An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge

Fyfe, Emily R.; DeCaro, Marci S.; Rittle‐Johnson, Bethany

doi:10.1111/bjep.12035

Cited by 39 publications

(30 citation statements)

References 65 publications

(85 reference statements)

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“…Children received conceptual instruction on the relational meaning of the equal sign that was nearly identical to instruction from our tutoring studies Fyfe et al, 2014). Specifically, four closed, non-standard equations (e.g., 3 + 4 = 3 + 4; 4 + 4 = 3 + 5; 7 = 3 + 4) were printed on laminated cardstock.…”

Section: Methodsmentioning

confidence: 99%

“…The mathematical equivalence assessment was a shortened version of the assessment used in our one-on-one tutoring studies Fyfe et al, 2014) to meet district standards for limiting classroom time spent on testing. The assessment included both procedural and conceptual knowledge scales.…”

Section: Assessment and Codingmentioning

confidence: 99%

“…This initial research shed light on when and why an explore-instruct approach is effective with elementary-school children learning mathematical equivalence. In two previous studies, elementary-school children solved novel math problems and received immediate trial-by-trial accuracy feedback either before or after receiving conceptual instruction on the meaning of the equal sign Fyfe, DeCaro, & Rittle-Johnson, 2014). Both studies occurred in a one-on-one tutoring context.…”

mentioning

confidence: 99%

“…A second study identified a boundary condition for when an explore-instruct approach supports greater learning (Fyfe et al, 2014). In this study, children again received trial-bytrial accuracy feedback (e.g., the correct answer).…”

mentioning

confidence: 99%

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Wait for it . . . Delaying Instruction Improves Mathematics Problem Solving: A Classroom Study

Loehr¹,

Fyfe²,

Rittle‐Johnson³

2014

The Journal of Problem Solving

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Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical equivalence problems either before or after receiving brief conceptual instruction. In Experiment 1 (n = 41), the explore-instruct approach was less effective at supporting learning than an instruct-solve approach. However, it did not include a common, but often overlooked feature of an explore-instruct approach, which is provision of a knowledge-application activity after instruction. In Experiment 2 (n = 47), we included a knowledge-application activity by having all children check their answers on previously solved problems. The explore-instruct approach in this experiment led to superior learning than an instruct-solve approach. Findings suggest promise for an explore-instruct approach, provided learners have the opportunity to apply knowledge from instruction.

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Section: Methodsmentioning

confidence: 99%

Section: Assessment and Codingmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Wait for it . . . Delaying Instruction Improves Mathematics Problem Solving: A Classroom Study

Loehr¹,

Fyfe²,

Rittle‐Johnson³

2014

The Journal of Problem Solving

Self Cite

View full text Add to dashboard Cite

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“…The purpose of RQ1 was to determine the impact of teacher knowledge as measured by the Mathematical Equivalence Knowledge Assessment (MEKA) (Fyfe et al, 2014;Rittle-Johnson, Matthews, Taylor & McEldoon, 2011) Examine explicit knowledge of the equal sign.…”

Section: Description Of Instrumentsmentioning

confidence: 99%

Understanding the meaning of the equal sign : an investigation of elementary students and teachers.

Bennett

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I would like to thank Dr. Karen Karp, my advisor and dissertation chair. Dr. Karp has long been a most supportive and encouraging mentor to me. As a student in her class and especially as her doctoral student, Dr. Karp inspired me to think critically and she has always expected me to succeed. I have the deepest respect and admiration for Dr. Karp.My words can never fully express the level of gratitude I have for the innumerable instances of guiding, supporting and teaching I have received from Dr. Karp. I thank Dr.Karp for the role she has played in my academic career. The purpose of this study was to investigate the impact of two different policies for implementing new mathematics standards in two schools, for grades two through five, on student understanding of the equal sign. The study also examined teachers' knowledge of the equal sign. The research used a mixed methods design to explore differences in student understanding of the equal sign as a result of how standards were implemented in two adjoining states with two different decisions as to when the standards would be implemented. This dissertation shares research that may be of interest to teachers, administrators, teacher educators and other stakeholders.The main constructs under investigation were student understanding of the equal sign, teacher knowledge regarding the equal sign including how it is taught and assessed, and the impact of different implementation schedules for new mathematics standards on student performance on their knowledge of the meaning of the equal sign -a standard that was not previously explicit in either state.The study was conducted in two adjoining Midwestern states in three separate schools (fifth grade students from one of the states are housed in a middle school building vii for overcrowding reasons and are equivalent to fifth grade students in an elementary setting). Each school as per their state mandates, followed the timeline for new mathematics standards implementation with one school in the fourth year of implementation and the other two (same district) in their first year.The sample was 1,182 students in second, third, fourth and fifth grade and their forty-two classroom teachers. Students and teachers from the three schools were given the Mathematical Equivalence Knowledge Assessment (MEKA) as a measurement of teacher knowledge and student understanding of the equal sign. Data from teacher interviews and surveys were used to complement findings related to their students' understanding of the equal sign and their classroom practices related to this topic. A hierarchical linear model was used to detect differences between student scores on the MEKA in each school in the two states.To determine the impact of teacher knowledge of the equal sign on student understanding of the equal sign an unconditional hierarchical linear model and a follow up ANCOVA were conducted using the MEKA results from both teacher and student participants. The same model was also used to detect significant differences found between student sc...

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PROTOCOL: Problem solving before instruction (PS‐I) to promote learning and motivation in child and adult students

González-Cabañes

García

Chase

et al. 2023

Campbell Systematic Reviews

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This is the protocol for a Campbell systematic review. The objectives are as follows: The purpose of this review is to synthesize the evidence about the efficacy of problem solving before instruction (PS‐I) to promote learning and motivation in students. Specifically, this review is designed to answer the following questions: To what degree does PS‐I affect learning and motivation, relative to alternative learning approaches? To what extent is the efficacy of PS‐I associated with the use of different design features within it, including the use of group work, contrasting cases, and metacognitive guidance in the initial problem‐solving activity, and the use of explanations that build upon students' solutions in the explicit instruction phase? To what extent is the relative efficacy of PS‐I associated with the contextual factors of activities used as control, age of students, duration of the interventions, and learning domain? What is the quality of the existent evidence to evaluate these questions in terms of number of studies included and potential biases derived from publication and methodological restrictions?

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An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge

Abstract: Providing conceptual instruction prior to problem solving was the more effective sequencing of activities than the reverse. We compare these results with previous, contrasting findings to outline a potential framework for understanding when instruction should or should not be delayed.

Cited by 39 publications

References 65 publications

Wait for it . . . Delaying Instruction Improves Mathematics Problem Solving: A Classroom Study

Wait for it . . . Delaying Instruction Improves Mathematics Problem Solving: A Classroom Study

Understanding the meaning of the equal sign : an investigation of elementary students and teachers.

PROTOCOL: Problem solving before instruction (PS‐I) to promote learning and motivation in child and adult students

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