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Title: Text properties as a factor in solving word problems with the use of Venn diagrams Author: Bc. Daniela Návarová Department: Department of Mathematics and Mathematical Education Supervisor: doc. RNDr. Jarmila Novotná, CSc. Supervisor's e-mail address: Jarmila.Novotna@pedf.cuni.cz This diploma thesis deals with the word problems where Venn diagrams can be used. The word problems are studied as texts and their specific text properties are scrutinised in the first, theoretical, part of the thesis. The second part describes an experiment that focuses on the importance of text properties of word problems for the problem solvers. The main aims of this diploma thesis are to show the possibility of textual examination of the chosen texts and to unfold some connections between the mathematical and linguistic views on the area of word problems. Keywords: text, word problem, Venn diagram

Schools in Florida used the multitiered system of support response to intervention framework to help students achieve the state and national standards but, in the national report card, 61% of the fourth-graders assessed in mathematics failed to achieve proficiency. Research indicated that the students lacked mathematical word problem-solving skills. The purpose of the qualitative study was to discover how fourth-grade special and general education teachers used the response to intervention framework evidence-based curriculum, instruction, intervention, assessment, and student data to teach math word problem-solving skills to children who have persistent and significant difficulties. Welner'€™s zone of mediation framework and Vygotsky'€™s sociocultural theory form the conceptual framework for the study. The teachers provided data through in-depth interviews, math intervention program, training document, teachers'€™ guides, assessment tools, and observation. All the data was uploaded to the latest version of NVivo and analyzed based on the research questions. The study findings showed that participants used all the features of the response to intervention framework to teach math word problem-solving skills and address the needs of at-risk students. Teachers should continuously reinforce math vocabulary, terminology, and math reading comprehension skills of students. Administrators and teachers should be able to use the findings of this study to improve the use of the response to intervention features to develop the math word problem-solving skills of students and influence teachers'€™ pedagogical practices.

Since the textbook has a prominent role in Swedish mathematics education it is of importance that textbooks has a focus on everyday life application that matches the requirements of the syllabuses and provide examples of practical usage of mathematics. The purpose of this qualitative case study of four randomly chosen textbooks in mathematics for the ninth grade, published during the 60s, 70s, 80s and 90s, from which a stratified random sample of word problems has been drawn, is to study the prevalence of word problems related to everyday life as well as to see how much of the everyday life related instructions in the syllabuses these textbooks implement. The result shows that the proportion of exercises that is made up from word problems has increased steadily from the 1960s to the 1990s in the textbooks that were analysed and at the same time has the proportion of exercises related to everyday life among the word problems decreased. The overarching impression regarding instructions related to everyday life in the syllabuses is that rather few of them have been implemented via word problems. / Då läroboken har en dominerande roll i den svenska matematikundervisningen är det av vikt att dessa böcker har ett fokus på vardagslivskopplingen som motsvarar budskapet i kursplanerna samt ger eleverna exempel på matematikens vardagliga tillämpningsområden. Syftet med denna kvalitativa fallstudie av fyra slumpmässigt valda läroböcker i matematik för årskurs 9, utgivna under 60-, 70-, 80- och 90-talet, ur vilka ett stratifierat slumpmässigt urval av textuppgifter dragits, är att studera förekomsten av vardagsrelaterade textuppgifter samt hur läroböckerna uppfyller anvisningarna i kursplanerna rörande den vardagslivsrelaterade kopplingen. Resultatet visar att andelen uppgifter som utgörs av textuppgifter har ökat stadigt från 60- till 90-talet i de studerade läroböckerna samtidigt som de vardagsrelaterade uppgifternas andel av textuppgifterna har minskat. Beträffande kursplanernas anvisningar är det övergripande intrycket att tämligen lite har implementerats via textuppgifterna.

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This research investigation examined the effects of GO Solve Word Problems math intervention on problem-solving skills of struggling 5th grade students. In a randomized controlled study, 16 5th grade students were given a 12-week intervention of GO Solve, a computer-based program designed to teach schema-based instruction strategies (SBI's) to solve math word problems and 16 control students continued with the standard school-based mathematics curriculum. A subset of items from the Massachusetts Comprehensive Assessment System (MCAS) as well as the Group Mathematics Assessment and Diagnostic Evaluation (GMADE) was used to measure student test performance. Examiner-made probes were given to both the treatment and control groups every other week to measure student progress. Results indicate that the mean difference scores of the experimental and control groups were statistically significant on a subtest of MCAS problems and a large effect size was reported. However, no statistically significant difference between the experimental and control groups was found on the on the Process and Application subtest of the GMADE. On examiner-made probes, there was a statistically significant difference between the experimental and control groups. Limitations of this study as well as implications for practice will be discussed.

Title: Ways and strategies of 10-12 years old pupils when solving selected type of word problems Abstract This Diploma thesis is focused on word problems that, to some extent, make pupils troubles with their solution. In the first theoretical part there are word problems that the work deals with. These are word problems with ant signal, dynamic, complementary, graphic and their characteristics. The next section is about the strategy of solving word problems and work with mistakes. The second part is focused on experiment of all types of word problems that are described in the theoretical part. This experiment is analysed according to strategies of pupils' and teachers' solutions. Those strategies are later described and commented in detail. Key words word problem, solving strategy, mistake, source of mistake, grasping of word problem

TITLE: The influence of the order of information in word problems on their difficulty for lower secondary pupils AUTHOR: Bc. David Hennlich DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: doc. RNDr. Naďa Vondrová, Ph.D. ABSTRACT: Research has shown an influence of various parameters of word problems on their success rate and solving strategies that are used by pupils. In case of the order of information variable, most of research has focused on word problems, in which the order of information corresponds, or not, with the order of events described in the problem statement. This thesis differs from them by aiming at word problems without the sequence of this kind in their situational models. Two sets of problems solved by ninth grade pupils of four secondary schools situated in Prague were analysed. In order to recognize the influence of the analysed parameter, the combination of qualitative and quantitative approach was used. Item Response Theory (IRT) was used to analyse the parameter from the quantitative point of view. The written solutions of pupils were also analysed in a qualitative way and later amended by additional interviews with pupils. No influence of the parameter was found on either success rate or solving strategies in any of the analysed word problems. There was...

Studien behandlar elevers erfarenheter kring inkonsekventa textuppgifter i matematik. Syftet är att bilda kunskap om elevers syn på tillvägagångssätt vid lösandet av och svårig­heter med uppgifterna. Studiens teori utgår från fenomenologin då den stämmer över­ens med studiens syfte. Datamaterialet i stu­dien utgår från tio semistrukturerade inter­vjuer med elever i årskurs 6. Eleverna har under intervjuerna fått delge tillväga­gångs­sätt och vad de erfar var svårt och lätt med olika textuppgifter. Resultatet visar att problemmodellering var den vanligast förekommande strategin bland eleverna, men även direktöversättning förekom. Eleverna menade att svårigheten med textuppgifter var att beräkna och förstå vad de skulle göra. Eleverna hade olika preferenser av den omformulerade uppgiften men alla elever förutom en ansåg att standardversionen eller versionen där sambanden var tydligare var enklast att förstå. Slutsatser som kunde dras var att eleverna tenderade att koppla samman signalord med ett visst räknesätt, oavsett vilken strategi de använde sig av. Eleverna var även mer medvetna om problematiken kring beräkningen än de språkliga faktorerna. Deras olika preferenser av formuleringen av en uppgift kunde bero på deras tidigare erfarenheter av textuppgifter. / This study discusses pupils’ experiences of inconsistent word problems within mathe­matics. The aim is to form knowledge about pupils’ views of strategies and difficulties when solving inconsistent word problems. The theory in the study is based on phenomenology as it corresponds to the aim of the study. The material consisted of ten semi-structured interviews with pupils in grade 6. In the interviews the pupils described how they solved word problems and which difficulties they experienced with word problems. The result displayed the problem model approach as most common among the pupils, but direct translation also occurred. Complex aspects which the pupils mentioned were to calculate and perceive which rule of arithmetic to use. The pupils preferred different forms of rewording, but all except one pupil chose the standard version or the conceptual rewording. Conclusions drawn from the study was that pupils tended to associate relation terms with a rule of arithmetic, regardless of which strategy they used. The pupils were more aware of complications of the computing than of linguistic aspects. The difference in preferences of rewording could be due to differences in experiences of word problems.