How Math Success by DMTI Aligns with Hattie's High-Impact Strategies

Math Success by DMTI empowers teachers with research-backed resources and professional development focused on teacher clarity, feedback, and collaborative learning.

Introduction:

Hattie's "Visible Learning" research has heightened our understanding of effective teaching practices (Hattie, 2008). By synthesizing over 800 meta-analyses, Hattie identified key factors significantly impacting student achievement, using effect sizes to quantify their influence. Note that an effect size of 1 means the sample population has shifted or increased by 1 standard deviation. Furthermore, it is important to note that an effect size of 0.40 represents one year's typical academic growth (Hattie, 2012). This framework allows educators to prioritize high-impact strategies, promoting evidence-based teaching practices.

While Hattie's work offers valuable insights, it is not without limitations. Critics argue that relying solely on effect sizes may oversimplify complex educational processes (Biesta, 2011) and that these rankings do not fully capture the context-dependent nature of interventions (Snook et al., 2009). Despite these concerns, Hattie's research remains a powerful tool for improving teaching and learning when applied thoughtfully.

The Developing Mathematical Thinking (DMT) Framework

It is one thing for a school administrator to suggest that teachers implement these high-impact strategies. However, it is important to truly understand how they can be utilized in teaching a topic such as mathematics. This overview focuses on the connections and implications of how the Developing Mathematical Thinking Institute incorporates some of these strategies.

The Developing Mathematical Thinking framework is built on key practices that influence how they deliver summer and embedded provisional development and the design of their curricular resources (Brendefur et al., 2015). These five practices are taking students' ideas seriously, encouraging multiple strategies and models, pressing students conceptually, focusing on the structure of mathematics, and addressing misconceptions.

Professional Development Through the DMT Framework

The Developing Mathematical Thinking (DMT) framework for professional development is a comprehensive, multiyear program designed to help teachers effectively implement its five key dimensions in their classrooms. The program begins with Intensive Summer Institutes, where teachers participate in multi-day workshops introducing the DMT framework and providing hands-on application experience. These workshops cover essential mathematical topics such as number, algebra, geometry, measurement, and data analysis. During this time, teachers explore how to take students’ ideas seriously, encourage multiple strategies and models, press students conceptually, focus on the structure of mathematics, and address misconceptions.

The professional development continues throughout the school year with ongoing support to ensure teachers can apply the principles learned during the summer. This support includes regular coaching and mentoring sessions customized to each teacher’s classroom needs. Teachers also participate in collaborative learning communities, where they meet regularly with DMT specialists and colleagues to share experiences, discuss challenges, and refine their practice. These meetings often include lesson and unit studies focused on implementing DMTI’s five practices. By working together to design and analyze lessons, teachers deepen their understanding of how to foster mathematical thinking in their students.

Another critical element of DMTI’s professional development is demonstration lessons, where specialized math educators teach Kindergarten through eighth-grade topics in real classrooms. These educators bring expertise from years of research and weekly teaching across all grade levels and math topics. Their insights into how students learn mathematics are invaluable for observing teachers. During these sessions, teachers take detailed notes on instructional strategies, student responses, and classroom dynamics as they prepare to implement these practices.

To further support implementation, DMTI offers classroom observations, where the DMT specialists provide constructive feedback on how teachers use DMT strategies in their classrooms. This feedback helps teachers identify areas of strength and opportunities for growth. Additionally, the program emphasizes reflective practice, encouraging teachers to evaluate their teaching methods and student learning outcomes continuously. By reflecting on what works well and needs adjustment, teachers can refine their instructional practices to meet their students' needs better.

Combining summer workshops, ongoing coaching, collaborative learning communities, demonstrated lessons, classroom observations, and reflective practice creates a robust professional development program that empowers teachers to transform their mathematics instruction. Through this comprehensive approach, the DMT framework ensures that educators are equipped with the tools and strategies to foster their students' deep mathematical understanding.

Historical Perspective

Examining math proficiency trends over the past few decades reveals progress and ongoing challenges. For instance, while 4th-grade proficiency rates increased from 13% in 1992 to 42% in 2013 before declining to 36% in 2022, 8thgrade proficiency saw a similar rise from 15% in 1992 to 35% in 2013, only to fall back to 26% in 2022 (National Center for Education Statistics, 2022). More alarmingly, less than 20% of 8th graders consistently demonstrated longterm retention of math facts over these periods, underscoring a persistent issue in mathematics education and highlighting the challenges students face maintaining fluency as they progress through higher grades (National Center for Education Statistics, 2022). Recent data shows a significant decline in math proficiency, particularly following the COVID-19 pandemic. The approach to teaching math facts has evolved over the past century.

DMTI’s Curricular Resources

In addition to its professional development offerings, the Developing Mathematical Thinking Institute (DMTI) has created a suite of curricular resources and assessments designed to support teachers in implementing research based instructional strategies. These resources include eight comprehensive curricular units per grade level, which guide teachers in applying the DMT framework's five practices to key mathematical topics, such as number, algebra, geometry, measurement, and data analysis (DMTI, 2019). Each unit is designed to promote deep conceptual understanding and problem-solving skills through carefully sequenced lessons that build on students' intuitive ideas and progressively formalize their mathematical thinking.

DMTI has developed the Primary Math Assessment (PMA) and Intermediate Math Assessment (IMA) to support differentiated instruction and intervention further. These diagnostic tools are designed to identify gaps in foundational math skills and provide targeted activities tailored to individual or small-group needs. The PMA focuses on six predictive topics—facts, sequencing, context, relational thinking, measurement, and spatial reasoning—while the IMA addresses seven key areas: multiplication and division, fraction concepts, place value, decimal concepts, ratio and proportion, algebraic reasoning, and geometric measurement. Both assessments generate detailed reports at the individual, classroom, and school levels, enabling teachers to pinpoint specific areas of need.

The targeted activities accompanying the PMA and IMA are engaging and adaptable resources that help students master critical areas. These activities include games and hands-on tasks that can be repeated multiple times to reinforce understanding. By combining high-quality curricular units with diagnostic tools like the PMA and IMA, DMTI equips educators with the resources to address student needs effectively.

DMTI’s High-Impact Strategies that Focus on Classroom Instruction and Student Engagement

Teacher Clarity (Effect Size: 0.75): The Developing Mathematical Thinking Institute (DMTI) emphasizes teacher clarity in its curricular resources, ensuring that lessons begin with clear learning intentions and success criteria. For example, in the Grade 3 multiplication unit, one of the learning intentions is: "We will understand multiplication as iterations (copies) of a unit and represent it with bar models, ratio tables, and equations." The success criteria for this learning intention are: "I can represent multiplication using bar models, ratio tables, and equations and explain how it represents iterations of a unit" or "I can solve a multiplication problem using a visual model and write the corresponding equation."

Feedback (Effect Size: 0.70): This approach incorporates the DMT practice of pressing students conceptually. Throughout each unit, teachers provide ongoing feedback as students explore concepts. For instance, when a student represents 1/4 on a number line in a fraction unit, the teacher might ask, "Explain what the digit 1 and the digit 4 mean in relation to the unit of 1?" In addition, the class is asked to repeat specific mathematical language.

Metacognitive Strategies (Effect Size: 0.69): This aligns with the DMT framework's emphasis on encouraging multiple strategies and models. The units encourage students to reflect on their thinking processes. For example, after solving a problem involving comparing fractions, students might be asked, "What strategy did you use to compare these fractions? Why did you choose that strategy? When might you use a different strategy?".

DMTI’s High-Impact Strategies that Focus on Conceptual Understanding and Problem-Solving

Piagetian Programs (Effect Size: 1.28): A key DMT practice is taking students' ideas seriously. This allows teachers to build on student understanding by meeting them where they are. The initial Kindergarten unit, Counting and Number Sense, embodies Piagetian principles by engaging students in enactive, hands-on activities promoting mathematical knowledge construction. For instance, lessons like "Visual Patterns and Counters" and "Collection Buckets" encourage children to manipulate physical objects, such as cubes and counters, to represent numerical quantities. This direct manipulation supports their understanding of cardinality and the relationship between numbers and real world objects, consistent with Piaget's emphasis on concrete operational thinking. Furthermore, the unit's progression from visual patterns to drawing models allows students to gradually transition from concrete to representational thinking, fostering their ability to abstract mathematical concepts. This sequencing aligns with Piaget's theory of cognitive development, making the DMTI unit an effective implementation of Piagetian principles in early mathematics instruction.

Conceptual Change Programs (Effect Size: 0.99): DMTI's emphasis on addressing misconceptions aligns closely with conceptual change programs, which focus on helping students confront and revise inaccurate mental models to develop deeper, more accurate understanding. DMTI uses mistakes and misconceptions as powerful tools for learning by encouraging teachers to view errors as opportunities to explore student thinking and guide conceptual shifts. For example, in a typical Grade 3 multiplication unit, a common misconception students may have is believing that multiplication always "makes numbers bigger." To address this, the DMTI lesson introduces problems like 4×2 and 4×1/2, where students are asked to represent the problem using visual models such as area models. As students work through the task, they realize that multiplication can involve fractions and result in smaller values, challenging their initial understanding.

This process of surfacing misconceptions is embedded in the DMT framework’s focus on pressing students conceptually and taking their ideas seriously. Teachers are encouraged to ask probing questions like, "Why do you think multiplication always makes numbers bigger?" or "What do you notice about this problem that challenges your thinking?" These discussions create cognitive conflict, prompting students to reflect on their prior beliefs and adjust their understanding. By addressing misconceptions directly and providing opportunities for students to test and revise their thinking through hands-on activities and discussions, DMTI ensures that conceptual change occurs, leading to more robust mathematical understanding.

Problem-Solving Teaching (Effect Size: 0.61): This strategy aligns with the DMT framework's focus on multiple strategies and models. Each module includes rich tasks allowing progressive formalization and encouraging students to improve their modeling and problem-solving. For example, students might be asked to solve the problem: "How can you divide a rectangular cake equally among 6 people?" Students are encouraged to model the problem using area models, ratio tables, and informal and formal algorithms. Then, teachers encourage students to use more formal models with understanding as new problems are introduced.

DMTI’s High-Impact Strategies that Focus on Targeted Interventions and Analysis

Cognitive Task Analysis (Effect Size: 1.29): The DMT framework's emphasis on pressing students conceptually aligns closely with cognitive task analysis (CTA), which involves breaking complex tasks into manageable components while uncovering the underlying mental processes required to perform them effectively. For example, in DMTI’s Grade 3 multiplication unit, students are guided through activities that encourage them to articulate their thinking and connect different strategies and models. A specific lesson involves solving 4×6 using an area model, where students first draw the area model, then explain how it represents equal groups, and finally connect this visual model to the multiplication equation. This process mirrors CTA’s focus on identifying decision points and linking strategies, as students must analyze their approach step by step while transitioning between representations. By encouraging students to verbalize their reasoning and explore multiple methods, DMTI helps teachers facilitate cognitive task analysis in the classroom, enhancing problem-solving skills and deepening conceptual understanding.

Response to Intervention (Effect Size: 1.29): DMTI supports differentiated instruction and intervention through its Primary Math Assessment (PMA) and Intermediate Math Assessment (IMA), designed to identify gaps in foundational math skills and provide targeted activities to address them. These diagnostic tools generate detailed reports at the individual, classroom, and school levels, enabling teachers to pinpoint specific areas of need. Accompanying these assessments are targeted activities such as games and hands-on tasks that can be used with individuals or small groups to build critical math skills. This approach aligns with Hattie's emphasis on response to intervention by equipping educators with actionable data and resources to support student growth effectively.

DMTI’s High-Impact Strategies that Focus on Broader Educational Approaches and Teacher Collaboration

Self-Reported Grades (Effect Size: 1.33): The DMT framework encourages students to reflect on their own learning and articulate their problem-solving processes. This aligns with self-reported grades, where students assess their performance. By promoting metacognition and self-assessment, DMTI helps students better understand their abilities and areas for improvement.

Collective Teacher Efficacy (Effect Size: 1.57): DMTI's professional development program fosters collective efficacy through a comprehensive, year-round approach that extends well beyond initial summer professional development, providing teachers with regular coaching and mentoring tailored to their classroom needs. A key component is the creation of collaborative learning communities where teachers and DMT specialists meet regularly to share experiences, address challenges, and refine practices. These communities focus on lesson and unit studies that emphasize DMTI's five key practices, enabling teachers to collaboratively design and analyze lessons while deepening their understanding of how to foster mathematical thinking in students.

The program also includes demonstration lessons from expert math educators who draw on extensive research and teaching experience across all grade levels. These sessions allow teachers to observe effective instructional strategies, student responses, and classroom dynamics, preparing them to implement these practices. Additionally, DMTI provides targeted classroom observations where specialists offer constructive feedback on using DMT strategies. Combined with reflective practice, this feedback helps teachers continuously evaluate and improve their methods, building a shared belief in their collective ability to impact student learning positively. Through this multifaceted approach, DMTI strengthens teacher collaboration and enhances instructional effectiveness.

Conclusion

The Developing Mathematical Thinking Institute (DMTI) framework provides a robust and comprehensive approach to mathematics education, deeply rooted in evidence-based practices identified by Hattie's "Visible Learning" research. By prioritizing teacher clarity, feedback, metacognitive strategies, problem-solving, and building on students' existing knowledge, DMTI's professional development and curricular resources effectively translate highimpact strategies into practical classroom applications. The focus on collective teacher efficacy and a commitment to addressing misconceptions further strengthen the framework, ensuring educators are well-equipped to foster deep conceptual understanding and enhance mathematical thinking in their students.

Through its meticulous alignment with Hattie's research and its emphasis on practical, hands-on implementation, the DMTI framework offers a powerful model for improving mathematics education. Diagnostic tools like the PMA and IMA, coupled with targeted activities and comprehensive curricular units, empower teachers to differentiate instruction, address individual student needs, and promote growth for all learners. As educators continue to seek effective strategies for enhancing student achievement, DMTI stands out as a valuable resource for transforming mathematics classrooms into vibrant learning environments where mathematical thinking flourishes.

References

Biesta, G. (2011). Good education in an age of measurement: Ethics, politics, democracy. Paradigm Publishers.

Brendefur, J. L., Champion, J., Strother, S., Thiede, K., & Osguthorpe, R. (2021). The effects of mathematics professional development on elementary student achievement. International Journal of Science and Mathematics Education.

Brendefur, J. L., Johnson, E. S., Thiede, K. W., Smith, E. V., Strother, S., Severson, H. H., & Beaulieu, J. (2015). Developing a comprehensive mathematical assessment tool to improve mathematics intervention for at-risk students. International Journal for Research in Learning Disabilities, 2(2), 65-90.

Brendefur, J. L., Thiede, K., Strother, S., Jesse, D., & Sutton, J. (2016). The effects of professional development on elementary students’ mathematics achievement. Journal of Curriculum and Teaching, 5(2), 95-111.

Developing Mathematical Thinking Institute (DMTI). (2019). Resource materials. Retrieved from dmtinstitute.com,

Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.

Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. Routledge.Snook, I., O'Neill, J., Clark, J., & O'Donoghue, T. (2009). Invisible pedagogies. Sense Publishers.

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Want to see Hattie's high-impact strategies in action? DMTI empowers teachers with research-backed resources and professional development focused on teacher clarity, feedback, and collaborative learning. Plus, explore how visual models, reflection, PMA/IMA assessments, and targeted activities unlock deeper math understanding!