar
Abstract
This study aims to investigate the use of backing and its relation to rebuttal and qualifier in prospective mathematics teachers’ (PMTs) argumentation when constructing a mathematical proof. It is qualitative research with phenomenology design which aims to explain a backing phenomenon that appears in argumentation with the reasons used. The data were collected through subjects' work on algebra proof, think aloud, field notes and task-based interviews. Data analysis was guided by Toulmin’s argumentation scheme. The results show that the backing used by PMTs is not only in the form of definitions or theorems (reference backing) but also examples of numbers (numerical backing) and graphs of functions (graphical backing). The PMTs use three types of backing to strengthen deductive warrant and inductive warrant. A numerical backing is used when a warrant cannot justify the truth of a claim. Graphical backing is used to convince oneself about the truth of the data that has been made while the reference backing is only explained because students have understood or have knowledge of the statement given. A numerical backing and graphical backing relate directly to rebuttal as well as provide the counter-example and correct assurance (qualifier) claim. A numerical backing makes students more confident (sure) about claims that are generated compared to reference backing.
Exploring the cognitive process of prospective mathematics teachers in constructing a graph
Dona Afriyani, Kurnia Rahmi Yuberta
Abstract
This article aims to analyze the strategy and process of translation by prospective mathematics teachers (PMTs) in constructing graphs. Forty-four PMTs participated in graph construction tasks (GCT) of composition function. Three of them were purposively selected as the subjects. Data were collected through subjects’ works on GCT and interviews on the basis of their works. Data analysis started with preparing and organizing the data, exploring and coding the database, describing findings and forming themes, representing and reporting findings, interpreting the meaning of the findings, and validating the accuracy of the findings. We found (1) two strategies used by the subjects in constructing graph namely translation and without translation and (2) The translation process in constructing the graph of the composition function begins by unpacking the source representation, preliminary coordination, constructing the target representation and end with determining the equivalence between the source representation and the target representation. The findings show that there are transfer variations in the conceptual content of the micro-source representation of the micro concept of target representation caused by differences in the types of mapping carried out at the initial coordination stage.
The validity and inter-rater reliability of project assessment in mathematics learning
Kusaeri, Sutini, Suparto, Faiqotul Wardah
Abstract
A common criticism of project assessment is the subjectivity and inconsistency of raters in scoring. In the present article, we provide the result of validity and inter-rater reliability test of the project assessment instrument. The project assessment is used to measure skills competency of grade eight students. The instrument has been tested to 10 raters/teachers and 94 grade eight students from three schools (in Surabaya and Gresik). Data were collected through project evaluation sheet, which was used to assess the project-based task, along with its rubric as the scoring guidance for the teachers. Construct validity was analyzed by using confirmatory factor analysis, while reliability analysis used inter-rater reliability method with Intraclass Correlation Coefficient. The result of the validity test shows that the assessment instrument did not fulfill the criteria of construct validity. It is indicated by the different number of factors between the initial construction and the empirical test result. In term of inter-rater reliability, the project assessment instrument is reliable with a high category. The findings indicate the need for testing the non-test assessment instrument provided on textbooks, hence the aspects of its assessment sheet fulfill the valid criteria.
Developing refutation text to resolve students’ misconceptions in addition and subtraction of integers
Syarifah Fadillah, Utin Desy Susiaty
Abstract
Students’ misconceptions in addition and subtraction of integers need to be addressed since this topic is a prerequisite for students to learn advanced mathematics topics such as algebra. Having misconceptions in understanding the prerequisite concepts will hamper the acquisition and integration of new knowledge. The purpose of this study was to develop refutation text to resolve the misconception of students in addition and subtraction of integers. Refutation text was developed in the form of student worksheet adopting the development model from Borg and Gall (1983). Tryout of refutation text involved fifteen seventh-grade students. The study found that (1) The experts’ validation reveals that refutation text is suitable to be used as learning media for students on addition and subtraction of integers; (2) The refutation text implemented in the tryout was effective to resolve students’ misconception in addition and subtraction of integers; and (3) The practitioner’s assessment and students’ response showed that refutation text is practical. Drawing from the findings, we argue that the developed refutation text help students correcting their misconceptions in the topics and could be used by the teachers in the classroom practices. However, the refutation text needs to be extended to anticipate students’ mistake in interpreting word problems by providing some possible mistakes and its correction.
Students’ conceptual understanding and motivation in learning mathematics through a scientific approach using mind mapping
Dewi Agustiani, Rahmah Johar, Bahrun
Abstract
Students' ability to understand the concept of number sequence remains problematic even though conceptual understanding is critical in learning mathematics. Therefore, efforts should be conducted to develop conceptual understanding by actively engaging students in mathematics learning. One of which is applying the scientific approach using mind mapping. This study aimed to investigate the development of junior high school students' conceptual understanding and motivation through the scientific approach using mind mapping in the sequences and series topics. This was a descriptive study using a qualitative approach involving 24 year 9 students from one of the junior high school in North Aceh, Indonesia, but only two students were selected as the participants representing the low and medium achieving students selected based on the test results and teacher consultation. The data collection was conducted by administering a conceptual understanding test, a semi-structured interview, and a student motivation questionnaire. The results showed that medium-achieving student fulfilled all conceptual understanding indicators in all five lessons, while low-achieving student only met the indicators in the third lesson. However, the posttest results showed that both students had a good conceptual understanding as both fulfilled more than 50% of conceptual understanding indicators; respectively achieved 6 and 4 out of 7 indicators. The questionnaire results showed that the students were motivated to learn in a classroom with a scientific approach using mind mapping.