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About this paper symposium
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| Panel 8. Education, Schooling |
| Paper #1 | |
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| Systematic Replication of Pre-K Mathematics Tutorial: Does the Implementation Delivery Model Matter? | |
| Author information | Role |
| Kylie Flynn, WestEd, United States | Presenting author |
| Alice Klein, WestEd, United States | Non-presenting author |
| Abstract | |
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Introduction and Hypotheses: The purpose of this project is twofold. The first is to conduct a replication study of Pre-K Mathematics Tutorial (PKMT), a Tier-2 tutoring intervention for improving the mathematical knowledge of pre-kindergarten (pre-k) children at risk for mathematics disabilities. The original efficacy study, which met WWC standards without reservations, found that PKMT had statistically significant positive effects on math outcomes for very low-performing children (Citation Omitted). The second purpose is to systematically vary the implementation of PKMT to compare the relative effectiveness of two delivery models for tutoring - a pull-out model and an in-class model. Both models were tested in randomized controlled trials (RCTs). The first study involved a “pull-out” model where tutors worked with pairs of children outside the classroom, and the second study involved an “in-class” model where classroom teaching staff worked with pairs of children in the classroom. For both RCTs, participating pre-k classrooms (unit of random assignment) were assigned to either the treatment condition or the business-as-usual (BAU) condition. We hypothesized that math outcomes would be higher at pre-k post-test for children in the treatment group than for children in the BAU group. Study Population: The RCTs took place in one large Head Start program and two midsize state preschool programs in CA. Our sample was comprised of ethnically and linguistically diverse children with Latinx comprising the largest group at 35%. About half the sample were girls. Methods: Assessors were trained to administer two math outcome measures, the Child Math Assessment (Citation Omitted) and the Test of Early Mathematics Ability (TEMA-3 Ginsburg & Baroody, 2003). At the beginning of each randomized study, all four-year-old children in participating classes were screened on a measure comprising three tasks from the CMA (Citation Omitted) that predicted risk for mathematics difficulties in kindergarten. Children who met the screening criterion for very low performance in math and had parental consent were included in the research sample and assessed individually on both math measures at pretest and again at post-test. The first study (pull-out model) included 216 children, and the second study (in-class model) included 180 children. For each RCT, the independent evaluator assessed baseline equivalence and estimated impacts on each math outcome measure for the treatment vs. BAU contrast. Impacts on each math achievement outcome was examined using a three-level hierarchical linear model in which children were nested within classrooms which were nested within randomization blocks. Hedges' g was used to compute effect sizes. Results: Impact analyses for the first study, the pull-out vs. BAU contrast, showed a substantively important and statistically significant impact on both math measures, the CMA (ES = 0.35, p = 0.006) and the TEMA Raw Score (ES = 0.37, p = 0.003). Attrition at post-test was low (7-8%). These findings are important, because they replicated the original study. Figures 1 and 2 illustrate the baseline and impact findings for each math outcome measure. Analyses for the second study, the in-class vs. BAU contrast, are underway and will be presented at the conference. |
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| Paper #2 | |
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| Examining the Impact of Intervention Onset of an Early Numeracy Intervention Through Systematic Replication | |
| Author information | Role |
| Benjamin Clarke, University of Oregon, United States | Presenting author |
| Chris Doabler, University of Texas, Austin, United States | Non-presenting author |
| Jessica Turtura, University of Oregon, United States | Non-presenting author |
| Derek Kosty, Oregon Research Institute, United States | Non-presenting author |
| Abstract | |
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The rationale for this study is twofold. The primary purpose was to conduct a systematic replication study of a previously validated kindergarten mathematics intervention (ROOTS) for students at risk for mathematics learning disabilities (MLD) across school types and student populations intentionally selected to differ from prior efficacy studies (Authors, 2021). A secondary purpose of the project was to investigate the relationship between intervention onset and student math outcomes. In this study, the onset of intervention was varied based on findings from a previous large scale efficacy trial (Authors, 2020). In the previous study, two cohorts of students participated. In one cohort, the intervention was delivered in the second half of the school year. In the other cohort, the intervention was delivered towards the beginning of the school year. Stronger effects were found in the cohort that received the intervention towards the beginning of the year (Authors, 2019). Based on these findings and because intervention onset was not systematically manipulated, the current study was designed to test the effect of intervention onset on student math outcomes. ROOTS is a 50-lesson kindergarten intervention program and is delivered to small groups consisting of 2 to 5 students, 5 times per week, for 10-12 weeks. Each ROOTS lesson is approximately 20 minutes in duration and includes 4 to 5 brief mathematics activities that center on whole number concepts and skills. ROOTS is aligned to the Common Core State Standards and provides in-depth instruction on critical whole number concepts including counting and cardinality, operations and algebraic thinking, and number operations in base 10. The professional development and instructional architecture support high implementation fidelity. ROOTS lessons provide teachers with guidelines for modeling and demonstrating what they want students to learn and providing specific academic feedback to students as they engage in learning activities. Blocking on classroom, students who were identified as at-risk for MLD were randomly assigned to one of three conditions: (a) a beginning of the year ROOTS condition (BOY-ROOTS), (b) a middle of the year ROOTS condition (MOY-ROOTS), and (c) a no-treatment, business-as-usual (BAU) control condition. Sample size for the study was 90 students. For comparisons between conditions, we utilized a partially nested randomized design and for comparisons between intervention groups, we utilized a fully cluster-randomized design. Student outcomes were assessed using both proximal and distal early numeracy measures. Initial analyses suggest a general pattern replicating the positive effects of the intervention on early numeracy, but not effects of intervention onset. Significant differences between treatment (BOY and MOY) and control (BAU) on end of the year math outcomes favoring treatment. Significant differences between BOY and MOY at the middle of the year (post BOY treatment and prior to MOY treatment) favoring BOY. No significant differences between BOY and MOY at the end of the year (after treatment had been revived by each treatment condition). Results from the study will be shared and implications for replication research and intervention delivery within Multi-tier Systems of Support (MTSS) will be discussed. |
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| Paper #3 | |
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| Developing a Mathematics Vocabulary Intervention for Upper Elementary Students with Mathematics Difficulty | |
| Author information | Role |
| Elizabeth Stevens, The University of Kansas, United States | Presenting author |
| Abstract | |
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Mathematics vocabulary knowledge is necessary for students to communicate about mathematics, read and understand text-based problems, and interpret mathematics content. Research demonstrates a positive association between students’ mathematics vocabulary knowledge and mathematics performance across the elementary grades (e.g., Lin et al., 2021). Students with mathematics difficulty (MD) perform significantly lower on math-vocabulary measures than students without MD (e.g., Forsyth & Powell, 2017). Mathematics vocabulary is challenging for students with MD and emergent bilinguals (Vukovic & Lesaux, 2013) because terms have multiple meanings across content areas (e.g., 25 is the product of 5 x 5 versus products sold) and within mathematics (e.g., round to the nearest ten versus a sphere is round). However, there are no existing interventions to support teachers with providing mathematics vocabulary instruction to students with MD. We present findings from an ongoing project to develop a mathematics vocabulary intervention for third and fourth grade students with MD. A challenge in providing effective vocabulary instruction is choosing which mathematics words to teach. Unfortunately, there is no common list of mathematics terms students need to know at each grade level in the U.S. In Year 1 of this project, we filled that void by creating a database of critical mathematics terms to teach informed by elementary textbook glossaries. This analysis informed the critical terms for the intervention materials we developed in Year 2. We asked: What mathematics terms are in elementary textbook glossaries and do authors provide visuals and translations of those terms for emergent bilinguals? What are high-priority terms (i.e., in all curricula) and vertically-aligned terms (i.e., in at least three consecutive grade levels)? Finally, what terms are critical (i.e., high priority and vertically aligned) and are they technical, subtechnical, symbolic, or general as Monroe and Panchshyn (1995) define? We digitally accessed three commonly used, Common Core-aligned elementary mathematics curricula. We coded glossaries at each grade level (i.e., K-5) for terms, definitions, Spanish translations, and visuals. All data extracted were double coded (99.3% reliability). We identified 866 unique terms students are expected to know by middle school (Authors, in review). Table 1 presents the results for our first research question. We identified 126 high-priority terms. Kindergarten had the fewest high-priority terms (n = 9), then first grade (n = 10), fifth grade (n = 17), third grade (n = 19), and second grade (n = 29). Fourth grade had the most high-priority terms (n = 42). We identified 151 vertically-aligned terms. Finally, we identified 67 critical terms; of these, 27 were technical, 40 were subtechnical, 20 were symbolic, and none were general. We will discuss the implications of these findings for researchers, practitioners, and publishers. Additionally, we will describe how we used these findings to collaboratively develop mathematics vocabulary materials. In Year 2, we iteratively piloted, revised, and refined intervention materials. Participating teachers reviewed the high-priority and vertically-aligned terms from the textbook glossary analysis and suggested which terms to teach. Additionally, through focus groups, teachers provided feedback on the feasibility and usability of the materials in real-world settings. |
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| Paper #4 | |
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| Evaluating the Effectiveness of Fraction Sense Interventions in Schools: Achievements and Obstacles | |
| Author information | Role |
| Nancy C. Jordan, University of Delaware, United States | Presenting author |
| Nancy Dyson, University of Delaware, United States | Non-presenting author |
| Taylor Paige Guba, University of Delaware, United States | Non-presenting author |
| Abstract | |
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Mastering fractions is a gateway to understanding algebra, yet for students with math difficulties (MD) this competency remains elusive. Many of these students leave 6th grade with a weak understanding of fractions, despite years of formal fraction instruction (e.g., Authors, 2023). Consequently, their opportunities to benefit from higher-level math and pursue successful STEM careers are severely limited. Recognizing this challenge, we developed a specialized fraction sense intervention (FSI) designed for 6th graders with MD. Our current focus is on assessing how effectively this FSI works when implemented by classroom teachers versus researchers. Participants included 32 sixth-grade mathematics intervention classes. There were 253 consenting students. Students qualified for intervention services in their school by performing at least two years below grade level in math. Fourteen schools within four public districts participated. The schools served students of mixed SES and race/ethnicity. Teachers within schools were randomly assigned to either the intervention or control condition. Teachers implemented the FSI within their regular intervention classes in middle school. The set of 24 30-minute animated PowerPoint lessons draws from research in the cognitive and learning sciences, emphasizing gestures, concreteness fading, interleaved and distributed practice, meaningful contexts, mathematical equivalence, and linear representations. Control teachers used their regular intervention curriculum, which included fractions. Our team administered assessments before and after the intervention, which measured proficiency in fraction concepts, fraction arithmetic, applied fraction problems, fraction comparisons, measurement, and fraction number line estimation. We conducted a 2-level mixed effects model to determine the effects of the intervention on student performance on fractions outcomes. Covariates included pretest scores on the outcome measures along with cognitive variables. Because data collection is ongoing, this analysis does not include other teacher level variables. Therefore, these results should be interpreted cautiously. There was a significant effect of the intervention on the overall posttest scores after controlling for pretest scores, working memory, vocabulary, proportional reasoning, and classroom attentive behavior, F (1, 182.956) = 36.288, p < .001, such that students in the FSI group outperformed students in the control group with an effect size of .58 (Cohen’s d). For the multivariate model with individual outcome measures, there were statistically significant differences (p < .05) between the FSI and control intervention group on all fraction measures except fraction comparisons. Table 1 presents the raw scores at posttest for all the fraction measures as well as the results of the mixed effects model for the individual fractions tasks and effect sizes. This study is part of a larger project aimed at evaluating the effectiveness of the FSI program when implemented by teachers. Our findings indicate that the FSI can be effectively delivered in intervention classrooms using animated PowerPoint slides. However, real-world classroom settings introduce variables beyond the control of experimenters, which can impact the results. We will explore the challenges of conducting school-based intervention research in the post-pandemic era, including issues related to recruitment, scheduling, dosage, and the implementation of interventions in different school settings. |
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Building foundational mathematics knowledge: Pre-kindergarten, elementary, and middle school interventions for learners with mathematics difficulties
Submission Type
Paper Symposium
Description
| Session Title | Building foundational mathematics knowledge: Pre-kindergarten, elementary, and middle school interventions for learners with mathematics difficulties |