Assessing Student Understanding of Reasoning using Argument-based Contrast Matrices

There is strong national interest in increasing student proficiency in STEM, which includes the learning and practice of scientific argumentation. The codevelopment of scientific knowledge and argumentation has shown to positively influence student general understanding of argument construction, scientific knowledge and principles. Research indicates students continue to struggle with constructing complete arguments, with specific difficulty in correctly incorporating reasoning. Numerous frameworks have been developed to support student learning about argumentation. These frameworks contain common teaching strategies for introducing and teaching reasoning within the context of a science classroom. However, these strategies do not specifically target student struggle with using reasoning, nor actively support ways for students to produce general knowledge about the importance of reasoning within argumentation. The purpose of this study was to gain insight into student process of understanding the importance of reasoning. An additional goal was to understand the usefulness of a contrasting cases activity for supporting student understanding of reasoning. Three interview sessions were conducted and recorded with pairs of 6th grade students, each session using a slight variation of a contrast matrix. A contrast matrix consists of a 2x2 table of arguments, where students compare arguments in order to identify a common differentiating feature, in this case reasoning. Transcripts of all interview sessions were analyzed for patterns of student process of isolating the contrast, and patterns for how students described the contrast and its importance within the argument. Overall, the results of this study indicate students can recognize reasoning is important as a general idea, while having only a vague idea of what reasoning is

EKSPLORASI PENGETAHUAN CALON GURU MATEMATIKA TENTANG PROSES PENALARAN MATEMATIS SISWA

The development of mathematical reasoning is part of an important process that needs to be taught to students, as reflected in teacher education. This study focuses on the education of prospective teachers of mathematics which aims to describe the knowledge of prospective teachers about students' mathematical reasoning processes. The subjects of this study were prospective mathematics teacher students who were selected by purposive sampling. The instruments used include math assignments and interview guidelines. Data analysis techniques with data reduction, data presentation, data interpretation, and making conclusions. The results of this study indicate that the knowledge of the reasoning process carried out by prospective mathematics teachers is organized into 3 levels of knowledge in each reasoning process that appears, namely generalizing, justifying, classifying, and exemplifying. At the level of knowledge of the reasoning process, student teacher candidates still have difficulty in analyzing students' reasoning processes, using the meaning of terms in everyday life, and only considering the correct reasoning process. An important aspect of the reasoning process is developing knowledge by completing the means as a medium to understand the reasoning process in each student's learning

Relationships Between Middle School Students\u27 Adaptive Reasoning When Creating Learner-Generated Drawings and Partner Talk During Inquiry-Based Mathematical Tasks

Adaptive reasoning is one of five components students use to develop mathematical expertise and become mathematically proficient. When students adapt their reasoning they are logically thinking about the mathematical relationships between concepts and adapting their thinking to solve problems. Three Act Math Tasks are popular math problems used in schools in which students engage in adaptive reasoning. These types of problems are beneficial to students because they engage students in inquiry-based learning, a kind of learning where students work to pose questions, interpret data, design ways to solve the problem and present their solutions. Little is known about how students adapt their reasoning as they partake in these types of tasks. The objective of this study is to better understand what adaptive reasoning strategies seventh graders used and how they used these strategies when engaged in inquiry-based mathematical tasks. To accomplish this, the study observed 18 seventh grade students as they worked through three mathematical tasks. The researcher observed student discussions and their drawings to see what adaptive reasoning strategies were being used by students and how the strategies were used throughout different stages of the tasks. In this way a more complete picture of how students adapted their reasoning was obtained. The researcher analyzed student use of six different adaptive reasoning indicators, including: 1) relationships and connections, 2) justifications, 3) alternates pursued, 4) prior knowledge, 5) legitimacy determined, and 6) pattern recognition. Results indicate that students used all six adaptive reasoning strategies. Students primarily adapted their reasoning by finding relationships and connections and making justifications. Additionally, each student demonstrated a unique pattern of adaptive reasoning strategies which was mediated by their partner. Use of the other four indicators, alternates pursued, prior knowledge, legitimacy determined and pattern recognition were used in conjunction with the two primary indicators. Additionally, different patterns of use were identified within the separate modalities of student drawings and discussions. This study is beneficial because it helps teachers and researchers better understand what adaptive reasoning strategies students are utilizing and the relationship between these strategies in a classroom setting. This affords teachers and researchers opportunities to develop better learning experiences and understand how students reason in light of mathematical proficiency

Using Case-Based Learning to Facilitate Clinical Reasoning Across Practice Courses in an Occupational Therapy Curriculum

Although occupational therapy educators have historically used cases as a means to prepare students for clinical practice, there is little evidence that this instructional method actually facilitates clinical reasoning. This convergent, parallel mixed methods study examined how the use of varied case formats, built on the tenets of case-based learning, facilitated specific components of clinical reasoning, and explored how the cases contributed to readiness for professional practice. Case formats included text, video, role-playing, simulated patients, and a client. Case-based learning activities included application of models and frames of reference, conducting assessments, planning and implementing interventions, clinical documentation, and identification of reasoning used. All cases included the opportunity for instructors to provide direct and appropriate feedback, and facilitation of student reflection on their performance. The Self-Assessment of Clinical Reflection and Reasoning (SACRR) was used for quantitative data analysis and detected statistically significant changes in the use of theory and frames of reference to inform practice and in student reasoning about interventions, following case-based learning. Student surveys allowed for pragmatic qualitative analysis, and identified the themes of self-awareness, confidence, and developing competence related to readiness for fieldwork and clinical practice. Student preferences for case format and benefits of varied types of cases were identified. Case-based learning used different case formats, and contributed to the occupational therapy student transition from a clinical reasoning novice to an advanced beginner. Knowledge of this process is useful to occupational therapy educators in structuring case-based learning activities to influencing reasoning

Student Questioning:what does questioning reveal about prior knowledge, historical reasoning and affect?

Students ask historical questions when they are engaged in historical reasoning and trying to understand a particular historical phenomenon. Student questioning can be regarded as the engine and a destination of historical reasoning. This study is aimed at deeper insight into thinking processes underlying students’ historical questions using a general model of questioning and a domain-specific model of historical reasoning. Thirty-three secondary school students were instructed to read a text and underline striking text segments. At the point of underlining, students were asked to verbalize their thoughts. In our protocol analysis we focused on the questions students spontaneously asked while verbalizing their prior knowledge, reasoning, and feelings. It appeared that in half of the 251 analyzed fragments (episodes) students verbalized an extent of historical reasoning and expressed feelings. Questions were mostly asked when students expressed a knowledge deficit, but spontaneous questions were also present in episodes with historical reasoning and episodes with affective responses. All components, activating prior knowledge, realizing a knowledge deficit, historical reasoning and experiencing affective thoughts, help students to ask their questions and help them to process the introduction into a historical topic

A fuzzy logic approach to manage uncertainty and improve the prediction accuracy in student model design

The intelligent tutoring systems (ITSs) are special classes of e-learning systems developed using artificial intelligent (AI) techniques to provide adaptive and personalized tutoring based on the individuality of each student. For an intelligent tutoring system to provide an interactive and adaptive assistance to students, it is important that the system knows something about the current knowledge state of each student and what learning goal he/she is trying to achieve. In other words, the ITS needs to perform two important tasks, to investigate and find out what knowledge the student has and at the same time make a plan to identify what learning objective the student intends to achieve at the end of a learning session. Both of these processes are modeling tasks that involve high level of uncertainty especially in situations where students are made to follow different reasoning paths and are not allowed to express the outcome of those reasoning in an explicit manner. The main goal of this paper is to employ the use Fuzzy logic technique as an effective and sound computational intelligence formalism to handle reasoning under uncertainty which is one major issue of great concern in student model design

In-service Teachers\u27 Reasoning about Scenarios of Teaching Mathematics to English Language Learners

The student population in the U.S. and worldwide is becoming increasingly diverse, creating a need to support all learners, especially linguistically and culturally diverse subpopulations such as English language learners (ELLs). From a social equity standpoint, the need to support these learners is critical especially in mathematics classrooms. In the U.S, the demand for mathematics teachers who are adequately prepared to teach ELLs has in fact risen. Yet, little is known about what knowledge base is essential to teach mathematics to ELLs. Driven by the need to explore this knowledge base, in this paper I explore what is involved in reasoning about teaching mathematics to ELLs. To this end, a set of instructional scenarios illustrating the work of teaching mathematics to ELLs was utilized within an assessment environment. Interviews with 10 mathematics teachers reasoning about the scenarios showed that they drew on the information provided about ELLs’ proficiency levels while reasoning through the scenarios. Also, teachers’ reasoning seems to be qualified by the extent to which they could both use their content knowledge in mathematics and modify their instructional choices according to ELLs’ language needs specified in the scenarios. This study motivates large-scale future studies examining what systematic teacher knowledge base might differentiate good teaching for ELLs from good teaching for all students

Using Contrasting Cases to Build Metacognitive Knowledge About the Impact of Salient Distracting Features in Physics Problems

Student reasoning on physics problems is often context dependent. A possible explanation is that salient distracting features (SDFs) in physics problems may cue students’ “spontaneous” reasoning. This cued reasoning is often accepted without question, even though it may be unproductive and may even preclude the use of relevant knowledge. One possible approach to address such reasoning difficulties is to strengthen students’ metacognitive skills, particularly their metacognitive knowledge. While metacognitive knowledge plays an important role in facilitating effective regulation, little is known about how to build student metacognitive knowledge. This dissertation explores the use of contrasting cases (e.g., a number of cases or instances having the same underlying knowledge across a range of contexts) to build transferable metacognitive knowledge. The goal of this dissertation is to understand how students can build general metacognitive knowledge (GMK) related to SDFs using contrasting case instruction. In particular, the GMK targeted in this work involves reflection on how and why SDFs can impact reasoning. Multiple sets of contrasting cases, or contrast pairs, were designed to highlight the GMK via descriptive vignettes of fictional students as they answered physics questions. In an experiment, in one condition (non-synthesis), college students compared each contrast pair separately. In the other condition (synthesis), students compared the same pairs together. All students received direct instruction on the potential value of reflecting on how SDFs could impact their reasoning, and then took a post-test. Results revealed that synthesis students could generate the GMK while no non-synthesis students did. Analysis also revealed that synthesis students demonstrated greater learning of the GMK on the post-test. Furthermore, no non-synthesis students could apply the GMK, even after being told the knowledge. Together, these findings suggest that synthesis may be an effective approach to building student GMK, while direct instruction on its own is not. More broadly, students may not generate GMK on their own without the appropriate instructional scaffolding

Instructional Framing and Student Learning of Community Interactions

Ecology is a broad field of science that encompasses many disciplines with large impacts in our society (AAAS, 2011; NRC, 2009). To understand the complex systems and concepts of this discipline requires a foundation of knowledge that students often gain in the classroom (Bransford, Brown, & Cocking, 2000). Helping students develop this foundation of knowledge requires an understanding of how they use surface and deep reasoning skills to understand and learn new material. In addition, using methods to teach students to transfer these skills between multiple contexts is key to expanding their ability to broadly apply knowledge. The purpose of this research was twofold. First, I wanted to understand the differences between students who used surface reasoning skills and students who used deep reasoning skills. Second, I wanted to understand the effects of two types of instructional framing that may improve students’ ability to apply knowledge between multiple contexts. In the first study, undergraduate introductory biology students were given during-instruction and post-instruction assessments that tested their ability to explain the effects of disturbances within a food web. Responses were coded to assess students’ surface and deep reasoning skills. Results showed a wide variation in student responses. Findings from this study suggest that when learning a new subject, students may use a combination of surface and deep reasoning to solve problems. Additionally, surface reasoning students have the potential to meet or exceed the same standards as deep reasoning students. In the second study, students were split into two instructional framing groups: bounded and expansive. Expansive framing is an instructional method designed to help students understand that the concepts and skills taught in a single context are applicable in multiple scenarios (Engle, Ngyuen, & Mendelson, 2011). Bounded framing involves presenting learning events as segmented ideas, separate from each other. The instructor focuses on developing the students’ understanding in a single context. Students were taught food web concepts and reasoning skills using either bounded framing or expansive framing methods. In a follow-up session, students were asked questions about the knowledge gained from the prior session and asked to reason about the effects of food web perturbations. Findings from the second study suggest that compared to bounded framing, expansive framing does not significantly affect the transfer of reasoning skills between contexts. In addition, regardless of prior knowledge about the subject, students were able to transfer reasoning skills and knowledge learned in the first session to the follow-up session. Advisor: Joseph T. Daue