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The purpose of this article is to share some initial thoughts on the recent release of Apple’s iPhone 16. While the latest and greatest iPhone will be remembered for the integration of artificial intelligence into the software, my attention has been focused on the new calculator app, which is also baked into the operating system. Apple’s new calculator app is, actually, three calculators housed in one app. While there have been minor, albeit welcome changes to the “Basic” and “Scientific” calculators, the third calculator, which is called “Math Notes”, is quite the calculator. One interesting feature, especially for those whose careers are dedicated to the learning and teaching of mathematics, is that answers now appear automatically as soon as you enter, by either writing (on an iPad) or typing (on an iPhone), an answerable math problem. Alternatively stated, your iPhone now, if you want, does the math for you. Before spiraling into a full-blown existential crisis, however, I look back at certain conversations regarding graphing calculators introduced in the 1990s. In doing so, I realize that everything changes and everything stays the same, which tempers, for now, my concerns about the impact Math Notes will have on the learning and teaching of mathematics.

The purpose of this mixed methods study was to investigate the effect of a graphing calculator (GC) intervention on Grade 11 learners' achievement in quadratic inequality problem solving. The quantitative aspects of the study involved an experimental and control group design in which the experimental group received instruction using the GC activities and the control group was taught without using the GC. The qualitative aspects of the study involved script analysis and task-based interviews. We used three data collection instruments: a quadratic inequality problem solving test used both as a pre- and a post-test administered to both the experimental and the control group learners, a written task analysis protocol and a task-based interview schedule. The results of the dependent samples t-test confirmed a statistically significant improvement in the quadratic inequality problem solving achievement of the experimental group with a Cohen's d effect size of 1.3. The dependent t-test results for the control group were also a statistically significant improvement but with a smaller Cohen's d of 1.2. The results of the independent t-test indicated that the experimental group achievement was significantly higher than that of the control group with a Cohen's d effect size of 0.79. Script analysis of selected learners' post-test solutions also showed that learners in the experimental group employed more problem-solving strategies (at least three - symbolic, numeric and graphical). Interview results of purposively selected learners also affirmed that experimental group participants perceived the GC intervention to have prepared them more effectively for multiple solution strategies of the quadratic inequality problem tasks. The researchers recommend the integration of GCs in the teaching and learning of mathematics in general and quadratic inequalities in particular. However, more research is needed in the integration of the GC in high-stakes assessment.

Integrating technology in the mathematics curriculum has become a necessary task for curriculum developers as well as mathematics practitioners across the world and time. In general research studies seeking a better understanding of how best to integrate mathematics analysis tools with mathematics subject matter normally observe mathematics lessons taught exclusively in a technology enriched environment or computer lab. In some universities where paper and pencil examination is the major assessment tool, undergraduate mathematics courses are still taught in a traditional manner that takes care of the algorithmic and procedural steps. This paper relates a study that embarks on the technology exposure claiming that human action is mediated by technological setting. Situated in a traditional classroom setting where there is more teaching and less hands-on, it reports foundation students' acceptance of technology-in-mathematics interaction in a typical course enriched with graphing calculator (GC) deliberated in the worksheets with printed GC commands alongside each question. Data was collected from students' worksheets and also questionnaire that measures attitudes towards technology in mathematics from a class of 763 pre-university students. The results may enlighten mathematics practitioners about the feasibility of taking full advantage of technology to teach mathematics in a partially technology incorporated mathematics course.

The number and variety of educational mathematics mobile applications (EMMAs) make it difficult to select mobile applications for mathematics learning and teaching. Therefore, in this study, multi-criteria decision-making (MCDM) techniques, which are effectively used in a wide variety of disciplines, were applied to choose among alternative applications according to specified criteria. In this context, it was aimed to determine which of the 13 considered EMMAs that work on Android-based tools and were proposed by experts according to certain features were most effective with the help of the TOPSIS algorithm, one of the popular MCDM methods. The results obtained from an evaluation using 10 criteria (4 evaluator-independent, 6 evaluator-dependent) were analysed with MATLAB. As a result, the Desmos: Graphing Calculator application was found to rank first among the 13 EMMAs in order of importance. Considering the results obtained, it can be said that the use of MCDM techniques in such decision problems can facilitate the work of decision-makers.

This paper examines how 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs implemented technology in their classrooms to teach for conceptual understanding in online, hybrid, and face to face classes during COVID-19. Using the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework, TCs, classroom mentor teachers, field experience supervisors, and university faculty formed a Networked Improvement Community (NIC) to discuss a commonly agreed upon problem of practice and a change idea to implement in the classroom. Through Plan-Do-Study-Act cycles, participants documented their improvement efforts and refinements to the change idea and then reported back to the NIC at the subsequent monthly meeting. The Technology Pedagogical Content Knowledge framework (TPACK) and the TPACK levels rubric were used to examine how teacher candidates implemented technology for Mathematics conceptual understanding. The Mathematics Classroom Observation Protocol for Practices (MCOP2) was used to further examine how effective mathematics teaching practices (e.g., student engagement) were implemented by TCs. MCOP2 results indicated that TCs increased their use of effective mathematics teaching practices. However, growth in TPACK was not significant. A relationship between TPACK and MCOP2 was not evident, indicating a potential need for explicit focus on using technology for mathematics conceptual understanding.

Due to the COVID-19 pandemic it was impossible to carry out on-campus teaching and examinations as planned for the first-year elementary school Bachelor's degree teacher training courses during the summer term of 2019/2020. Therefore, we moved our on-campus STEAM (Science, Technology, Engineering, Arts and Mathematics) related courses to schooling at home. For their course examination, students designed outdoor trails in groups with the educational technology MathCityMap based on an integrated STEAM approach. Hence, they combined STEAM with real-world situations (e.g., monuments, marketplaces, playgrounds). The tasks within the trails required the use of technologies such as augmented reality (AR), digital modelling (e.g., GeoGebra 3D Graphing Calculator), and GPS. Analogue measuring tools (e.g., triangle ruler) were also used in the task designs. We collected data from 21 trails with 259 tasks from 49 pre-service teachers to analyse the effects on professional growth in STEAM education. Through hierarchical cluster analysis we identified three different clusters with patterns regarding STEAM in outdoor trails. This paper will describe a pedagogical framework for the integrated STEAM approach to designing and evaluating outdoor trails. Furthermore, we will explain patterns pre-service teachers developed during this professional development.

The present study aimed to compare the effects of information and communication technology (ICT)-based and conventional methods of instruction on ninth-grade students’ academic enthusiasm for L2 learning (English). The statistical population included all ninth-grade students from lower secondary schools for girls located in the city of Tehran, Iran, in 2019–2020. For this purpose, applied research with a quasiexperimental design was employed to meet the study objectives. To select the statistical sample, the convenience sampling method was used, so one school equipped with the essential facilities was chosen to implement the ICT-based education. Then, two classrooms at the given school were selected as the experimental and control groups, each one consisting of 27 students, based on the random sampling method. The research tool was the 15-item Academic Enthusiasm Questionnaire (AEQ) containing behavioral, emotional, and cognitive subscales, and recruiting a five-point Likert-type scale. All the classrooms initially received a pretest, and then the experimental group was instructed by the ICT-based education. Finally, all the study groups completed a posttest. Moreover, inferential and descriptive statistics were applied for data analysis. The study results demonstrated a significant difference in terms of the baseline academic enthusiasm between the experimental and control groups. In addition, the ICT-based method of instruction showed stronger effects on students’ academic enthusiasm than the conventional one.

An interview with Jeff Irvine, teacher, administrator, researcher, and general education officer for the Ontario Ministry of Education, is presented. Among other things, he discusses the earliest technological tools employed in mathematics classrooms, the introduction of calculators in the seventies and eighties and how he sees coding differently from just another technological tool.

In the United States, the first course in single-variable calculus is considered tertiary level mathematics. Initially offered in high schools as a means for strong students to do college-level work, it is now taken by over 20% of high school students and perceived to be a prerequisite for admission into selective colleges and universities. This article describes the growth of this phenomenon and its effects on issues of educational equity. Because U.S. schools are funded locally, there is tremendous variation in the availability of calculus instruction in high school, with the most privileged students having the greatest access. This has profound effects on issues of equity because few universities are effectively addressing the vast disparities in student preparation. This article concludes with observations on what can and should be done to ameliorate the strange situation in the United States with regard to calculus.

In this study, we seek to describe how the meaning of a tool was co-constructed by the students and their teacher and how the students used the tool to construct mathematical meaning out of particular tasks. We report the results of a qualitative, classroom-based study that examined (1) the role, knowledge and beliefs of a pre-calculus teacher, (2) how students used graphing calculators in support of their learning of mathematics, (3) the relationship and interactions between the teacher's role, knowledge and beliefs and the students' use of the graphing calculator in learning mathematics, and (4) some constraints of the graphing calculator technology that emerged within the classroom practice. We found five patterns and modes of graphing calculator tool use emerged in this practice: computational tool, transformational tool, data collection and analysis tool, visualizing tool, and checking tool. The results of this study suggest that nature of the mathematical tasks and the role, knowledge and beliefs of the teacher influenced the emergence of such rich usage of the graphing calculator. We also found that the use of the calculator as a personal device can inhibit communication in a small group setting, while its use as a shared device supported mathematical learning in the whole class setting.