The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding  . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.

The study examines the effectiveness of employing semiosis in the teaching and learning of the Quadratic Equation. The first goal is to compare results of De Saussure and Peirce models within the semiotic theory. The second goal is to determine the commonest effective semiotic objects student teachers mostly employ to solve for the roots in quadratic equations. This research method was mixed methods concurrent and adopted both quantitative and qualitative approach. The instruments for the study were teacher-made tests and interview guide structured on the likert scale. In the teacher-made tests, two sets of twenty questions were set and distributed to the respondents. The sets of questions were similar and each twenty questions were based on De Saussure and Peirce Semiotic Models. The analyses employed both quantitative and qualitative. In the quantitative analysis, three categorical independent variables were fixed on and Pierre and De Saussaure models, objects of Pierre and De Saussaure models, and diachronicity, trichronicity, categorization and quadratic equations, after satisfying normality and independent assumptions of t-test and ANOVA techniques. The qualitative analysis with ensured anonymity, confidentiality and privacy of respondents and transcribed responses from semi-structured interview guide. The results of the commonest semiotic objects improved significantly classroom interactions with Peirce model than with De Saussure model. They perceived the Peirce model as being broader, comprehensive, universal and ICT-compliant. We therefore recommended further quasi-experimental studies on semiotic objects to improve upon the use of cultural objects.

This study aimed to develop a two-tiers diagnostic test to assess the high school, junior high school, and elementary pre-service teachers about the heat and the temperature concepts in a general physics course. There are two tiers in this test: The first tier composed of six items consisting of multiple-choice questions related to the heat and the temperature, including the correct answer. The second tier of each item contains reasons for students choosing their answer to the first tier. The second tier included four or five responses, one of which is a correct conceptual understanding. The wrong answers, also called distractors, were based on students’ misconceptions. To this end, 128 pre-service teachers from Quebec in Canada completed a pencil-paper questionnaire of sixty minutes duration composing of six questions (four open-ended questions and two multiple choice questions with justifications). As illustrations, the following  conceptual understandings have been identified in our qualitative analysis of the data collected: 1. The change of state of the matter does not require a constant temperature; 2.  The temperature is a measure in degrees to indicate the level of heat of an object or person; 3. The mercury contained in a thermometer expands when it is heated so that the particles which constitute it expand; and 4. The sensation of cold (or warm) is related to the difference in temperature.

In Nigeria, most teachers among other things lack the necessary teaching skills, and mastery of subject matter for effective teaching of mathematics at the secondary school level. These deficiencies have often resulted in high and repeated failure rates in national and standard mathematics examinations. The present study investigated the ability of mathematics teachers to construct practical and realistic word problems in bearing and distance toward mitigating the deficiencies. The research methods adopted were exploratory and descriptive surveys due to the need to explore and analyze the abilities using quantitative techniques. Sample consisted of 292 (35.48%) mathematics teachers who took part in the in-service training workshop organized by the Mathematical Association of Nigeria (MAN) in Plateau state, Nigeria. Purposive sampling technique was used to select the sample that involved the workshop participants only. The instrument ‘construction of practical and realistic word problems in bearing and distance test (CPRWPBDT)’ was used for data collection while the analysis was carried out using simple percentages, mean scores and one-way ANOVA. The findings of the study among other things revealed that the mathematics teacher participants constructed practical and realistic word problems in bearing and distance within 91.67% completion rate, 70.45% of the problems constructed were within the context, at least 75% rate of correctness with little difficulties/errors was observed in sketching (65.90%), and reality (40.90%). The variations observed within the participants in the construction of the problems were statistically not significant. Thus it was recommended among other things that mathematics teachers should undergo regular in-service workshop training to help in developing essential skills themselves for constructing practical/realistic word problems in bearing and distance; and should avoid unnecessary errors for meaningful teaching and learning of bearing and distance.

As international concerns about the prevalence of out-of-field teaching have grown, so have discussions about how to support out-of-field teachers. In Ireland, the Professional Diploma in Mathematics for Teaching, a two-year professional development program, was created for out-of-field mathematics teachers. A pre-test, post-test, and final survey examined the program’s impact on participating teachers’ mathematical knowledge, confidence in teaching curricular content, and classroom practice. Findings offer evidence of development in participating teachers’ mathematical knowledge and self-efficacy after completing the program. They also raise important concerns about persistent weaknesses in participating teachers’ mathematical knowledge, particularly related to key areas of the curriculum.