Student test scores related to mathematical word problems have been declining in a rural school district in western Louisiana. Word problems constitute a major component of the Algebra 1 End of Course examination, which students must be able to pass to graduate. Mathematics teachers have struggled to find appropriate strategies to teach students to answer constructed response questions (CRQs) effectively. The purpose of this study was to investigate the perceptions of math teachers about effective teaching strategies for improving student performance on CRQs. Guided by Piaget's constructivist theory, which is characterized by an emphasis on learner control of the learning process through active engagement and activation of prior knowledge, this study investigated teachers' perceptions and practices in relation to teaching the skills needed for CRQs. The research questions focused on math teachers' perceptions of current teaching practices, instructional effectiveness, and professional development needs. A case study design was used to capture the insights of 8 participants through semistructured interviews and observations. Emergent themes were identified from the data through a code-recode approach, and findings were developed and validated through triangulation and member checking. The key results were that math teachers expressed a need to collaborate with their colleagues to develop effective strategies that would incorporate literacy and hands-on learning. A project was designed to engage teachers in collaboration and planning to prepare students to think critically and problem solve. This study may promote positive social change by providing teachers with the tools necessary to improve students' thinking skills, problem-solving skills, and learning strategies.

Problem Statement: Nowadays, multiple choice (MC) tests are very common, and replace many constructed response (CR) tests. However, literature reveals that there is no consensus whether both test formats are equally suitable for measuring students' ability or knowledge. This might be due to the fact that neither the type of MC question nor the scoring rule used when comparing test formats are mentioned. Hence, educators do not have any guidelines which test format or scoring rule is appropriate. Purpose of Study: The study focuses on the comparison of CR and MC tests. More precisely, short answer questions are contrasted to equivalent MC questions with multiple responses which are graded with three different scoring rules. Research Methods: An experiment was conducted based on three instruments: A CR and a MC test using a similar stem to assure that the questions are of an equivalent level of difficulty. This procedure enables the comparison of the scores students gained in the two forms of examination. Additionally, a questionnaire was handed out for further insights into students' learning strategy, test preference, motivation, and demographics. In contrast to previous studies the present study applies the many-facet Rasch measurement approach for analyzing data which allows improving the reliability of an assessment and applying small datasets. Findings: Results indicate that CR tests are equal to MC tests with multiple responses if Number Correct (NC) scoring is used. An explanation seems straight forward since the grader of the CR tests did not penalize wrong answers and rewarded partially correct answers. This means that s/he uses the same logic as NC scoring. All other scoring methods such as the All or-Nothing or University-Specific rule neither reward partial knowledge nor penalize guessing. Therefore, these methods are found to be stricter than NC scoring or CR tests and cannot be used interchangeably. Conclusions: CR tests can be replaced by MC tests with multiple responses if NC scoring is used, due to the fact that the multiple response format measures more complex thinking skills than conventional MC questions. Hence, educators can take advantage of low grading costs, consistent grading, no scoring biases, and greater coverage of the syllabus while students benefit from timely feedback. (authors' abstract)

Das Testen kognitiver Fähigkeiten ist ein Standardproblem in der Leistungsdiagnostik. Typische Anwendungsfelder sind Lernstandsüberprüfungen, Zulassungs- und Auswahlverfahren an Schulen und Hochschulen, aber auch Eignungs- und Einstellungsverfahren im betrieblichen Kontext. Sollen nicht nur einige wenige Personen, sondern größere Kohorten getestet werden, kommen aus testökonomischen Gründen vermehrt computerbasierte Tests (E-Assessments) und Aufgaben mit geschlossenem Antwortformat (Selected-Response, SR) zum Einsatz. Auf diese Weise lassen sich Tests automatisch auswerten, was gegenüber papierbasierten Tests den Testaufwand erheblich reduziert und eine zeitnahe Rückmeldung der Ergebnisse an die getesteten Personen erlaubt (Michel, Goertz, Radomski, Fritsch, & Baschour, 2015). Neben der guten Testökonomie besitzen SR-Tests auch aus psychometrischer Sicht Vorteile. So lassen sie sich nicht nur objektiver auswerten, sondern auch zeitsparender beantworten, wodurch eine größere Zahl an Aufgaben bei gleicher Testdauer gestellt werden kann Lindner, Strobel, & Köller, 2015). Dennoch werden SR-Tests insbesondere an Hochschulen häufig als besonders rigide Prüfungsform wahrgenommen (Kubinger, 2014). Eine wiederkehrend zu beobachtende Strategie scheint deshalb – wohl auch um die Akzeptanz dieser Prüfungsform zu erhöhen – die Ergänzung von E-Assessments um Freitextaufgaben (Constructed-Response, CR) zu sein. Hochschulprüfungen entscheiden über den Zugang zu erstrebenswerten Gütern einer Gesellschaft (Huinink & Schröder, 2014) und ziehen berufliche Auswahlentscheidungen nach sich (Rekrutierungsfunktion; Tsarouha, 2019). Vor dem Hintergrund der grundgesetzlich geregelten Berufswahlfreiheit (Artikel 12, GG) ergibt sich die berechtigte Forderung nach einer hohen diagnostischen Güte der eingesetzten Tests. Gleichzeitig erfordern die institutionellen Rahmenbedingungen an Hochschulen ökonomische Testmethoden. Aktuell fehlt es an Arbeiten, die den Verlust an Testökonomie durch Hinzunahme von CR-Items quantifizieren und den möglichen Gewinn an diagnostischer Güte zueinander ins Verhältnis setzen. Zudem weisen Schulleistungsstudien (Lafontaine & Monseur, 2009; Lissitz, Hou, & Slater, 2012; Reardon, Kalogrides, Fahle, Podolsky, & Zárate, 2018) und Untersuchungen aus dem Hochschulkontext (Arthur & Everaert, 2012) auf geschlechterdifferenzielle Effekte verschiedener Itemformate hin, die zu einem Problem für die Testfairness werden können. Beide Forschungsfragen adressiert der vorliegende Beitrag anhand einer empirischen Analyse von Daten einer E-Klausur, die die Abschlussprüfung eines erziehungswissenschaftlichen Moduls im universitären Lehramtsstudium bildet. [...aus der Einleitung]

The purpose of this study was to investigate how writing in mathematics is treated in one 4th grade National Science Foundation (NSF)-funded mathematics textbook titled Everyday Mathematics and one publisher-generated textbook titled enVision MATH. The developed framework provided categories to support each of the research questions. The results indicate that writing is supported in both traditional and NSF developed 4th grade mathematics textbooks Results also indicated the number of exercises and writing prompts was higher in the enVision MATH textbook. However, Everyday Mathematics had a higher percentage of exercises that were coded as writing prompts. The framework domains of content strand in enVision MATH and Everyday Mathematics are similar in percentages with the exception of prompts coded in the other category. Everyday Mathematics appeared to be the only textbook analyzed to support writing across different content areas. Furthermore, the content strand of number sense had the largest percentage of writing prompts coded between both textbook series. Other findings from this study suggest that the type of vocabulary coded within the writing prompts was similar in all categories between both textbook series analyzed. Additionally, vocabulary specific to the domain of mathematics and symbols appeared to have the largest percentage in this category for both textbook series. The teacher and student editions were explored in enVision MATH and Everyday Mathematics to provide more depth to the research. An exploration of the teacher edition indicated how writing was supported for instructional purposes. The teacher editions in both textbook series had the largest percentage of support in the form of one sample response. Within the student edition category, the layout varied in the enVision MATH and Everyday Mathematics textbook series. As a result, only the language of Everyday MATH could be analyzed for patterns in the sections, sub-sections, and additional sub-sections of where the prompts were located. Although this investigation did not involve analyzing student responses to the writing prompts, the findings provide information regarding the expectations of the writer in order to construct a mathematical response. For example, the domain specific vocabulary (DSV) and symbols category was rated the highest in percentage for both textbooks indicating that students will need to have command of the language and symbols of mathematics in order to engage in meaning making written discourse. Because most of the math prompts were specific to the problem solving category, it was determined after a linguistic analysis that the affordance of the prompt is much more complex than then binary categories of content and process Additionally, in order for students to respond to these content writing prompts, many process words known as meta-language (i.e., explanation, description, why question, how question) need to be comprehended in order for composition to begin. In light of these findings, I recommend that special attention be given to the teacher and student editions regarding the implementation of writing in mathematics. The development of these materials has important implications regarding instruction and learning of mathematical concepts through writing, potentially impacting student performance on national and international assessments.

The study takes a close look at relationships between scores on a Mathematics standardized test in two different testing formats - Multiple-Choice (MC) and Constructed Response (CR). Many studies have been dedicated to finding correlations between item format characteristics with regards to race and gender. Few studies, however, have attempted to explore differences in the performance of English Learners in a low performing, predominantly Latino high school. The study also determined relationships between math scores and gender and math scores and language proficiency, as well as relationships between CAHSEE and CST scores. Statistical analyses were performed using correlations, descriptive statistics, and t-tests. Empirical data were also disaggregated and analyzed by gender, and language proficiency. Results revealed significant positive correlations between MC and CR formats. T-tests displayed statistically significant differences between the means of the formats, with boys and English Only students having better scores than their counterparts. Frequency tables examining proficiency levels of students by gender and language proficiency revealed differences between MC and CR tests, with boys and English Only students earning better levels of proficiency. Significant positive correlations were shown between CST scores and multiple-choice items, but none were found for CST scores and constructed response items.

In this study, I investigate how successful provided response questions, such as multiple choice questions, are as an assessment format compared to the conventional constructed response questions. Based on the literature on mathematics assessment, I firstly identify an assessment taxonomy, consisting of seven mathematics assessment components, ordered by cognitive levels of difficulty and cognitive skills. I then develop a theoretical framework, for determining the quality of a question, with respect to three measuring criteria: discrimination index, confidence index and expert opinion. The theoretical framework forms the foundation against which I construct the Quality Index (QI) model for measuring how good a mathematics question is. The QI model gives a quantitative value to the quality of a question. I also give a visual representation of the quality of a question in terms of a radar plot. I illustrate the use of the QI model for quantifying the quality of mathematics questions in a particular undergraduate mathematics course, in both of the two assessment formats – provided response questions (PRQs) and constructed response questions (CRQs). I then determine which of the seven assessment components can best be assessed in the PRQ format and which can best be assessed in the CRQ format. In addition I also investigate student preferences between the two assessment formats. / Thesis (PhD)--University of Pretoria, 2009. / Mathematics and Applied Mathematics / unrestricted

Made available in DSpace on 2016-06-02T20:30:08Z (GMT). No. of bitstreams: 1 5361.pdf: 1037300 bytes, checksum: f6d3f569ec96dcb450a7aee8bd65999b (MD5) Previous issue date: 2013-04-10 / Universidade Federal de Minas Gerais / Several studies are interested in the acquisition of reading and spelling as well as in the role the acquisition of one ability plays in the acquisition of the other. However, many of these studies focus on reading rather than on spelling. This study aimed to teach spelling skills and verify whether it would affect the reading repertoire. To teach spelling, a constructed response matching to sample task was employed. In this task, a sample (that could be a printed word, a picture, a picture and its correspondent printed word or a dictated word) was presented as well as a pool of randomly chosen letters. Children had to select in the correct order the letters to spell the word correspondent to the sample. Thirty Portuguese words were taught. Five studies were conducted. In Study 1, each word was taught till criterion and once it was achieved the word was no longer presented during training. Two students took part but only one achieved the criterion for the totality of the words. Although the criterion was achieved rapidly for most words, the performance decreased on the posttest probes. Study 2 employed a mixed training: groups of three words were taught together so that in each trial one of the words worked as a sample. Study 3 employed the mixed training and a cumulative baseline: words previously taught were interspersed with words to be taught. Study 4 introduced a new variable, besides the mixed training and the cumulative baseline: a compound sample. In this study, words should be constructed under the control of a sample compounded by a picture and its correspondent printed word. After training, all participants of the Studies 2, 3 and 4 showed high spelling performances and excepting one participant, all of them had great improvements in reading. Reading scores were more variable than spelling scores. Performances with new words (compounded by the syllables of the taught words) were variable and some participants did not show recombinative repertoire. Also, some participants showed performances with some words before they were actually trained. Because of that, Study 5 employed a group design to evaluate the effect of the teaching procedure. The Experimental Group took the teaching procedure lessons (the same version employed in Study 4) while the Control Group was exposed only to the assessment sessions. The Experimental Group performances in spelling, reading and other relations evaluated were significantly higher than the Control Group performances. These results showed that the procedure have been effective in teaching spelling and also in promoting the emerge of reading. / Vários estudos têm investigado a aquisição de leitura e escrita, bem como a relação entre os repertórios. Em muitos deles, as relações ensinadas privilegiam o desenvolvimento da leitura e os efeitos observados no repertório de escrita são secundários. O presente estudo teve por objetivo ensinar escrita sob controle de ditado e verificar os possíveis efeitos sobre a leitura. Para isso foi empregada uma tarefa computadorizada de construção de palavras. Nesse tipo de tarefa, um estímulo modelo (que pode ser uma palavra impressa, uma figura, uma figura e a palavra impressa correspondente ou uma palavra ditada) é apresentado juntamente com um conjunto de letras (estímulos de escolha). A tarefa do participante consiste em selecionar, entre os estímulos de escolha disponíveis, na sequência correta, as letras que permitem construir uma palavra correspondente ao modelo. Foram conduzidos cinco estudos. Em cada estudo foi ensinada a construção de 30 palavras, constituídas por sílabas simples do tipo consoante vogal. No Estudo 1 foi empregado um procedimento que previa o ensino separado de cada uma das palavras. Além disso, uma vez aprendidas, as palavras não eram revisadas. Um, entre dois participantes atingiu rapidamente o critério para cada palavra, mas a avaliação final detectou falta de manutenção do repertório. No Estudo 2, as palavras foram ensinadas de maneira intercalada e no Estudo 3, além do ensino intercalado, as palavras já aprendidas passaram a ser reapresentadas juntamente com as palavras novas nos passos subsequentes, constituindo uma linha de base cumulativa. O Estudo 4 manteve as manipulações introduzidas nos Estudos 2 e 3 e acrescentou uma nova variável: o ensino da construção da resposta sob controle de estímulo composto (figura e palavra impressa correspondente). Após a exposição ao procedimento, todos os participantes dos Estudos 2, 3 e 4 apresentaram ganhos em ditado e com exceção de um, os demais também apresentaram ganhos em leitura. Os desempenhos em leitura foram mais variáveis do que os desempenhos em ditado. Os desempenhos com palavras novas (compostas pela recombinação de sílabas das palavras ensinadas) também variaram entre os participantes e alguns deles não demonstraram repertórios recombinativos. Alguns participantes apresentaram desempenho com as palavras do conjunto não ensinado. Em virtude disso, o Estudo 5 investigou o efeito do procedimento por meio de um delineamento de grupo. O Grupo Experimental foi exposto ao procedimento do Estudo 4 (por ter sido o que gerou um responder mais estável) e o Grupo Controle foi exposto apenas às avaliações previstas pelo procedimento. O GE apresentou desempenho significativamente superior ao do GC em ditado, leitura e na maioria das outras relações testadas, o que demonstra a efetividade do procedimento de ensino no estabelecimento de escrita sob controle de ditado e também na emergência de leitura.