Meets Common Core Standards for Math Think Through Math TTM s skills are aligned to the Common Core State Standards, providing comprehensive coverage of math concepts and applications. With TTM s state standards alignments, you can easily find unlimited practice questions specifically tailored to each required standard. If a standard is not addressed, it is because the standard cannot be addressed online. The standards and related lessons span grades 3-8, as well as Foundations of Algebra, Algebra 1 and Geometry. Coherence TTM lessons are linked to precursor lessons based on learning progressions. If a student is struggling with grade level content, they are assigned related lessons. The mathematics is not taught in isolated chunks. Rigor Think Through Math delivers a balance of conceptual, procedural, and applications work. The program provides instruction and practice on procedures and progresses to applications. TTM focuses on building deep conceptual understanding of concepts by providing effective strategies and instructional support to help students learn essential mathematical connections. Procedural Fluency We know that practice is an important element of developing procedural fluency, but students don t want more boring drill and kill worksheets. TTM s games provide opportunities for students to practice math facts in a fun and engaging context. In our number line game, students practice placing rational numbers on number lines while earning points, trying to beat the clock, and being entertained by the construction of goofy characters. Place value concepts are reinforced in our arcade-like target games. Students launch snowballs and water balloons at moving targets while using their understanding of place value to construct numbers. These and other games are designed to motivate and engage students while targeting specific skills for practice. Our brief, interactive games provide 20 or more practice opportunities within a three-minute episode of game play. One danger of traditional practice exercises is that misconceptions can be reinforced through repetition. TTM games provide scaffolds and corrective feedback to students moment by moment so that students recognize and correct misconceptions and errors as they go.
Conceptual Understanding Students can only develop conceptual understanding when they are working within their zone of proximal development. Students have to be able to connect new ideas to ideas that they already understand, so the first way that we support students in developing conceptual understanding is by using our placement test and adaptive logic to ensure that students are always working on the content that they are prepared to learn. From a content development perspective, we always start by considering the math concept(s) that we want students to understand, and not just the math we want students to be able to do. Then, we design items to teach understanding of the math we re addressing. Often, we design items around misconceptions in an effort to present an opportunity to address these misconceptions head-on with our instruction. Instruction can happen in multiple ways within a lesson: Feedback served based on student responses Direct instruction via the coach help upon student request Live instruction via a TTM teacher upon student request We ensure that instruction will help students understand the math concept (not simply get the answer to the problem in front of them) in several ways. We use multiple representations of mathematical relationships, especially visual representations. We never prescribe a solution method or algorithm (unless a standard calls for it explicitly), instead allowing students to enter into problems and explore the relationships in ways that make sense to them. Strategic Competence and Adaptive Reasoning Strategic Competence is characterized by the ability to articulate the problem being posed and to develop and carry out a strategy for solving the problem. Students who are adaptive reasoners can reflect on their thinking and can consider how they can adjust their thinking to address new problems in novel situations. We support students in developing these abilities throughout the program, but it is most explicit in the Problem Solving Process (PSP) items. One of the primary goals of our PSP items is to help students learn a process of approaching and solving complex problems that is systematic and includes opportunities for meta-cognitive reflection. Our 5 step process teaches students to: ANALYZE THE PROBLEM SITUATION: Identify the question that is being asked. Name and identify the values of the quantities in the problem. Identify any unknown quantities. Select a visual model that can be used to model how the quantities in the problem are related (e.g. a part-part-whole model). MAKE A PLAN FOR SOLVING THE PROBLEM: In this step the student identifies a useful problem solving strategy and articulates how the quantities in the problem are related in words in preparation for creating a symbolic representation. SOLVE THE PROBLEM: This step includes interpreting the numeric solution in the problem context. JUSTIFY THE SOLUTION: In this step, students think about not how they solved the problem, but how they know the solution is correct. Students are asked to do this in many ways including working backwards, using a different representation and using estimation. EVALUATE THE PROBLEM SOLVING PROCESS: Here students consider the efficacy of the process they used by reviewing the process and articulating why it was helpful or by considering whether another strategy would have been more efficient or produced a more precise result.
Adaptive Reasoning Students have opportunities to complete reasoning statements and to analyze student work and critique student reasoning throughout the program. Notably, the addition of interactive item types has provided increased opportunities for students to construct these critiques and analyses. We help students develop their adaptive reasoning skills by providing immediate feedback based on their responses and opportunities to revise their thinking in response to this feedback. Productive Disposition/Confidence First, and most importantly, we avoid contextualizing math in textbook problems and instead situate the mathematics in meaningful and authentic problems that deserve students time and attention. Secondly, we provide supports for students both upon their request (helps, math tools, live teacher access) and automatically in response to their work (feedback, a constantly adapting pathway). These supports ensure that the math they are learning is always within their zone of proximal development and that they have the necessary tools for success. In all virtual and live interactions with students we use language that supports the development of a growth mindset. We avoid empty praise and all criticism, instead focusing on math concepts and evidence statements. Finally, we recognize students efforts by always rewarding success, no matter how many attempts it takes for students to succeed. TTM s unique motivation system encourages students to persevere and allows students to set personal, group, and altruistic goals.
Incorporates All Mathematical Practices Items that address the Standards for Mathematical Practice are embedded throughout TTM, both in the instructional and assessment activities of each lesson. Further, TTM supports students in developing these habits of mind both through the nature of its instruction and by providing students plenty of opportunities to use these practices. MP.1: Make sense of problems and persevere in solving them Most problems are situated in real-world contexts. Both real-world and mathematical problem situations require students to analyze the mathematics at hand to determine a correct solution path. TTM s point system and feedback reward effort and encourage perseverance. Progress and points are never taken away for incorrect attempts. Points are always awarded for correct responses, no matter how long it takes the student to solve the problem. Feedback is written to address students misconceptions and to redirect their thinking. MP.2: Reason abstractly and quantitatively Since most problems are situated in real world contexts, students must abstract numeric values and interpret the meaning of their solutions in the context of the problems. Students are asked what particular values represent in a problem and to represent problem situations symbolically. MP.3: Construct viable arguments and critique the reasoning of others Many items require students to distinguish between correct and flawed explanations or reasoning. Students are asked to identify the best argument for a particular solution. This is especially helpful for students who are ELL or struggling readers because it models mathematical language and reasoning.
MP.4: Model with mathematics Students solve authentic problems by selecting and analyzing mathematical models, including expressions and equations, diagrams and graphs, area models, tables, statistical representations, and others. In Problem Solving Process (PSP) items, students construct equations to model complex problem situations. MP.5: Use appropriate tools strategically Math tools are available to students to use as needed. MP.6: Attend to precision Incorrect answer choices are written deliberately to present choices that students may arrive at if they make common calculation errors, mislabel units, round inappropriately, or make errors with respect to place value and/or sign of number. Feedback is written to address these particular misconceptions or errors. Items throughout the program teach and expect students to use precise mathematical vocabulary. MP.7: Look for and make use of structure Students are required to make use of the structure of numbers, operations, expressions and equations, and geometric figures. For example: Students identify an area model to represent a multiplication expression. Students solve 7 x 13 by seeing 13 as 10 + 3. Students recognize the x-coefficient of an equation in point-slope form as representing the rate of change of the line that models the equation. Instruction addresses the mathematics underpinning each problem, rather than the specifics of a problem itself. For example: Instructional support for a problem about place value and rounding focuses on the base ten structure of a number, not the specific values within the problem. MP.8: Look for and express regularity in repeated reasoning Students make observations of and select explanations for properties of operations and equality. Students make generalizations about mathematical relationships both verbally and algebraically