Mar 3, 2015 by

Nakonia (Niki) Hayes


By Nakonia (Niki) Hayes


For the purpose of this report, I analyzed the 4th grade TEKS Introduction, paragraphs #1-#3; then, #4-#5.  The actual Mathematics Process Standards follow the Introduction. The TEKS statements themselves are italicized, followed by my comments which open with “Hayes.”    (http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111a.html#111.6.)


(1)             The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on computational thinking, mathematical fluency, and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.


Hayes: This is typical wording used in education materials. It’s okay.


(2)             The process standards describe ways in which students are expected to engage in the content.


Hayes: If too many students are not engaged (contrasted to being entertained) in the lessons [that is, not learning and not transcending to the next lesson with required knowledge and skills], then the lessons/teaching are at fault. Change the lessons to show clarity and successful results in the next lesson if you want to engage students and change behaviors and learning in ALL groups.


The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course.


Hayes: This paragraph does reflect the philosophy of those who support the old Type #2 TEKS standards.


When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace.


Hayes:When possible” means that lessons must not revolve continually around “real world” activities.


Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.


Hayes: See Section (B.1.b) in “Knowledge and Skills” for a sample of Type 1 teaching that follows the above expectations.


Students will select appropriate tools such as real objects, manipulatives, algorithms, paper and pencil, and technology and techniques such as mental math, estimation, number sense, and generalization and abstraction to solve problems.


Hayes:Such as” means students do not have to do everything that is listed in this paragraph!


Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, computer programs, and language.


Hayes: Again, “such as” allows limited, proven selections of methods.


Students will use mathematical relationships to generate solutions and make connections and predictions.


Hayes: We have studied this in mathematics education for hundreds of years: How are adding and subtracting operations related? How are multiplying and dividing operations related? How are fractions and decimals related? Why do you have to have linear mastery of one operation in order to succeed in the other? What is the prediction for accurate solutions and being successful as a student if you don’t have that mastery in each prerequisite operation?


Students will analyze mathematical relationships to connect and communicate mathematical ideas.


Hayes: See above comments on relationships with adding, subtracting, etc.


Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.


Hayes: The “or” gives options of methods for individual students. “Precise mathematical language” means the answers must be mathematically correct and not based on student “creativity” that does not show accuracy or on “effort.” Showing precision in computation is required.


(3) For students to become fluent in mathematics, students must develop a robust sense of number. The National Research Council’s report, “Adding It Up,” defines procedural fluency as “skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.” As students develop procedural fluency, they must also realize that true problem solving may take time, effort, and perseverance.


Hayes: Procedural knowledge and skill are, therefore, of great importance and at least as equal as “process.”


Students in Grade 4 are expected to perform their work without the use of calculators.


Hayes: Yea! It was a battle, but we got this in the document.


Section of “Introduction,” #4-#5, Showing Specific Content Topics


(4) The primary focal areas in Grade 4 are use of operations, fractions, and decimals and describing and analyzing geometry and measurement. These focal areas are supported throughout the mathematical strands of number and operations, algebraic reasoning, geometry and measurement, and data analysis. In Grades 3-5, the number set is limited to positive rational numbers.


In number and operations, students will apply place value and represent points on a number line that correspond to a given fraction or terminating decimal.


In algebraic reasoning, students will represent and solve multi-step problems involving the four operations with whole numbers with expressions and equations and generate and analyze patterns.


In geometry and measurement, students will classify two-dimensional figures, measure angles, and convert units of measure.


In data analysis, students will represent and interpret data.


(5) Statements that contain the word “including” reference content that must be mastered, while those containing the phrase “such as” are intended as possible illustrative examples.


Hayes: It is extremely important to read standards closely to see which ones say “including” and which ones say “such as.” That helps determine lesson plans, student learning expectations, and assessments.






(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


(A) apply mathematics to problems arising in everyday life, society, and the workplace;


Hayes: This process has been used at least since the 1950’s in Texas textbooks and it was called “word problems.” I used those books as a student and have copies of them. Projects with lots of activities and manipulatives are not necessary to meet this standard if the teaching materials have rich word problems. Faux “real world” word problems, however, that preach social justice should not be the function of word problems to prove math skills.


(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;


Hayes: The following is a personal example of how I used Type 1 (explicit, direct, traditional) teaching while representing this particular standard to 4th grade students last fall. They were expanding their skills in long division by using one divisor and a three-digit dividend. We used the standard algorithm, or the procedure recognized internationally and by parents. (Teaching the standard algorithm is required in TEKS, although other algorithms may also be taught. This was a concession some of us made when writing the standards. Regardless, all students must show “procedural fluency as in carrying out procedures flexibly, accurately, efficiently, and appropriately,” according to the Introduction.)


“Use a problem-solving model”Label and learn the historical model with its divisor, dividend, quotient, and radical sign. Use arrows to show visible directions required in each step. With multiple digits in the dividend, there are specific and repetitive procedures.


“Analyze given information”Understand the need to know multiplication facts, subtraction accuracy, and placing digits in the proper space.


“Formulate plan or strategy”Walk through every step to solve the problem before students start writing.


“Determine a solution”Solve the problem; get an answer.


“Justify the solution”Use multiplication of the quotient times the divisor to see if it equals the dividend.


“Evaluate the problem-solving process”Review the many steps needed to solve this problem: multiplication, subtraction, repetition of the steps inside the problem, if necessary, and directionality. (Division is the great proof of automaticity in multiplication skills and a student’s being able to follow the many changes in physical direction while placing numbers in correct locations within the problem. Directionality is a huge task for many students to master in division.)


“Evaluate reasonableness of the solution”Use estimation to show if multiplying the rounded off divisor and dividend produces a solution close to the final answer.


(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;


Hayes: We have long known that use of manipulatives and projects have NOT produced smarter or more competent students. The first question is, “Is the activity appropriate  and proven for the needed learning?” The second question is, “Do the activities and projects provide proven transcendence of knowledge and skills for the next learning level?” The best answer for the second question is a good objective-based test, not subjective opinions.


(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;


Hayes: The key phrase is “as appropriate.”  It does not mean doing ALL of these things. It means selecting an activity appropriate for the students.


(E) create and use representations to organize, record, and communicate mathematical ideas;


Hayes: This does not have to be a drawing or a written paragraph. It can be the actual numerical problem showing the setup and correct solution.


(F) analyze mathematical relationships to connect and communicate mathematical ideas; and


Hayes: This can be accomplished in lessons similar to the one in [B] above.


(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.


Hayes: Because of the word “or”, this can also be supported by completing a lesson similar in [B] above.





By the wording used in “NUMBER AND OPERATIONS” (and other concept areas), the TEKS math standards do, after all, support Type 1 teaching from its Introduction through its last page.


To see this, say before each standard, “THE STUDENT WILL…” This helps show that each “standard” is specific, clear, and direct. This supports Type 1, or traditional, teaching of mathematical concepts.


Other conclusions of this report:


If the Common Core has similar information, it doesn’t matter. The Math TEKS document, elementary through high school, is written for Texas students. Common Core is not. And, remember: It is ILLEGAL TO USE COMMON CORE in “any aspect” of the Texas math curricula, according to state law, HB 462. We don’t need to waste precious training, planning and teaching time to discuss comparisons between the TEKS and Common Core.


We also know the high school Common Core standards are weak and will not prepare students for select colleges, for STEM professions that require a background in math, or even for degrees in other fields such as business administration. Why would anyone want to use the Common Core’s weak high school standards or the out-of-state elementary standards that “prepare” for those weak standards?


Nakonia (Niki) Hayes is a retired mathematics teacher, principal, and was a member of the 2012 TEKS mathematics writing team. She now tutors grades K-8 in math.


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