I want to zero in today on what holistic learning looks like in first grade math lessons. For an overview of the essentials of first grade please see this post and to read more about the first grade math main lesson blocks please see here and here.

How do you teach counting and skip counting? You can work with movement and rhythm, using your body to march, skip, gallop, walk, stomp, clap, toss beanbags, etc. as you speak. See this post for ideas on how to incorporate active math in circle. You can work with imagination, pretending that you are crossing a stream on stepping stones or chopping wood with an axe. You can work with verse and poetry (for example with the Strange Family verse).


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How do you teach the four processes? You can start with an imaginative story to show the ways that numbers can be related to each other. You can use characters in your story to represent each process and present it in a rich way, drawing on temperament, verse, and real problems that must be solved. You can work with manipulatives including fingers, acorns, or counting stones to make each problem very concrete, visual, and kinesthetic. You can draw the problems as well using little pictures before moving into the more abstract with dots and then numbers and symbols. You can move into practicing math facts and multiplication tables using movement and rhythm once the concepts are understood. You can keep the four processes in the holistic realm by learning not just the mechanics and not just the facts, but also learning how the processes are related, how they undo each other, how the amazing patterns in numbers and shapes translate into these relationships.

Making Math Meaningful by Jamie York is an excellent overview of the Waldorf math curriculum for grades 1-4. The opening chapters on how to teach math effectively and avoid math phobia are priceless. The curriculum and objectives for each grade and main lesson block are given in detail but the particulars on how to bring the subject to life (with games, verses, art, stories, and so on) are left up to the teacher.

The table below shows the number of states/jurisdictions with score increases or decreases in 2022 and how many states/jurisdictions scored higher, lower, or not significantly different than the nation (public) in NAEP mathematics.

To view score changes for fourth-grade public school students in mathematics between 2022 and previous assessment years, or between other combinations of assessment years, use the drop-down menu to select a comparison year. To see whether the score change in one state/jurisdiction is statistically different from the score change in another state/jurisdiction, use the NAEP State Profiles Tool. Find out how statistical significance is determined.

NOTE: Beginning with the 2017 assessment, NAEP mathematics results are from a digitally based assessment; prior to 2017, results were from a paper-and-pencil-based assessment. Accommodations were not permitted in NAEP mathematics assessments prior to 2000 at the state level. Results are not shown for those states that did not participate or did not meet the minimum participation guidelines for reporting in a given assessment year. Although the estimates (e.g., average scores or percentages) are shown as rounded numbers, the positions of the data points in the graphics are based on the unrounded numbers. Unrounded numbers were used for calculating the differences between the estimates, and for the statistical comparison test when the estimates were compared to each other. Not all apparent differences between estimates are statistically significant.

Your child will learn and develop mathematical ways of thinking through (mathematical practices). Some examples of math practices are using math to model authentic situations, persevering in solving problems, constructing and critiquing mathematical justifications, and representing mathematical ideas visually.

Effective math instruction begins by building a strong conceptual understanding of how numbers work (number sense). This is the foundation that leads students towards procedural fluency (using flexible, efficient, and accurate strategies). Effective math instruction includes opportunities for students to apply their understanding and fluency to real-world mathematical problems.

Your child  will learn and develop mathematical ways of thinking through (mathematical practices). Some examples of math practices are using math to model authentic situations, persevering in solving problems, constructing and critiquing mathematical justifications, and representing mathematical ideas visually. Read more about the Standards for Mathematical Practices.

Effective math instruction  begins by building a strong conceptual understanding of how numbers work (number sense). This is the foundation that leads students towards procedural fluency (using flexible, efficient, and accurate strategies). Effective math instruction includes opportunities for students to apply their understanding and fluency to real-world mathematical problems.

When your child goes to 3rd grade, this knowledge will serve as the foundation for the concepts of multiplication and division, the understanding of fractions, and further problem solving with the four operations.

Strand: MATHEMATICAL PRACTICES (3.MP) 

 The Standards for Mathematical Practice in Third Grade describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes (Standards 3.MP.1-8).

Standard 3.MP.3 

 Construct viable arguments and critique the reasoning of others. Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.

Standard 3.MP.4 

 Model with mathematics. Identify the mathematical elements of a situation and create a mathematical model that shows the relationships among them. Identify important quantities in a contextual situation, use mathematical models to show the relationships of those quantities, analyze the relationships, and draw conclusions. Models may be verbal, contextual, visual, symbolic, or physical.

Standard 3.MP.5 

 Use appropriate tools strategically. Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.

Standard 3.MP.6 

 Attend to precision. Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.

Standard 3.MP.7 

 Look for and make use of structure. Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.

Standard 3.MP.8 

 Look for and express regularity in repeated reasoning. Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.

Standard 3.MD.8 

 Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

The 2023 Mathematics Standards of Learning were approved by the Virginia Board of Education on August 31, 2023. The 2023 Mathematics Standards of Learning represent "best in class" standards and comprise the mathematics content that teachers in Virginia are expected to teach and students are expected to learn. The 2023 Mathematics Standards of Learning will be fully implemented during the 2024-2025 school year.

The 2016 Mathematics Standards of Learning Curriculum Framework, a companion document to the 2016 Mathematics Standards of Learning, amplifies the standards and further defines the content knowledge, skills, and understandings that are measured by the Standards of Learning assessments. The standards and Curriculum Framework are not intended to encompass the entire curriculum for a given grade level or course. School divisions are encouraged to incorporate the standards and Curriculum Framework into a broader, locally designed curriculum. The Curriculum Framework delineates in greater specificity the minimum content that all teachers should teach and all students should learn. Teachers are encouraged to go beyond the standards as well as to select instructional strategies and assessment methods appropriate for all students.

The content of the mathematics standards is intended to support the following five process goals for students: becoming mathematical problem solvers, communicating mathematically, reasoning mathematically, making mathematical connections, and using mathematical representations to model and interpret practical situations. Practical situations include real-world problems and problems that model real-world situations. e24fc04721

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