Pre-service Middle School Teachers’ Knowledge of Algebraic Thinking

In this study we examined the relationship between 18 pre-service middle school teachers’ own ability to use algebraic thinking to solve problems and their ability to recognize and interpret the algebraic thinking of middle school students. We assessed the pre-service teachers’ own algebraic thinking by examining their solutions and explanations to multiple algebra-based tasks posed during a semester-long mathematics content course. We assessed their ability to recognize and interpret the algebraic thinking of students in two ways. The first was by analyzing the preservice teachers’ ability to interpret students’ written solutions to open-ended algebra-based tasks. The second was by analyzing their ability to plan, conduct, and analyze algebraic thinking (AT) interviews of middle school students during a concurrent semester-long, field-based education class. We used algebraic habits of mind as a framework to identify the algebraic thinking that pre-service teachers exhibited in their own problem solving, and we asked students to use them to analyze the algebraic thinking of middle school students. The data revealed that pre-service teachers’ AT abilities varied across different features of algebraic thinking. In particular, their ability to justify a rule was the weakest of seven AT features. The ability to recognize and interpret the algebraic thinking of students was strongly correlated with the strength of the pre-service teachers’ own algebraic thinking. Implications for mathematics teacher education are discussed

Pre-Service Teachers’ Knowledge of Algebraic Thinking and the Characteristics of the Questions Posed for Students

In this study, we explored the relationship between the strength of pre-service teachers’ algebraic thinking and the characteristics of the questions they posed during cognitive interviews that focused on probing the algebraic thinking of middle school students. We developed a performance rubric to evaluate the strength of pre-service teachers’ algebraic thinking across 130 algebra-based tasks. We used an existing coding scheme found in the literature to analyze the characteristics of the questions pre-service teachers posed during clinical interviews. We found that pre-service teachers with higher algebraic thinking abilities were able to pose probing questions that uncovered student thinking through the use of follow up questions. In comparison, pre-service teachers with lower algebraic thinking abilities asked factual questions; moving from one question to the next without posing follow up questions to probe student thinking

EUS-Guided Pancreatic Cyst Ablation: a Clinical and Technical Review

Purpose of Review Pancreatic cystic lesions represent a growing public health dilemma, particularly as our population ages and cross-sectional imaging becomes more sensitive. Mucinous cysts carry a clinically significant risk of developing pancreatic cancer, which carries an extremely poor prognosis. Determining which cysts will develop cancer may be challenging, and surgical resection of the pancreas carries significant morbidity. The goal of this paper is to review the rationale for cyst ablation and discuss prior and current research on cyst ablation techniques and efficacy. Indications, contraindications, and factors related to optimal patient selection are outlined. Recent Findings Endoscopic ultrasound-guided chemoablation of pancreatic cysts has been performed in neoplastic cysts, with varying levels of efficacy. Safety concerns arose due to the risk of pancreatitis in alcohol-based treatments; however, the most recent data using a non-alcohol chemoablation cocktail suggests that ablation is effective without the need for alcohol, resulting in a significantly more favorable adverse event profile. Summary Endoscopic ultrasound-guided chemoablation of neoplastic pancreatic cysts is a promising, minimally invasive approach for treatment of cysts, with recent significant advances in safety and efficacy, suggesting that it should play a role in the treatment algorithm

Prospective K-8 Teachers’ Knowledge of Relational Thinking

The goal of this study was to examine two issues: First, pre-service teachers’ ability and inclination to think relationally prior to instruction about the role relational thinking plays in the K-8 mathematics curriculum. Second, to examine task specific variables possibly associated with pre-service teachers’ inclination to engage in relational thinking. The results revealed that preservice teachers engage in relational thinking about equality, however, their inclination to do so is rather limited. Furthermore, they tend to engage in relational thinking more frequently in the context of arithmetic than algebra-related tasks. Pre-service teachers’ inclination to engage in relational thinking appeared to also relate to the overall task complexity and the use of variables. Implications of these findings for pre-service teacher education are provided

Regional comparisons of nano-mechanical properties of the human meniscus; structure and function

Osteoarthritis (OA) is a debilitating disease that is becoming more prevalent in today’s society. OA affects approximately 28 million adults in the United States alone and when present in the knee joint, usually leads to a total knee replacement. Numerous studies have been conducted to determine possible methods to halt the initiation of OA, but the structural integrity of the menisci has been shown have a direct effect on the progression of OA. Menisci are two C-shaped structures that are attached to the tibial plateau and aid in facilitating proper load transmission within the knee. The meniscal cross-section is wedge-like to fit the contour of the femoral condyles and help attenuate stresses on the tibial plateau. While meniscal tears are common, only the outer 1/3 of the meniscus is vascularized and has the capacity to heal, hence tears of the inner 2/3rds are generally treated via meniscectomy, leading to OA. To help combat this OA epidemic, an effective biomimetric meniscal replacement is needed. Numerous mechanical and biochemical studies have been conducted on the human meniscus, but very little is known about the mechanical properties on the nano-scale and how meniscal constituents are distributed in the meniscal cross-section. The regional (anterior, central and posterior) nano-mechanical properties of the meniscal superficial layers (both tibial and femoral contacting) and meniscal deep zone were investigated via nanoindentation to examine the regional inhomogeneity of both the lateral and medial menisci. Additionally, these results were compared to quantitative histological values to better formulate a structure-function relationship on the nano-scale. These data will prove imperative for further advancements of a tissue engineered meniscal replacement

K-8 Pre-service Teachers’ Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers\u27 ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers\u27 ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed

Exploring the Relationship between K-8 Prospective Teachers’ Algebraic Thinking Proficiency and the Questions They Pose during Diagnostic Algebraic Thinking Interviews

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. In contrast, prospective teachers with higher algebraic thinking proficiency were able to pose probing questions to investigate student thinking or help students clarify their thinking. However, less than half of their questions were of this probing type. These results suggest that prospective teachers’ algebraic thinking proficiency is related to the types of questions they ask to explore the algebraic thinking of students. Implications for mathematics teacher education are discussed

Mathematical Problem Posing as a Measure of Curricular Effect on Students\u27 Learning

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students\u27 learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students\u27 responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed