Developing a Learning Progression for Curriculum,Instruction, and Student Learning: An Example from Mathematics Education

Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked understanding of students learning over time through careful articulation of a curricular framework and progression, instructional sequence, assessments, and levels of sophistication in student learning. Under this broadened conceptualization, we advance a methodology for developing and validating learning progressions, and advance several design considerations that can guide research concerned with engendering forms of mathematics learning, and curricular and instructional support for that learning. We advance a two-phase methodology of (a) research and development, and (b) testing and revision. Each phase involves iterative cycles of design and experimentation with the aim of developing a validated learning progression. In particular, we gathered empirical data to revise our hypothesized curricular framework and progression and to measure change in students. thinking over time as a means to validate both the effectiveness of our instructional sequence and of the assessments designed to capture learning. We use the context of early algebra to exemplify our approach to learning progressions in mathematics education with a focus on the concept of mathematical equivalence across Grades 3-5. The domain of work on research on learning over time is evolving; our work contributes a broadened role for learning progressions work in mathematics education research and practice.     

初中生班级团体依恋、自悯与学习倦怠的关系

本研究采用青少年学习倦怠量表、班级团体依恋问卷、自悯量表、青少年父母同伴依恋问卷、生活满意度量表、和自编学业满意度问题对658名初中生进行问卷调查,考察当代初中生对其所在班级的团体依恋和自悯与学习倦怠之间的关系,并检验自悯在班级团体依恋和学习倦怠关系中的中介作用。结果发现：在控制了人口学变量、父母依恋、同伴依恋、学业满意度和生活满意度之后,（1）班级团体依恋焦虑和回避均能显著正向预测学习倦怠;（2）自悯显著负向预测学习倦怠;（3）自悯在班级团体依恋焦虑和学习倦怠的关系中起到完全中介的作用,而在班级团体依恋回避和学习倦怠的关系中起部分中介的作用。研究结果对于从班级团体依恋和自悯的角度理解中学生学习倦怠具有重要意义。     

交流语境对学习双方语言准确性的影响

研究安排了交流任务和个人迁移任务,创设了三种交流语境,比较不同语境下交流学习双方的语言准确性。结果显示：（1）三种语境中仅语言交流时语言准确性水平最高,交流语境中的对象可视性阻碍了语言准确性提高的速率,表情可视性降低了语言准确性水平;交流语言相似性水平高的被试,语言准确性水平提高的效率和效果均高于低的一方;（2）交流任务中仅语言交流时语言准确性最高,个人任务中对象可视语境下准确性最低;和交流任务相比,高相似被试个人任务中的准确性更高。表明：语言认知不完全代表交流认知,对象可视性阻碍语言认知和交流认知水平,表情可视性辅助语言共同提高交流认知水平。     

情绪确定性对学习判断的影响

为了揭示情绪的确定性维度对学习判断的影响,本研究通过使用即时学习判断范式的两个实验,分别探讨了高确定性情绪(愤怒、快乐)和低确定性情绪(恐惧、惊喜)的被试在学习判断中的表现。结果显示:(1)愤怒组和快乐组花费在项目学习上的时间显著少于恐惧组和惊喜组;(2)愤怒组的学习判断值显著高于恐惧组;(3)愤怒组的学习判断准确性显著低于恐惧组。从而证明了情绪的确定性维度与学习判断之间的因果关系。     

Context Matters for Social-Emotional Learning: Examining Variation in Program Impact by Dimensions of School Climate

This paper examines whether three dimensions of school climate—leadership, accountability, and safety/respect—moderated the impacts of the INSIGHTS program on students’ social‐emotional, behavioral, and academic outcomes. Twenty‐two urban schools and N = 435 low‐income racial/ethnic minority students were enrolled in the study and received intervention services across the course of 2 years, in both kindergarten and first grade. Intervention effects on math and reading achievement were larger for students enrolled in schools with lower overall levels of leadership, accountability, and safety/respect at baseline. Program impacts on disruptive behaviors were greater in schools with lower levels of accountability at baseline; impacts on sustained attention were greater in schools with lower levels of safety/respect at baseline. Implications for Social‐Emotional Learning program implementation, replication, and scale‐up are discussed.     

Learning General Phonological Rules From Distributional Information: A Computational Model

Phonological rules create alternations in the phonetic realizations of related words. These rules must be learned by infants in order to identify the phonological inventory, the morphological structure, and the lexicon of a language. Recent work proposes a computational model for the learning of one kind of phonological alternation, allophony (Peperkamp, Le Calvez, Nadal, & Dupoux, 2006). This paper extends the model to account for learning of a broader set of phonological alternations and the formalization of these alternations as general rules. In Experiment 1, we apply the original model to new data in Dutch and demonstrate its limitations in learning nonallophonic rules. In Experiment 2, we extend the model to allow it to learn general rules for alternations that apply to a class of segments. In Experiment 3, the model is further extended to allow for generalization by context; we argue that this generalization must be constrained by linguistic principles.     

Making Probabilistic Relational Categories Learnable

Theories of relational concept acquisition (e.g., schema induction) based on structured intersection discovery predict that relational concepts with a probabilistic (i.e., family resemblance) structure ought to be extremely difficult to learn. We report four experiments testing this prediction by investigating conditions hypothesized to facilitate the learning of such categories. Experiment 1 showed that changing the task from a category‐learning task to choosing the “winning” object in each stimulus greatly facilitated participants' ability to learn probabilistic relational categories. Experiments 2 and 3 further investigated the mechanisms underlying this “who's winning” effect. Experiment 4 replicated and generalized the “who's winning” effect with more natural stimuli. Together, our findings suggest that people learn relational concepts by a process of intersection discovery akin to schema induction, and that any task that encourages people to discover a higher order relation that remains invariant over members of a category will facilitate the learning of putatively probabilistic relational concepts.     

Non‐Bayesian Noun Generalization in 3‐ to 5‐Year‐Old Children: Probing the Role of Prior Knowledge in the Suspicious Coincidence Effect

It is unclear how children learn labels for multiple overlapping categories such as “Labrador,” “dog,” and “animal.” Xu and Tenenbaum (2007a) suggested that learners infer correct meanings with the help of Bayesian inference. They instantiated these claims in a Bayesian model, which they tested with preschoolers and adults. Here, we report data testing a developmental prediction of the Bayesian model—that more knowledge should lead to narrower category inferences when presented with multiple subordinate exemplars. Two experiments did not support this prediction. Children with more category knowledge showed broader generalization when presented with multiple subordinate exemplars, compared to less knowledgeable children and adults. This implies a U‐shaped developmental trend. The Bayesian model was not able to account for these data, even with inputs that reflected the similarity judgments of children. We discuss implications for the Bayesian model, including a combined Bayesian/morphological knowledge account that could explain the demonstrated U‐shaped trend.     

Development of Different Forms of Skill Learning Throughout the Lifespan

The acquisition of complex motor, cognitive, and social skills, like playing a musical instrument or mastering sports or a language, is generally associated with implicit skill learning (SL). Although it is a general view that SL is most effective in childhood, and such skills are best acquired if learning starts early, this idea has rarely been tested by systematic empirical studies on the developmental pathways of SL from childhood to old age. In this paper, we challenge the view that childhood and early school years are the prime time for skill learning by tracking age‐related changes in performance in three different paradigms of SL. We collected data from participants between 7 and 87 years for (1) a Serial Reaction Time Task (SRT) testing the learning of motor sequences, (2) an Artificial Grammar Learning (AGL) task testing the extraction of regularities from auditory sequences, and (3) Probabilistic Category Learning in the Weather Prediction task (WP), a non‐sequential categorization task. Results on all three tasks show that adolescence and adulthood are the most efficient periods for skill learning, since instead of becoming less and less effective with age, SL improves from childhood into adulthood and then later declines with aging.