Evidence Based Education

###### enVision Math

The enVision Math program was a difficult program to review for several reasons. To the best of my knowledge, it does not make publicly available full samples of its lesson plans or its curriculum. However it is advertised as adhering to the Common Core curriculum. The company does publicly share their lesson format, their program principles, and two efficacy studies, this article will attempt to review the enVision math program based on the above. One disclaimer that I will make first, is that I have not personally used this program and my perspective will be primarily based on the program principles and what the research shows, not personal experience.

The enVision program does have some interesting elements, the program is offered completely through the company’s online software, and individualizes instruction specifically to students assessed needs. Within the subject of math instruction there does exist a political spectrum of ideas, with traditional math instruction being on the far right and constructivism being on the far left. This program appears to be very far to the left on that spectrum. That being said, I would argue it is a fallacy to attempt to interpret pedagogical programs through politicized lenses, and that they should instead be analyzed via their individual merits. There are both “right wing” and “left wing” pedagogies that are evidence based.

The enVision program uses a three part math lesson; however, their lesson format is quite different from the often promoted “I do, we do, you do”. Instead, the first step has students try to solve a complex situational math problem, often involving virtual manipulatives, the second step gives students explicit explanations of concepts and procedures coupled with visual diagrams. The third step provides students with an assessment which allows the AI to then offer the student additional instruction based on the students conceptual deficits. This lesson plan model is essentially a twist on the traditional CRA model, which as I have recently written about is an evidence-based model of instruction. However, I have many objections to this model of instruction.

Firstly, it has students complete the most challenging part of their lesson first. While providing the explanation how to do this second. This means that students will often not have the prerequisite skills to effectively complete the first part of the lesson. The first part of the lesson is based on application skills; however, as application skills are a synthesis of conceptual, procedural, and computational skills, it makes far more sense to me to put this work at the end of a lesson or unit, not the beginning. Additionally problematic, is the consistent inclusion of multi-step word problems for young students, as the 2022 Myer’s, Et al, meta-analysis showed half the impact for multi-step word problems as for single-step word problems in elementary school.

I also found it very problematic that the program appeared to severely limit fluency instruction. Indeed, there is no mention of abstract, fluency, procedural, or computational work in their program description. Instead it appears that the program emphasizes the instruction of constructivist meta-cognition strategies for computation. While these strategies might help students with their mental math abilities, they do not help to build computational or procedural automaticity (fluency) and therefore cannot replace fluency work. While, Dr. Bethany Rittle has pointed out that purely conceptual programs out perform purely procedural programs, it is important to remember that her research showed that programs which included both conceptual and procedural instruction outperformed conceptual or procedural ones.

The program includes an individualization component, which the Steenbergen-Hu meta-analysis showed could be one of the most powerful tools for increasing education achievement. However, it appears that the program only offers additional instruction based on students' conceptual deficits. In my opinion this is extremely reductive and diminishes the value of the pedagogical tool, because it makes the strange assumption that student math deficits are always based on conceptual knowledge.

Ultimately, a pedagogical program includes many different pedagogical ideas and concepts. Given the relatively small amount of research on the enVision program, I have conducted a secondary meta-analysis on the pedagogical concepts behind the enVision program. A secondary meta-analysis synthesizes the effect sizes from a variety of other meta-analyses on a related topic, to establish the efficacy of multiple research questions at once. Generally speaking these effect sizes can be interpreted based on the below chart. A glossary will be included at the bottom that includes a brief explanation, discussion, and reference.

Ultimately, to examine the efficacy of a pedagogical program, we should look to a peer-reviewed meta-analysis. However, in this case, that is not possible, as there currently exists only 2 studies on the program. One by Miriam, Resendez Et, al in 2007 and one by the company in 2017. Moreover, in my opinion only the 2007 study was of high enough quality, to be worth reporting on.

The Resendez study was an RCT study that compared using the enVision program to business as usual, for grade 2 and grade 4 students. The study was 2 years long and used standardized testing to determine the program’s efficacy. The results of the study can be seen in the below graph.

All study results were low to statistically insignificant. To be fair to the Savas company, it is difficult to properly assess the program, due to lack of public access and research. However, based on the available research and curriculum materials, I am inclined to say that the program does not appear to be evidence or science based.

Final Grade: C

The program has one high quality study showing a statistically insignificant effect. The program principles are not well with the Science of Math in the views of this author.

Qualitative Grade: 4/8

The program includes the following essential elements: Direct Instruction, individualization, conceptual instruction, and includes all math strands.

Written by Nathaniel Hansford

Last Edited 2022-06-28

Glossary & References:

Problem Based Learning: Problem based learning originates from medical schools and typically involves students solving complex or open ended problems. The Marcucci meta-analysis was referenced for this effect size as it was the only meta-analysis specifically on problem based learning in core elementary math instruction.

R, Marcucci. (1980). A Meta-Analysis of Research On Methods of Teaching Mathematical Problem Solving. Retrieved from <https://www.proquest.com/openview/92be6987ec257cf7d504db2f78a5e269/1?pq-origsite=gscholar&cbl=18750&diss=y>.

Manipulatives: Concrete items meant to help students better understand the concepts behind abstract math and their links to mathematical procedures. The Carbonneau meta-analysis was used here as it is the most up to date meta-analysis on the topic.

Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380-400. doi:http://dx.doi.org/10.1037/a0031084

Direct Instruction: Explicitly explaining curriculum to students. The Getsen meta-analysis was chosen here, as to the best of my knowledge it was the only meta-analysis looking at DI in math instruction for more than one strand.

R, Getsen, Et al. (2009). A Meta-analysis of Mathematics Instructional Interventions for Students with Learning Disabilities:

Mathematical Modeling: “The process of encountering an indeterminate situation, problematizing it, and bringing inquiry, reasoning, and mathematical structures to bear to transform the situation. The modeling produces an outcome - a model - which is a description or a representation of the situation, drawn from the mathematical disciplines, in relation to the person's experience, which itself has changed through the modeling process (p.60).” The Sokolowski meta-analysis was the only meta-analysis that has looked at this topic in my opinion. However, while the enVision program uses some modeling, I am not sure that their definition is congruent with Sokolowski’s interpretation. Moreover, his meta-analysis was on secondary and graduate level students, which might also make it incongruent with the program at hand.

Sokolowski, A. (2015). The Effects of Mathematical Modeling on Students’ Achievement-Meta-Analysis of Research. IAFOR Journal of Education, 3(1), 93–114. https://doi-org.ezproxy.lakeheadu.ca/10.22492/ije.3.1.06

Student Choice: Increasing student control over learning, based on interest. Karich, Et, al conducted the most up-to-date meta-analysis of this topic.

Karich, Abbey & Burns, Matthew & Maki, Kathrin. (2014). Updated Meta-Analysis of Learner Control Within Educational Technology. Review of Educational Research. 84. 392-410. 10.3102/0034654314526064.

Individualization: Individualizing instruction to students' learning and curriculum needs.

To the best of my knowledge, Steenbergen-Hu conducted the only meta-analysis of this topic.

Steenbergen-Hu, S. (2016). What One Hundred Years of Research Says About the Effects of Ability Grouping and Acceleration on K–12 Students’ Academic Achievement. Review of Educational Research, 86(4), 849–899.

Technology: The use of technology in math instruction. Ran, Et al conducted the most recent meta-analysis of this topic.

Ran. (2022). A meta‐analysis on the effects of technology’s functions and roles on students’ mathematics achievement in K‐12 classrooms. Journal of Computer Assisted Learning., 38(1), 258–284.

Math Vocabulary: The explicit instruction of math terminology. To the best of my knowledge Lingyun, Et al conducted the only meta-analysis of this topic in 2018.

J, Hattie. (2018). Vocabulary. Hattie Metax. Retrieved from <https://www.visiblelearningmetax.com/influences/view/vocabulary_programs>.

Self Assessment: Having students first assess their own work, to improve student clarity of expectations. There was only one meta-analysis on this topic specific to math instruction.

Karich, Abbey & Burns, Matthew & Maki, Kathrin. (2014). Updated Meta-Analysis of Learner Control Within Educational Technology. Review of Educational Research. 84. 392-410. 10.3102/0034654314526064.

Formative Assessment: Monitoring student learning with assessment. This strategy has been shown to be in general most useful when it is paired with meaningful instruction and not only used for the sake of data collection. The Kingston, Et al meta-analysis was chosen for this effect size because it was the most modern meta-analysis of this topic in English, on efficacy.

Kingston, N. and Nash, B. (2011), Formative Assessment: A Meta-Analysis and a Call for Research. Educational Measurement: Issues and Practice, 30: 28-37. https://doi.org/10.1111/j.1745-3992.2011.00220.x

Constructivist: Based on the idea that knowledge must be built on pre-existing knowledge. Constructivist math programs often promote the use of meta-cognition strategies over traditional fluency practice to build computational competency. Constructivist teaching methodologies often emphasize student centered approaches such as increasing student choice, inquiry-based learning, and teaching to learning styles. To the best of my knowledge, there exists only two meta-analyses on the topic. One by Abrami, Et al and one by Erisen, Et al. The Erisen paper was more modern, found a much higher effect size and included far more studies. However, it was not peer-reviewed and the Abrami one was, so I included the Abrami meta-analysis over the Erisen one.

Abrami, Philip & Bernard, Robert & Wade, C. Anne & Schmid, Richard & Borokhovski, Eugene & Tamim, Rana & Surkes, Michael & Lowerison, Gretchen & Zhang, Dai & Nicolaidou, Iolie & Newman, Sherry & Wozney, Lori. (2008). A Review of E-learning in Canada: A Rough Sketch A Review of E-learning in Canada: A Rough Sketch of the Evidence, Gaps and Promising Directions of the Evidence, Gaps and Promising Directions 1. Canadian Journal of Learning and Technology / La revue canadienne de l’apprentissage et de la technologie. 32. 10.21432/T2QS3K.

CRA: Concrete Representational Abstract. In this lesson format teachers teach with manipulatives first, diagrams second, and the abstract third. The enVision program does use a CRA style lesson format; however, it excludes the abstract component and therefore might be too dissimilar to compare to other CRA studies. This meta-analysis was non-peer reviewed and written by the same author as this paper. However, it is the only meta-analysis on the topic.

N, Hansford. (2022). CRA. Teaching by Science. Retrieved from <https://www.teachingbyscience.com/cra>.

Other Citations:

Savas. (2022). enVision Math Digital Brochure. Retrieved from <https://cloud.3dissue.com/202077/205776/241865/enVision-Mathematics-K-5-Overview-Brochure/index.html>.

Bethany Rittle-Johnson, and Michael Schneider. (2011). Developing Conceptual and Procedural Knowledge of Mathematics. Oxford Press. Page 9.