Developing Math Skills throughout Primary Schooling
Learning Math is a Journey!
Mathematics is a subject that inherently builds upon itself, with each concept serving as a foundation for the next. As students progress through their education, they are introduced to increasingly complex ideas that rely on their understanding of prior material. For example, mastering basic arithmetic in early grades paves the way for success in more advanced topics like algebra and geometry in later years. This gradual development ensures that students have adequate time to practice and solidify their skills, preparing them for more challenging concepts as they advance. Parents play a crucial role in supporting this learning process by encouraging consistent practice and fostering a positive attitude towards math throughout their child's educational journey. Tutors, too, can provide a significant supporting role in a child's development of strong math foundations skills.
Developmental Skills Progressions
In their "Educators Practice Guide", the Institute of Education Sciences analyzes various educational scientific studies and ultimately posits that utilizing developmental progressions and progress monitoring against standards is cornerstone to quality mathematics instruction."Effective instruction depends on identifying the knowledge children already possess and building on that knowledge to help them take the next developmental step. Developmental progressions can help identify the next step by providing teachers with a road map for developmentally appropriate instruction for learning different skills".
We at Big Sky Tutoring agree with this model and utilize it daily. By first gaining a baseline understanding of a child's location upon the standardized skills-development progression, we are able to identify previous skills that need additional attention. After a student receives adequate tutoring on their below-grade level skills, we then can turn our focus to ensure that students have mastered everything they need to get and stay on track in the rest of the developmental progression.
Our tutoring team utilizes the Montana Mathematics Content Standards to make informed decisions as to what we will work on with our students. Our goal is to constantly align our math tutoring sessions to what students are learning in the classroom. We also find it is our responsibility as math tutors to ensure that our students are meeting grade-level benchmarks in every domain of math.
Montana Mathematics Standards Progressions (K-8)
To simplify the progression of math skills, we have summarized the Montana Mathematics Content Standards below for your reference. This should provide a clearer picture for parents as to what their child should know and what they will learn next. Our outline below is a comprehensive progression of key mathematical concepts and skills from Kindergarten through Grade 8. The full Montana Mathematics Standards Progressions document, in its entirety, is available here. Below is a summary of the progression for each major math domain:
Counting and Cardinality (K-2)
Kindergarten: Focus on knowing number names, the count sequence, counting to tell the number of objects, and comparing numbers.
Grade 1 and 2: Build on these skills with no specific new standards; foundation is laid for operations and algebraic thinking.
Operations and Algebraic Thinking (K-5)
Kindergarten: Introduction to addition and subtraction through simple problems and hands-on activities.
Grade 1: Represent and solve addition and subtraction problems within 20, understand properties of operations.
Grade 2: Solve problems involving addition and subtraction within 100; introduce basic concepts of multiplication.
Grade 3: Emphasis on understanding multiplication and division, and solving related word problems.
Grade 4: Extend multiplication and division to larger numbers and multi-step problems.
Grade 5: Add, subtract, multiply, and divide fractions and decimals, and apply these operations to solve real-world problems.
Number and Operations in Base Ten (K-5)
Kindergarten: Introduction to numbers 11-19 to build a foundation for place value.
Grade 1: Extend counting sequence to 120, understand place value for two-digit numbers.
Grade 2: Understand place value for three-digit numbers, add and subtract within 1000.
Grade 3: Use place value to perform multi-digit arithmetic, including rounding numbers.
Grade 4: Generalize place value understanding to multi-digit whole numbers, fluently add and subtract multi-digit numbers.
Grade 5: Perform operations with multi-digit whole numbers and decimals to hundredths.
Number and Operations - Fractions (3-5)
Grade 3: Understand fractions as numbers, represent fractions on a number line.
Grade 4: Build on the concept of equivalent fractions, compare and order fractions.
Grade 5: Use equivalent fractions to add and subtract fractions, and multiply and divide fractions in real-world situations.
Measurement and Data (K-5)
Kindergarten: Describe and compare measurable attributes, classify objects and count them.
Grade 1: Measure lengths indirectly and by iterating length units, tell and write time.
Grade 2: Measure and estimate lengths, relate addition and subtraction to length, work with time and money.
Grade 3: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses; represent and interpret data.
Grade 4: Solve problems involving measurement and conversion of measurements, apply area and perimeter formulas.
Grade 5: Convert like measurement units, represent and interpret data, understand concepts of volume.
Geometry (K-5)
Kindergarten: Identify and describe shapes, create and compose shapes.
Grade 1: Work with shapes and their attributes, compose shapes.
Grade 2: Recognize and draw shapes with specific attributes, partition shapes.
Grade 3: Understand shared attributes among shapes, partition shapes into equal parts.
Grade 4: Draw and identify lines and angles, classify shapes by their properties.
Grade 5: Graph points on the coordinate plane, classify 2D figures.
Ratios and Proportional Relationships (6-7)
Grade 6: Understand ratios and use ratio reasoning to solve problems.
Grade 7: Analyze proportional relationships to solve real-world and mathematical problems.
The Number System (6-8)
Grade 6: Extend previous knowledge of multiplication and division to divide fractions, compute fluently with multi-digit numbers, and understand positive and negative numbers.
Grade 7: Add, subtract, multiply, and divide rational numbers, and solve real-world problems.
Grade 8: Apply properties of integer exponents, work with square and cube roots, and approximate irrational numbers.
Expressions and Equations (6-8)
Grade 6: Write and evaluate numerical and algebraic expressions, and solve equations and inequalities.
Grade 7: Use operation properties to generate equivalent expressions and solve problems with numeric and algebraic equations.
Grade 8: Work with radicals and integer exponents, understand connections between proportional relationships and linear equations, and analyze and solve linear equations and systems.
Functions (8)
Grade 8: Understand the concept of a function and use functions to model relationships between quantities.
Statistics and Probability (6-8)
Grade 6: Understand statistical variability and summarize distributions.
Grade 7: Use random sampling to make inferences about a population, compare two populations, and explore chance processes.
Grade 8: Analyze patterns in bivariate data, create and interpret scatter plots, and apply linear models to data.
In conclusion, it is essential for parents to recognize the importance of a solid foundation in mathematical skills, as any delays can lead to compounded difficulties in the future. A small diversion from the developmental progression can turn into significant learning impairments if not addressed early. If you receive feedback from your child's teacher indicating they are behind grade-level, or if you notice your child is missing the mark in any of the math content areas, our recommendation is to get help now!
Early Tutoring Intervention is Key!
Research consistently shows that targeted individual math interventions in elementary school significantly improve student learning outcomes. The Report on Individualized Math Support published by the Institute of Education Sciences (IES) found that students receiving individualized math support made greater gains in math achievement compared to their peers who did not receive such interventions. Additionally, a meta-analysis by the What Works Clearinghouse indicates that personalized instruction, especially in early grades, leads to substantial improvements in mathematical understanding and problem-solving skills. These findings underscore the effectiveness of tailored interventions in fostering foundational math skills in young learners.
Early intervention and individualized instruction are key to ensuring lifelong math success for your child. Big Sky Tutoring is always available to provide individualized private tutoring to your child. Our math tutors will work diligently to ensure your child is on track to follow standardized developmental progressions. We'll help clarify what the issues are and provide a straightforward path to overcoming your child's math challenges. Investment in early intervention can save you a significant headache later. Elementary math tutoring may, also, prevent your child from damaged self-esteem that often follows years of unresolved learning gaps.