PUBLIC SERVICE ANNOUNCEMENT!
Do not assume the Future Focused Indiana Math Standards for grades K-Algebra 2 are the same math standards we have always used in Indiana with some slight name changes to protect the innocent!
For the first time in my 34 year teaching career, coaching and leading with the Indiana Mathematics Standards we finally have adopted standards that mirror national research and trends regarding WHAT and HOW math should be taught in grades K-Algebra 2. I know Indiana educators are used to slight, subtle changes in new standards compared to the previous set of grade level standards, however, don’t be fooled by the past. These new future focused math standards and the supporting IDOE documentation are comprehensive, equitable, and innovative. So what are the changes and shifts we will see as grades 3-8 begin to teach the new standards and prepare for the new ILEARN? Most Indiana districts decided to move forward in grades K-2 and high school with the future focused math standards this school year, however we all held back in the tested grades because ILEARN won’t shift this Spring. Below are the Big Math Ideas to pay attention to and suggestions on how you can prepare yourself, your students, and parents for what is coming.
Modeling Mathematics
The consistent shift to a balance of Concrete-Representational (Visual)-Abstract representations within the math content across grade levels is the MOST important and impactful change in the new math standards. In the 2020 math standards, many began with the word ‘understand’ while the future focused math standards begin with ‘model’ using concrete manipulatives or visual models. Here are a few examples along with the tools we will consistently use in our classrooms.
Grade 3:
| 3.CA.3 | Model the concept of multiplication of whole numbers using equal-sized groups, arrays, area models, and equal intervals on a number line. Model the properties of 0 and 1 in multiplication using objects or drawings. (E) |
Grade 6:
| 6.RP.4 | Solve real-world and other mathematical problems involving rates and ratios using models and strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (E) |
Algebra 1:
| AI.L.3 | Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables, including with technology. Translate fluently among these representations and interpret the slope and intercepts. (E) |
Modeling using concrete tools in grades K-12
Modeling using visual tools in grades K-12
We are now going to hold students accountable to modeling a math concept rather than just ‘doing’ a math skill. This move to a focus on concrete and visual models to build conceptual understanding is completely aligned with current national research on how to support ALL students in truly understanding mathematics. Although many elementary teachers have been using manipulatives and visual models, these new standards make a call for a substantial increase in the use of models in grades K-12. In my experience, this shift might be uncomfortable for secondary math teachers who are used to jumping straight to the abstract representation (naked math problems). Approximately 80% of students learn best with visual and concrete representations. We can equitably serve ALL our students by teaching math using multiple representations. For the first time, the Indiana Math Standards truly support learning for all learners.
Data Science
We live in a world of data. In this rapidly changing world of technological advances, our students must be able to adapt, interpret, and analyze the data surrounding them.
The goal is to turn data into information, and information into insight.
Carly Fiorina, Former CEO of HP
Teaching data science is usually regulated to May as a ‘fun’ unit that doesn’t really matter to ILEARN or SAT. Those days are over! For the last 4 years there has been a national push, primarily based on the efforts of Jo Boaler, Stanford Mathematician and Educator who authored much of the new California Mathematics Frameworks which identify Data Science as a foundational skill for K-12 students. Most states have already made the shift to placing a high priority on the ability to gather, organize, and analyze data in each grade level. Here are some examples:
Kindergarten:
| K.DA.1 | With guidance, collect and organize data into simple bar graphs, pictographs, and/or tables to identify patterns and make comparisons. (E) |
Grade 4:
| 4.DA.1 | Formulate questions that can be addressed with data. Collect, organize, and graph data from observations, surveys, and experiments using line plots with whole number intervals, single- and scaled bar graphs, and frequency tables. Solve real-world problems by analyzing and interpreting the data using grade-level computation and comparison strategies. (E) |
Algebra 1:
| AI.DS.2 | Understand that statistics and data are non-neutral and designed to serve a particular interest. Analyze the possibilities for whose interest might be served and how the representations might be misleading. (E) |
Try these fantastic websites:
What’s going on in this graph? (New York Times)
Conceptual Understanding
The final major shift in the Future Focused Indiana Math Standards is a strong emphasis on building a students’ conceptual understanding rather than allowing them to mimic the procedure/algorithm that allows students to NOT think in a math classroom. These new standards have utilized the research related to supporting students to build an authentic understanding of why the math works rather than simply memorizing a procedure to get an answer. By the way, this procedural approach, which was utilized to teach most adults in the US, is the reason we have generations of adults who do not have strong number sense and most of them feel they were ‘bad at math’. The research of Peter Liljedahl in Building Thinking Classrooms and NCTM’s 8 Effective Mathematics Teaching Practices lead us to the shift Indiana has finally made in not only encouraging conceptual understanding but demanding it in the standards. By using concrete and visual models students are more apt to build mathematical understanding. When we only teach abstract strategies like the standard algorithm for addition, subtraction, slope, and factoring quadratic equations it often leads to a significant lack of student thinking. Here are some examples of the shifts:
Grade 2:
| 2.NS.4 | Define and model a “hundred” as a group of ten tens. Model place value concepts of three-digit numbers, multiples of 100, and equivalent forms of whole numbers using objects and drawings. (E) |
Grade 5:
| 5.CA.5 | Use visual fraction models to multiply a fraction by a fraction or a whole number. (E) |
Grade 7:
| 7.GM.3 | Solve real-world and other mathematical problems involving volume of cylinders and three-dimensional objects composed of right rectangular prisms. (E) |
Recommendations:
The Future Focused Indiana Math Standards require flexible, adaptable, and creative thinking about math instruction. Most teachers will not have extensive experience teaching math using the pedagogical approaches outlined in the new standards. We want to set up educators and students for success as they embark on teaching these math standards. Below are my recommendations for preparing yourself and other educators.
- Utilize all of the fantastic resources created by the IDOE’s mathematics team. The Mathematics Framework documents contain the most impactful guidance.
- Seek out grade level specific, job-embedded, and curriculum aligned professional learning focused on teaching using concrete and visual models, teaching data science, and building conceptual understanding in students.
- Use a textbook/curricular resource based in building conceptual understanding using concrete and visual models. Ensure the resource includes significant work on data science.
- Focus PLC meetings on digging into the standards documents to support a clearer understanding of the future focused math standards.
We are entering a pivotal time in teaching and learning mathematics, be sure you are prepared for this opportunity.