Florida's B.E.S.T. Mathematical Thinking and Reasoning Standards
Florida's B.E.S.T. Mathematical Thinking and Reasoning Standards
December 10, 2021|Education, Florida, B.E.S.T. Standards, Florida's Standards
What They Are and How to Teach Them
Florida’s decision to adopt state specific B.E.S.T. standards means that at the end of the 2021-2022 school year, we will be bidding a final farewell to the controversial, and arguably overly politicized, Common Core standards. Much is different between the two sets of standards, but one element that has remained is the overarching expectations for mathematical thinking. With Common Core, we called these the Standards for Mathematical Practice; with B.E.S.T., the name is shifting slightly to the Mathematical Thinking and Reasoning Standards (MTRs). Click here for a side-by-side infographic from the two sets of thinking standards.
So, what are the MTRs? As with the former Common Core Practice Standards (of which there were eight), the B.E.S.T. Thinking and Reasoning Standards (of which there are seven) are overarching expectations for students to use in all K-12 math classes. The intent is to “promote deeper learning and understanding” and act as a “self-monitoring” tool for students (B.E.S.T. Math Manual,p.8).
From Big Ideas Learning - Click to Download
Don’t poo-poo them. Often teachers and school leaders feel the pressure of accountability and will solely focus on the grade-level “tested” benchmarks, mistakenly neglecting the big picture thinking standards like the MTR. If you are struggling with moving the proverbial math needle, this is likely why. It may feel like you are saving time in the short-term by ignoring the MTR, but in reality you will be playing a consistently losing game of catch-up and band-aids in the long-term when you deny students the more important skills of learning how to problem-solve, think critically, and engage fully in math.
When do we teach them? Dedicate time at the beginning of the school year to teaching classroom routines and expectations for behavior as well as for academics, such as with the MTR and the ELA (English Language Arts) Expectations. Set the stage for developing lifelong learners, but do not stop there. If you want to take your classroom and your school to the next level, make the MTR a consistent element of your everyday math lessons. Keep reading for practical strategies for teaching and integrating each of Florida’s MTRs and for making our students into Exceptional Thinkers.
MA.K12.MTR.1.1 Actively participate in effortful learning both individually and collectively.
What Does it Mean?
Compared to its Common Core counterpart (“Make sense of problems and persevere in solving them.”) http://www.corestandards.org/Math/Practice/ this MTR leans on cultivating a growth mindset in learners. Students will understand that we are not identified as “good at math or not”; math is a skill like any other. With practice and effort, we can overcome math challenges on our own or as part of a group.
Pg. 8 of the B.E.S.T. Math Manual
When Can We Use It?
This MTR is the most universal of all seven standards. Not only is this standard applicable to math, but also to every subject and aspect of school. This is one of the standards that can and should be up in every single teacher’s classroom in the building. Think of the difference in school culture you could create if this was expected, taught, supported, and practiced.
How Do We Do It?
Begin by shifting all fixed mindset language we hear from adults in the building such as “I’m not good at math” or “I’m just not a math person.” Shift your actions by shifting your thinking.
Adapted from https://www.growthmindsetmaths.com/
Teach strategies for perseverance, such as breaking down the problem, solving what you know, using resources, asking questions, or skipping the problem and coming back to it later. The teaching strategies found in this Prodigy article can give you tangible ways to have a classroom of growth mindset in math.
Finally, what we reward gets duplicated. Encourage, reward, and celebrate the process over the product. Be just as interested in how a student got an answer wrong as you are when a student gets an answer right. Remain neutral – do not change your affect. Show you value the thinking process by asking all students to explain their thinking.
MA.K12.MTR.2.1 Demonstrate understanding by representing problems in multiple ways.
What Does it Mean?
If a student can show you multiple ways to solve a problem, then you can be confident that the student has demonstrated understanding of that problem. An example of this would be if a student can solve a three-digit addition problem using the standard algorithm, but can also explain it by drawing tens blocks, manipulating 3-d blocks, or demonstrating with money.
Pg. 9 of the B.E.S.T. Math Manual
When Can We Use It?
In every level of math, from Kindergarten to Calculus, solutions to problems can be represented in at least two ways. The lower level the math, the more options for representing a solution to a problem.
How Do We Do It?
As mentioned previously, encourage process over, or at least as much as, product. Unless you are explicitly working on math fact fluency and automaticity, it is best for students to deeply understand a problem before practicing a procedure through simple rote memorization. Create environments where student thinking goes deeper than just surface level understanding.
Questions to Ask, Directions to Give:
How could you use manipulatives or a drawing to show your thinking?
Which tool/manipulative would be best for this problem?
What other resources help you solve this problem?
How can you represent the problem with symbols and numbers?
Create a representation of the problem.
Write a number sentence to describe the situation.
In addition, use models and manipulatives whenever you can. Many schools have a resource room full of hands-on materials that students can use to explore learning, deepen their understanding, and show multiple ways to represent a problem and solution. But what if you do not have hands-on manipulatives? What if you teach intermediate or secondary math where manipulatives are much more challenging to get your hands on? Solution: Digital manipulatives. Here are my two favorites!
Just some of the FREE apps from https://www.mathlearningcenter.org/apps
The Math Learning Center has FREE online apps that you can use as a demonstration to the class, students can pull up on their own devices during your lesson, or students can access at a center, independently, or at home. There are even class codes where students can share screen shots of solutions to you. This site is best for elementary classrooms with their various manipulatives. Explore some of the free online manipulatives above or by visiting the site here.
One of many math explorations from Gizmos and Explore Learning: https://gizmos.explorelearning.com/
Gizmos, from Explore Learning, has been long known for having online science experiments for grades third and up. But did you know they have math explorations as well? Not only are there engaging math gizmos for intermediate grades, but secondary teachers and students are likely to find what they need at this site as well. You can search a gizmo by academic standard, by grade and topic, or even by textbook. While they do not have everything available, this is certainly a site that you do not want to miss.
MA.K12.MTR.3.1 Complete tasks with mathematical fluency.
What Does it Mean?
The wording for this MTR is misleading. Many teachers may see “fluency” and associate that with the same level of automaticity we might find in reading or in reciting math facts. No doubt, there is a need for automaticity in recalling facts, but that is represented in an entirely separate set of B.E.S.T. standards. No, this MTR refers to the fluidity at which a student might move between strategies to solve problems and asks them to determine the most efficient strategy.
Pg. 9 of the B.E.S.T. Math Manual
When Can We Use It?
This MTR is perfect for word problems or multi-step equations. While it most certainly can be implemented with shorter equations, such as in primary grades, finding the most efficient strategy is best used for the developmental minds of third graders and beyond.
How Do We Do It?
How do we teach discernment in efficiency? Again, this must be modeled and explicitly taught. One of the most effective ways to accomplish this is through Number Talks. There are several books and videos on the subject, from kindergarten to secondary. Click here for a video of the author, Sherry Parrish, presenting a Scholastic Learning professional development on the concept of number talks. Sherry Parrish: Number Talks: Building Numerical Reasoning If you are short of time, start the video at 46:01 to see an example of a fifth-grade classroom solving a problem using multiple strategies, then discussing which would be the most efficient.
Questions to Ask, Directions to Give:
Is this working, or do you need to change your model?
How do you know your answer is correct?
Did you use the most efficient way to solve the problem? How do you know?
Can you find a shortcut to solve the problem? How would your shortcut make the problem easier? How can you be sure your shortcut is reliable in terms of accuracy?
For more information about implementing the Number Talks routine in your classroom, check out this site: http://globalcognition.net/SiteImages/NumberTalks.html
MA.K12.MTR.4.1 Engage in discussions that reflect on the mathematical thinking of self and others.
What Does it Mean?
According to the research of John Hattie, class discussion has the “potential to considerably accelerate student achievement” with an effect size of 0.82 (0.4 is average). This tells us that class discussion is an instructional strategy we want to implement often in our classrooms. It is a strategy we should prioritize. However, we must conduct our class discussions to derive the greatest impact from all students. Hattie defines class discussion as:
A form of instruction in which students are invited to speak about the topic at hand. It
involves much more than a teacher asking a class a question, then another, etc., but
involves students discussing with each other, often prompted from an open and not
closed set of questions.
https://www.visiblelearningmetax.com/influences/view/classroom_discussion
Students must first understand their thinking, then appropriately share, listen, question, and evaluate the thinking of themselves and of others. As seen in the excerpt from the manual below, students must be able to communicate ideas, analyze others’ thinking, compare strategies, recognize errors and propose solutions, justify results, and construct arguments.
Pg. 10 of the B.E.S.T. Math Manual
When Can We Use It?
All. The. Time. Well, not when practicing automaticity and fact fluency, but in every other area of math this can and should be encouraged and intentionally planned for students.
How Do We Do It?
First, we must model thinking aloud to solve problems. As teachers, the think-aloud is one of the most powerful tools we must implement to make our thinking visible and give students the information they need to fully participate in an effective classroom discussion. Next, have students think-aloud to a partner, a group, or to the class.
Ask scaffolding questions like the ones below:
What is this problem asking?
How could you start this problem?
How could you make this problem easier to solve?
How is __’s way of solving the problem like/different from yours?
What are you having trouble with?
How can you check this?
How is your answer different than __’s?
What math language will help you prove your answer?
How did you solve this problem?
Math Talk Cards: Brittany Beaumont, TPT
Finally, provide students with their own question or statement prompts so they can participate in classroom discourse in terms of math discussions. Check out this free resource from Brittany Beaumont on Teachers Pay Teachers
MA.K12.MTR.5.1 Use patterns and structure to help understand and connect mathematical concepts.
What Does it Mean?
Students focus on relevant details in a problem. This is an area you can easily link with English Language Arts, as distinguishing between relevant and irrelevant details is a key skill in ELA as well as in math. Also included in this MTR is decomposing complex problems, relate other processes to unfamiliar problems, and connecting similarities and differences between big mathematical concepts (for example, the relationship between multiplication, division, fractions, and ratios).
Pg. 10 of the B.E.S.T. Math Manual
When Can We Use It?
While we want our students to be on the lookout for patterns with commonalities in all problems, I expect this is the least tapped skill of the MTR. As a teacher, you would need to intentionally call attention to and show a problem that would fit the application of this standard.
How Do We Do It?
The “Pattern Hunter” would be an engaging way to initially teach this standard to your students. Present students with several problems –either already solved or for them to solve first. Consider playing detective music, like the Pink Panther theme song, and have them look for clues or patterns that link the problems together. This activity can easily be carried out through a gallery walk or QR code hunt in your room as well. After the first introduction of this MTR, use it as a checklist when reflecting on the process of solving a problem.
Check out some questions you may ask your students or use as a think-aloud below:
How is related to ?
Why is this important to the problem?
What do you know about ___ that you can apply to this situation?
How can you use what you know to explain why this works?
What patterns do you see?
How could this problem help you solve another problem?
MA.K12.MTR.6.1 Assess the reasonableness of solutions.
What Does it Mean?
A challenging, but important skill, students reflect upon their solution and decide if the answer is reasonable. This requires estimation skills, synthesis of what the problem was asking, checking their work, and justifying their answer.
Pg. 11 of the B.E.S.T. Math Manual
When Can We Use It?
While this MTR can be used any time, it will be most helpful for word problems or in data and measurement analysis.
How Do We Do It?
Again, we need to encourage and value the process. Celebrate when students can explain and justify their thinking, even if their answer is wrong. Many times, as students speak to justify, they find their own errors – a great lesson learned by the student.
Graphic Organizer for Making Math Predictions. Click for a FREE download!
We can call upon our ELA strategies yet again to teach and reinforce the importance of assessing reasonableness. For example, have students predict or estimate what the solution may be, even if it is in a range. After solving, check their predictions (estimates). Consider offering extra credit or part of a fully correct answer if students can justify their answer by checking their work by using an alternative strategy or by explaining and justifying with words or models.
Ask verbally, at the bottom of an assignment, or better yet, have students ask themselves the following questions:
Does my answer make sense? Why or why not?
How can I check this?
How do I know my answer is correct?
Try using thinking maps such as the one pictured above to give students the prompts to predict, estimate, and verify.
MA.K12.MTR.7.1 Apply mathematics to real-world contexts.
What Does it Mean?
Students can connect what they are doing in math class to a real-world application. Rather than view “fake” data to solve problems and solutions, they perform investigations to collect actual data and determine procedures, problems, and solutions for their real-world data collection.
Pg. 11 of the B.E.S.T. Math Manual
When Can We Use It?
Connecting what students are learning to its application in the real world is a critical engagement tool, in and of itself. However, this MTR can lend itself to powerful and simple real-world connections through geometry, measurement, data, science, and finance, economics, and commerce.
How Do We Do It?
Use project- or problem-based learning to provide a real-world connection. Connect your science lessons to collect data or to measure results, and graph them using mathematical practices. Provide opportunities to research and develop their own connections, whether concrete or abstract, and conduct investigations using mathematics processes.
Check out concrete examples, including home-school connections here: https://www.imaginelearning.com/blog/2017/04/math-real-life-examples
There are also some highly effective and engaging resources made by Teacher Created Materials, find a 5th-8th workbook here and a 3rd-5th workbook here. And don’t forget to use Gizmos for excellent dives into real-world problems.
Putting it All Together
Being intentional about teaching these Mathematical Thinking and Reasoning Standards at the beginning of each school year, K through 12, is a perfect place to start when helping our students become great mathematical thinkers. However, when the school year moves forward, as it always does, the challenge will be continuing to loop these skills in on a consistent basis. To add to that, the B.E.S.T. writers rightfully expect students to use the MTR as a self-monitoring tool as well.
Getting Our Students to Self-Monitor: Creating Independent Mathematical Thinkers
While we must model and explicitly teach the MTR, we also expect our students to use the standards independently. So, how do we do that? Check out some ideas below:
On an assignment, write which MTR is most applicable to the problem. Have the students write to explain how it helped them solve.
Create an anchor chart in class. Add a question at the bottom of assignments that has students write which MTR(s) used and why.
Click the Image for this FREE Download
Use our FREE MTR Self-Assessment tool:
Print out sticky notes: Have students check the box next to the MTR(s) they used and stick it on their work before turning it in.
Print, laminate, adhere: Place the checklist on student desks. Have them refer to the list while practicing math. Encourage them to name the MTR in discussions or as a short response on an assignment.
In Summary
Mathematical thinking and reasoning will create students who are critical thinkers. We must consistently model, teach, reinforce, and expect the MTR to be a daily part of our math classes. Teach them explicitly at the beginning of the year along with your other routines. Plan them into your lessons. Include a spot on your lesson plans to easily check which one(s) you will reference. Write them on sentence strips and place them on your agenda board when you refer to them in a lesson. Make it a “spotlight” in the room as to which MTR you will be explicitly modeling that day. Play MTR charades – model one of the MTR and have students determine which one you are using. Students can try this too!
Whichever way works best for your style, your classroom, and your students, make the MTR a prioritized aspect of your math instruction. You will see the long-term results, not just in math, but in behavior, responsibility, and other subjects as well.
Written by Ashley Doty of Uncomplicate ED. CLICK HERE to subscribe to our newsletters and blogs. Thank you!
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