Remember when THS’ math classes were dominated by Written Practices, Cumulative Tests, and STAR reviews? Looking back at it today, many aspects of the class have changed - with the changes of the 2022-2023 school year being the biggest in the history of the school. A previous staple of THS’ math curriculum, Saxon Math, was removed and replaced with the current system of enVision Mathematics after over 12 years of continued use, according to THS’ Primary & Middle School principal, Mrs. Christine Greenberg. After this breaking change to the school’s curriculum, everyone involved at THS had to adapt, most importantly the staff and students. Why was this choice made, and what were its effects?

What is a (math) curriculum, and what is the difference between the two curriculums?

According to THS’ Math Coordinator and Middle School Math teacher, Ms. Dana Koniuch, a curriculum is a system that guides teachers and students on the goals and skills in a particular subject, thus preparing the students with the knowledge and competencies required for the future, in studying, working, and beyond. All schools need a curriculum for every subject, and as THS is an American international school,  the school utilizes curriculums that follow American educational standards, which in THS’ case is Common Core for Math. 

Common Core is a math curriculum standard that guides curriculums’ content by giving standards for teaching. According to its official website learning.ccsso.org, there are eight general Standards for Mathematical Practice in its curriculum standard, which “describe varieties of expertise that mathematics educators at all levels should seek to develop in their students”:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

The Common Core standard then defines the topics which should be taught in the specific grade - individual curriculums that follow Common Core will base their lessons on these topics, and can also extend or simplify them depending on the target audience’ level. To learn more in-depth information`123as4dg  about these standards above and the exact guides in the curriculum standard, head to the official website linked above.

According to Ms. Koniuch, although Saxon and enVision both share the same Common Core standard, they implement it extremely differently - Saxon takes a cyclical approach, while enVision is a more traditional linear curriculum. Linear math curriculums like Envision split the topics into organized units. or example, a typical Grade 6 linear math curriculum might start by revisiting fractions for two weeks, then move to teaching ratios for another two weeks, which require fractions as base knowledge - giving you the required knowledge to progress and learn more complicated topics (you could compare this to video games with storylines). As Ms. Koniuch noted, “[In a linear curriculum,] to learn XYZ you [first] need to learn TUV.” A cyclical system, however, differs from linear progression in a critical way: instead of organizing the topics in groups, the topics repeat themselves every few lessons, adding a small sliver of new skill each time. One day an average Grade 6 student could be learning about fractions, then the next about mean average deviation, then the next about inequalities, and so on. Then every single topic is covered, the curriculum loops back to the first topic, revisiting it and adding a little more - hence the name cyclical, which relates to circle. You could compare this one to video games where you do repeated tasks over and over again, but also unlock new things along the way.

Ms. Koniuch also noted a few key reasons the school switched to enVision:

1. Both Saxon and enVision follow the Common Core standard.

2. enVision heavily focuses on mathematical practice and word problems, whereas Saxon contained more straightforward questions 

3. The school favors enVision’s method of incorporating the Common Core standard over Saxon’s method.

4. The mathematical skills and thinking involved in enVision helps students transition to any other school or even curriculum and still be successful.

How do teachers teach their students math?

Contrary to what some think, teachers have to do many things every day at work, not just what a student would see on the surface, in the form of teaching. They have to do complicated and/or time-consuming tasks such as grading tests, getting students engaged in class, and even something that seems as basic as just planning a lesson - it takes much, much more than just one basic black-and-white slideshow and a few math questions added on top to call one lesson plan even close to complete. Just teaching a lesson by itself already is complicated in ways including explaining topics with clarity to the students and making sure they are not off-task.

According to Ms. Koniuch, test grading is more complicated than just looking at an answer sheet and checking if a student’s answer matches what is on the sheet. Sometimes, a teacher might not have an answer sheet with them, especially if they created the questions themselves rather than using ready-made templates from the internet; the teacher would need to do the questions themselves too. Teachers also have to read the students’ working out and explanation of their answers to check their understanding. According to JG1 (Junior Grade 1) teacher Ms. Scarlet Lai, in younger grades, such as hers, the students won’t have formal tests; instead, they complete assessments through activities with the teacher, which helps the teacher identify their level and understanding of the concepts.

When making a lesson plan, teachers have to consider many things, according to Ms. Koniuch. Teachers base their lessons on the curriculum used, in THS’ case enVision; a curriculum gives ideas for lessons and activities, and teachers adapt them to be more meaningful and relatable to the students’ personalities and needs. For example, someone who doesn’t understand why variables exist would learn math much slower than someone who could grasp all of the basic concepts of linear equations in a week - the teachers fix that by adapting their lessons to the level and speed of learning of their students. Some schools, including THS, also split their students into math groups, placing them in a group suitable for their levels, which would make them work together with people of a similar level, helping them learn in a better environment.

Lessons have to be interesting for students too. Ms. Koniuch noted that each student has different interests, which means lessons have to be tailor-made to the class a teacher teaches - from the themes word problems have to the games played to teach specific concepts. Every time a teacher wants to, they try different games with their students; they then find the most effective games to teach topics, and use them sparsely. Depending on the students’ interests, the games chosen would integrate these interests with math. Ms. Koniuch notes that “[when using math games,] doing the same thing is redundant.” Grade 4 Math teacher, Ms. Sonia Hiranandani, explains that she uses math games by pairing them with a “weekly theme”, giving students hands-on experience to practice and review previously-learned concepts. As an example, Ms. Ali’s students built a pacman-like remaining fractions project for a week - then, at the end of the school year, they built a geometry-related project. Ms. Ali’s class also has “Fun Fridays” where students work on their projects and also have fun in other ways such as puzzles and math games. Similarly, Grade 4 Math teacher, Mr. Giovanni Tengga, also uses games in his lessons; instead of playing games on a weekly basis, however, he gives his students a few Kahoot (an online quiz app) sessions and one Prodigy (a gamified Math learning experience) math battle per week - but the games are only played as a reward.

Two of Ms. Scarlet’s students, Orlando and Gayatri, described that their experiences in Math class included a game where students created exactly 100 by making things that represent 100, such as a house made out of exactly 100 components, and an activity where students counted how many classmates there were. Ms. Scarlet also plays math songs and utilizes toys to review simple topics in a fun way for the younger students. Despite all of the engaging interactions, the kids still dislike the activities where they need to sit on the floor, in which Orlando adds that she can’t sit properly.

In addition to customizing the games played, teachers also explore different strategies to solve math problems. Ms. Koniuch and many others believe that teaching only a single solution to solve a math problem will obstruct understanding of the problem to many if not most of the students in a class. Teaching multiple strategies to solve the problem, on the other hand, would let each and every student use the method that they think works best for them, allowing them to understand a topic or problem in their own way. As an example, I find using slope-intercept form when calculating equations for lines better than using point-slope form, but some might think otherwise.

As Ms. Koniuch explains, each and every teacher has their own teaching style - and collaboration is key. Every Wednesday, according to Ms. Scarlet, “Teachers have department meetings to discuss the ongoing activities and issues at school. [The coordinator] will also meet with all of us every term to support us and ask us how our experience has been and if there is anything she can help us with.” Mr. Van notes that the meetings also check if teachers are on the right track with teaching; if a teacher is slightly behind in teaching, the coordinator can allow them to skip a few redundant lessons. Grade 6 Math Teachers Mr. Kyle Van Rensburg and Mr. Toby Kallander also note that the school has a Slack (team communication app) page dedicated to math class and sharing ideas. Continuing with Ms. Koniuch’s explanation, casual meetings can also happen where teachers share experiences, problems, and ideas with each other. Interestingly, each teacher’s lesson plans don’t have to match others’ lessons or even be similar to theirs; as long as the teacher teaches the required skills for that lesson, it is completely fine and even suggested.

How has the switch to enVision Math from Saxon affected the school’s math classes?

The switch to enVision from Saxon Math did not completely overhaul math class; it did, however, make some smaller changes to the lesson content and teaching methods. Besides the changes to the curriculum itself, teachers also adapted to the new curriculum, where some activities stuck around and others were replaced by new, better methods. Ms. Ali explains that enVision Math comes with a platform called Savvas Realize which “has online resources that can be assigned [to students.]” According to her, the platform also includes “visualizing, explanation videos with prompts and more problem solving, [and] different teaching slides people can use.” In the past, when THS underwent VC@T (see my old article, linked next to this text, for more) during COVID-19, teachers like Ms. Ali had to create many Google Forms as assignments for students to complete. When Saxon was used, teachers also had to take boring, dry screenshots of problems for slides, but with the wide range of tools baked into Savvas Realize, they can now use Envision’s ready-made enriched lesson content. To her and her students, no more of a need to find random videos on YouTube allows having a “same” math language, which is easier to understand; because different people have different terms for parts of math, one unified platform helps to unify the terms used, reducing confusion.

Now, according to Ms. Ali, teachers can just head to Savvas Realize and assign homework designed with the textbook in mind to the students’ computers. This is less time consuming for both teachers and students; Ms. Ali explains that it is easier for students to complete their tasks because everything is in one place and because it is more explicit about instructions.

In terms of the problem style, Mr. Van dislikes that the enVision lessons are quite wordy, and that he needs to only pick some parts of one lesson in order to complete it in an hour. Ms. Ali describes enVision’s math problems as being mostly word problems and math reasoning, whereas she believes Saxon has relatively more computational problems. For Ms. Scarlet, she finds that the new style of problems are quite complicated for her JG1 students, as they are on average only 5 years old. As Ms. Scarlet notes, “the wording is a little difficult for the students so we have to simplify the language for our Junior Grade 1 students.” In contrast, Grade 6 Math Teachers Mr. Kyle Van Rensburg and Mr. Toby Kallander describe enVision as “[being] designed to be more interactive and engaging, with hands-on activities and real-world applications of math concepts.” According to them, Saxon “places a strong emphasis on repetition and practice, with students often completing a large number of problems in each lesson.” For them, enVision also provides more space for customization and adaptations to student needs than Saxon does. 

When adapting to the new curriculum, many staff and students had trouble with using the curriculum. Mr. Van found it difficult at the start of the school year to teach students, as he needed to make sure that he understood first; there were a lot of word problems to cover and hence it took a lot of time. When his students started using enVision Math, they found it tricky for the first six topics; as time went on, their scores improved, as they got used to the new format of Envision’s word problems. Mr. Van also notes that due to this change of question style some students previously ahead of the average level had dropped back to the average level class.

It has been just less than a year (from the time of writing) since THS swapped out its signature Math curriculum, Saxon Math, with the more linear enVision Math curriculum. Although they both are based on the Common Core standards, they have significant differences between each other, as one is cyclical and the other is unit-based. enVision builds students’ knowledge topic by topic, while Saxon keeps bringing more review to solidify previously learned topics and somewhat less new skills. enVision’s supplemental platform, Savvas Realize, puts many parts of the Math class, such as assignments, lesson templates, and others together in one place. The entire school community had to adapt to the new changes, in ways such as using the newly provided software and just practicing math. Many teachers and students had trouble understanding the newer question styles at first; after some time, they adapted and were ready to teach confidently, understanding the many benefits of the new curriculum. And none of THS’ Math classes could operate without their biggest component: the wonderful, caring teachers that do immense amounts of work behind the scenes. As Mr. Van exclaims, “Math is everywhere, not just numbers; if you have good mental math, it would work wonders!”