Multiplication by 10 base-5: Making Sense of Place Value Structure Through an Alternate Base

2015 ◽  
Vol 3 (2) ◽  
pp. 83-98
Author(s):  
Jodi Fasteen ◽  
Kathleen Melhuish ◽  
Eva Thanheiser
Keyword(s):  
Preservice Teachers ◽  
Conceptual Understanding ◽  
Sense Of Place ◽  
Number System ◽  
Place Value ◽  
Mathematical Activity ◽  
Making Sense ◽  
Procedural Fluency ◽  
Whole Number

Prior research has shown that preservice teachers (PSTs) are able to demonstrate procedural fluency with whole number rules and operations, but struggle to explain why these procedures work. Alternate bases provide a context for building conceptual understanding for overly routine rules. In this study, we analyze how PSTs are able to make sense of multiplication by 10five in base five. PSTs' mathematical activity shifted from a procedurally based concatenated digits approach to an explanation based on the structure of the place value number system.

Making sense of sensemaking: using the sensemaking epistemic game to investigate student discourse during a collaborative gas law activity

2021 ◽  
Author(s):  
Kevin H. Hunter ◽  
Jon-Marc G. Rodriguez ◽  
Nicole M. Becker
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Ideal Gas ◽  
Interactive Simulation ◽  
Structural Components ◽  
Student Discourse ◽  
Coding Scheme ◽  
Making Sense ◽  
Ideal Gas Law ◽  
The Ideal

Beyond students’ ability to manipulate variables and solve problems, chemistry instructors are also interested in students developing a deeper conceptual understanding of chemistry, that is, engaging in the process of sensemaking. The concept of sensemaking transcends problem-solving and focuses on students recognizing a gap in knowledge and working to construct an explanation that resolves this gap, leading them to “make sense” of a concept. Here, we focus on adapting and applying sensemaking as a framework to analyze three groups of students working through a collaborative gas law activity. The activity was designed around the learning cycle to aid students in constructing the ideal gas law using an interactive simulation. For this analysis, we characterized student discourse using the structural components of the sensemaking epistemic game using a deductive coding scheme. Next, we further analyzed students’ epistemic form by assessing features of the activity and student discourse related to sensemaking: whether the question was framed in a real-world context, the extent of student engagement in robust explanation building, and analysis of written scientific explanations. Our work provides further insight regarding the application and use of the sensemaking framework for analyzing students’ problem solving by providing a framework for inferring the depth with which students engage in the process of sensemaking.

Slums in India: making sense of place in urban planning

GeoJournal ◽  
2021 ◽  
Author(s):  
Jaidul Islam ◽  
Md. Julfikar Ali ◽  
Sk Mithun
Keyword(s):  
Urban Planning ◽  
Sense Of Place ◽  
Making Sense

scholarly journals Formatively assessing prospective teachers’ skills in leading mathematics discussions

2021 ◽  
Author(s):  
Meghan Shaughnessy ◽  
Nicole M. Garcia ◽  
Michaela Krug O’Neill ◽  
Sarah Kate Selling ◽  
Amber T. Willis ◽  
...  
Keyword(s):  
Elementary Teachers ◽  
Formative Assessment ◽  
Conceptual Understanding ◽  
Prospective Teachers ◽  
First Year ◽  
Teacher Education Programs ◽  
First Year Teachers ◽  
Education Programs ◽  
Prospective Elementary Teachers ◽  
Making Sense

AbstractMathematics discussions are important for helping students to develop conceptual understanding and to learn disciplinary norms and practices. In recent years, there has been increased attention to teaching prospective teachers to lead discussions with students. This paper examines the possibilities of designing a formative assessment that gathers information about prospective elementary teachers’ skills with leading problem-based mathematics discussions and makes sense of such information. A decomposition of the practice of leading discussions was developed and used to design the assessment. Nine first-year teachers who graduated from a range of different teacher education programs participated in the study. The findings reveal that our formative assessment works to gather information about teachers’ capabilities with leading discussions and that the associated tools support making sense of the information gathered. This suggests that such tools could be useful to support the formative assessment of the developing capabilities of prospective teachers.

scholarly journals Developing The Mathematics Conceptual Understanding and Procedural Fluency through Didactical Anticipatory Approach Equipped with Teaching AIDS

2018 ◽  
Vol 3 (2) ◽  
pp. 367
Author(s):  
Asmida Asmida ◽  
Sugiatno Sugiatno ◽  
Agung Hartoyo
Keyword(s):  
Conceptual Understanding ◽  
Junior High School ◽  
Mathematics Learning ◽  
Posttest Score ◽  
Mathematics Textbook ◽  
Teaching Aids ◽  
Procedural Fluency ◽  
Mathematical Problems ◽  
Epistemological Obstacles ◽  
And Mathematics

The students’ conceptual understanding and procedural fluency have not been yet integrated into the mathematics learning as the teachers’ common mathematics textbook has not explicitly explained the conceptual understanding and procedural fluency in solving the mathematical problems that the teachers have not yet connected it to the mathematics learning. The interview result shows that the students only memorize the procedures without understanding. If the procedure is continuously applied, it is predicted that the students may face the epistemological obstacles in solving the mathematical problems. This research aims at developing the students' mathematics conceptual understanding and procedural fluency through the Didactic Anticipatory Approach equipped with the teaching aids in learning the operations of integer multiplication at Junior High School in Grade VIII. This pedagogical action research involves 14 students. The research data are collected using tests, interviews, voice recorders and cameras. The result shows that learning mathematics through the Didactic Anticipatory Approach equipped with teaching aids may develop the students' conceptual understanding and mathematics procedural fluency marked by the reduced students’ epistemological obstacles. However, they are not yet been completely resolved. The students' conceptual understanding and mathematics procedural fluency also supported with the average posttest score higher than that of the pretest score.

Early Conceptual Understanding of Cardinality Predicts Superior School-Entry Number-System Knowledge

2017 ◽  
Vol 29 (2) ◽  
pp. 191-205 ◽  
Author(s):  
David C. Geary ◽  
Kristy vanMarle ◽  
Felicia W. Chu ◽  
Jeffrey Rouder ◽  
Mary K. Hoard ◽  
...  
Keyword(s):  
Reading Achievement ◽  
School Readiness ◽  
Conceptual Understanding ◽  
Parental Education ◽  
First Grade ◽  
Number System ◽  
School Entry ◽  
Number Words ◽  
Education Levels ◽  
System Knowledge

We demonstrate a link between preschoolers’ quantitative competencies and their school-entry knowledge of the relations among numbers (number-system knowledge). The quantitative competencies of 141 children (69 boys) were assessed at the beginning of preschool and throughout the next 2 years of preschool, as was their mathematics and reading achievement at the end of kindergarten and their number-system knowledge at the beginning of first grade. A combination of Bayes analyses and standard regressions revealed that the age at which the children had the conceptual insight that number words represent specific quantities (cardinal value) was strongly related to their later number-system knowledge and was more consistently related to broader mathematics than to reading achievement, controlling for intelligence, executive function, and parental education levels. The key implication is that it is not simply knowledge of cardinal value but the age of acquisition of this principle that is central to later mathematical development and school readiness.

Gypsy-Traveller narratives: Making sense of place

2012 ◽  
Vol 22 (2) ◽  
pp. 332-347 ◽  
Author(s):  
Ian Convery ◽  
Vincent O'Brien
Keyword(s):  
Sense Of Place ◽  
Family Relations ◽  
Growing Up ◽  
Self Identity ◽  
Making Sense ◽  
Ethnographic Approach ◽  
Internal Relationships

Using a co-ethnographic approach to focus on one person’s story, we explore how a sense of place may be evident in self constructed Gypsy-Traveller identity and narrative. Mary’s recounting of her experiences of living and growing up in the Caldewgate district of Carlisle (UK) illustrates the place of family relations as a key element of Gypsy-Traveller self identity and suggests, we believe, the centrality of family and internal relationships as a strong feature in the construction of personal notions and narratives of place for Gypsy-Traveller people.

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