Den här studien är en systematisk litteraturstudie som går ut på att presentera och analysera vad forskning visar beträffande svårigheter som elever möter inom området ”derivata” samt hur undervisningen kan utformas för att stötta eleverna i sitt lärande inom ”derivata”. Via systematiska sökningar som skedde både i databaser och manuellt valdes artiklar som passade in på urvalskriterier. Artiklarna analyserades utifrån frågeställningarna. Elevens svårigheter i sin förståelse för begreppet ”derivata” delades upp i tre huvudsakliga kategorier: tangentens ekvation och dess lutning i förhållande till ”derivata”, gränsvärde i förhållande till ”derivata” och förändringshastighet i förhållande till ”derivata”. Studien fann att eleverna uppvisade svårigheter när de gäller tangenten, tangentens lutning, förändringshastighet och gränsvärde. Att eleverna hade svårt med att förstå begreppet ”derivata” gjorde att de fick även svårare att se sambandet mellan alla andra begrepp. Gällande undervisningens utformning fann studien att användandet av olika representationer och digitala verktyg förebygger elevens svårigheter för begreppet ”derivata”. / This study is a systematic literature study aiming at presenting and analyzing what research shows regarding difficulties students encounter in the field of derivatives and how teaching can be designed to support students in their learning in derivatives. Through systematic searches which were done both in databases and manually, articles that matched given criteria were selected. The articles were analyzed based on the research questions. The students' difficulties in understanding the concept of derivatives were divided into three main categories: the tangent equation and its slope in relation to derivatives, the limit value in relation to derivatives and the rate of change in relation to derivatives. The study found that students experienced difficulties in the concept of the derivative, such as the tangent, the slope of the tangent, the rate of change and the limit. The fact that the students had difficulty with the concepts made them even more difficult to understand the connection between these concepts. Regarding the teaching, the study found that different representations and the using of digital tools prevent the students' difficulties in the concept of derivatives.

The South African education system is under a serious strain in relation to Mathematics attainment. Only 40% of learners in SA pass the final school leaving examination and only 5% of learners manage to pass Mathematics with more than 50%, according to The Economist (2014). In a bid to solve this problem the government proposes the use of ICTs (such as computer hardware and software, tablets, and smartphones) within teaching and learning. The assumption is ICTs can be utilised to address this important challenge and “facilitate ongoing improvement of educator skills” (The National Integrated ICT Policy White Paper: The White Paper, 2016: p.8). Research shows that teachers’ perceptions regarding the use of ICTs impact on their practices (Mwendwa, 2017; Munyengabe, Yiyi, He Haiyan, & Hitimana, 2017; Alharbi, 2012; Yuan & Chun-Yi Lee, 2012). This project intends to explore six grade 6 Mathematics teachers’ perceptions about whether and how pedagogy shifts with the use ICTs in the classrooms utilising Cultural Historical Activity Theory. This research utilises interviews as a method for the collection of empirical data to describe a group of research participants’ (or teachers’) perceptions who happen to be directly interviewed. These interviews have been conducted across two no-fee paying primary schools in the Western Cape Province (WCP), in South Africa (SA). Interviews were analysed along the CHAT dimensions: object, subject, tools, rules, community and division of labour to establish whether pedagogy altered along any of these dimensions. Findings indicate that teachers think pedagogy shifts in the ICT based lessons with division of labour becoming more fluid. Findings also show that the object of the activity system grows to encompass more than mere mathematical compression but also motivation, creativity and cognitive development. Besides, teachers stated that ICT based learning could assist learners in their mathematical attainment. This project is an investigation and not an intervention study. Recommendations are also suggested in this thesis for further research such as video-taping teaching and learning of mathematic contents and concepts in both traditional and computer-based classrooms. Further study in utilising classroom observations to focus on student-student interaction in relation to ICTs is also recommended.

This Diploma thesis is based on the teaching practice done online. It looks at the possibilities of online teaching of Mathematics and its concepts, and at how to teach Mathematics online well. The aim of the thesis is to compare distance learning in the Czech Republic and chosen countries in the European Union. The current situation changed in the European schooling and teaching was done remotely since Spring 2020. This thesis takes this situation and looks at three main areas: literature search, where theoretical background is described, summarized data for distance learning in the World, which I got from the internet, and lastly a part where I observed teaching in the given context, both as an observing student and as a teacher. The teaching practice was done in the first year of the lower secondary school, during a focus on the topic of solving equations. The analysis and the reflection of the class are put into the context with the analysis of the topic of solving equations as presented in chosen textbooks both at primary and lower secondary school level. The thesis also includes a summary of all the reports published during the pandemic by CSI that examined the impact of the pandemic on the teachers, the students, and the parents. The final part of the thesis presents a summary of gained...

During a year-long professional development, the faculty members at an elementary school received instruction on mathematics and how to use the Comprehensive Mathematics Instruction framework. The instruction and the framework were consistent with the standards suggested by the National Council of Teacher of Mathematics (2000). This thesis analyzes the mathematical language used by three fifth-grade teachers who participated in lesson study to create a research lesson based upon the Comprehensive Mathematics Instruction framework.

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The second semester of the high school senior year has been associated with a lack of motivation among students and increased frustrations among parents and teachers. This qualitative study examines the achievement goals and engagement outcomes of second semester high school seniors in their mathematics classes. Data were collected from eight high school seniors, three of their parents, and two teachers enrolled at an all male college preparatory school in Pennsylvania. In-depth interviews were used to gather participants’ definitions of success prior to their senior year and during the second semester of their senior year. Student participants’ behavioral, emotional and cognitive engagements were assessed through directed interview questions and observations. Data were analyzed using a three goal framework of task-involvement, ego-involvement, and work-avoidance (Nicholls, Patashnick, & Nolen, 1985). The participants’ definitions of success suggested four themes. First, student participants defined success in mathematics consistently as they recalled their four years of high school and transition into the second semester of their senior year. Second, the phenomenon of senioritis was found to be more perceived than real for most of the participants. The work-avoidant participants described feeling the effects of senioritis for most of the second semester whereas the task-involved and ego-involved students reported brief effects before regaining focus. Third, students’ achievement goals in mathematics were found to be more closely aligned to their parents’ goals and less aligned to their teachers’ goals. Lastly, students described different achievement goals from one class to another during the same semester, at times even within the same discipline. Implications for practice and suggestions for future research were also discussed. / Math & Science Education

An operational definition of Systemic Reform is used to document a case study of mathematics education reforms occurring in the mathematics classrooms of one middle school in one school division in one state. The middle school had two lead teachers who participated in the training component of a National Science Foundation-funded state-wide Systemic Reform Initiative. Systemic Reform conceptualized reform as combining bottom-up reform with top-down support. Therefore, the research methodology confronted the challenges of the breadth and complexity of Systemic Reform through the use of selective data in the form of artifacts, interviews, and observations from four populations: (1) classroom teachers, (2) building administrators, (3) district administrators, and (4) state-level staff. The study was conducted at four levels over a five-year period to provide the focus for longitudinal data collection to document: (1) the status of mathematics education during the 1995-96 primary data collection year, (2) the evolution of mathematics education reform over the course of the five year period, and (3) the manner in which Systemic Reform occurred. All levels of educators involved made an initial five-year commitment as active participants in the State's Systemic Reform Initiative, but only the Lead Teacher actually carried through with this commitment. After the first year division-level administrators shifted the focus of reform efforts to the elementary schools and discontinued support for the middle schools; after the second year both the division and state-level administrators withdrew all support. Although changes were made at the school level which supported reform in mathematics education (i.e., adoption of constructivist-type instructional materials, purchase of classroom sets of manipulatives and calculators, implementation of block scheduling, and the organization of teachers in interdisciplinary teams) the necessary changes in technology, curriculum and assessment were not in place to support the reform efforts. Through the perseverance of the Lead Teacher some changes in mathematics classrooms were documented, but the lack of consistent administrative leadership/support and emphasis on multiple reforms ended in the all to common bandwagon phenomena at the building, division and state levels so characteristic of change efforts in schools. / Ph. D.

The purpose of this research was to examine the effect on students' mathematics achievement and attitudes when children's literature was integrated into the mathematics curriculum. A major goal of the National Council of Teachers of Mathematics (NCTM, 1999; 2000) is for students to increase the amount and quality of their mathematical communication skills. This study researched how children's literature when integrated into mathematics might enrich the fourth grade curriculum and provide meaningful experiences for students to communicate their ideas and reasoning, thereby improving achievement. Through my research, I examined if infusing quality children's literature can improve student achievement and motivation in mathematics with three different treatment groups of fourth grade students. The children's literature treatment group received a mathematics lesson integrating children's literature, the textbook treatment group received a textbook-based lesson, and the control treatment group received no instruction. The results indicated that the students who received a lesson had an increase in student achievement and the children's literature treatment group had the highest student achievement in problem solving. Attitudes across all groups did not improve from the one lesson; thus, further research will need to be conducted to see if multiple lessons can change students' attitudes positively.

ABSTRACT This qualitative content analysis study examined different middle school mathematics pathways from a large urban district in Florida to determine possible gaps in the accelerated pathways and differences between the district’s learning targets and Florida’s Benchmarks for Excellent Student Thinking (B.E.S.T.) Standards. Additionally, the accelerated pathways were compared to the Southern Regional Educational Board (SREB) 12 Indicators to identify possible missing content necessary to succeed in Algebra I Honors and Geometry Honors. The study aimed to answer three research questions: (1) In what ways do Florida’s B.E.S.T. Standards included in the non-accelerated and accelerated pathways for middle school mathematics differ in a large urban school district in Florida? (2) Which of the SREB 12 Indicators are absent from the accelerated pathways in middle school in a large urban school district in Florida? and (3) In what ways do Florida’s B.E.S.T. Standards differ from the district’s learning targets in the non-accelerated pathway for middle school mathematics in a large urban school district in Florida? Data collected included the sixth through eighth grade Florida’s B.E.S.T. Standards for Mathematics and the 2022-2023 learning targets from a large district in Florida. The SREB 12 Content-Specific Readiness Indicators that classify the skills necessary for a student to be successful in Algebra were used as coding tools. Findings suggest that in most of the pathways available for students in middle school, students miss half of the seventh-grade standards, the entire eighth-grade standards, or half of the seventh-grade and the entire eighth-grade standards. The study also found inconsistencies between the district’s learning targets and Florida’s B.E.S.T. Standards for Mathematics. Likewise, the study suggests that the students who follow three main accelerated pathways (Mixed Pathway One, Mixed Pathway Two, and Doubled-Accelerated Pathway) do not receive all the content needed to succeed in Algebra I and Geometry as recommended by the SREB 12 Indicators. The results from this study can be used to improve or develop a middle school mathematics curriculum that considers the impact of the standards missed during accelerated pathways and provides all students with access to the necessary skills to succeed in Algebra I Honors and Geometry Honors.