On April 18th the Texas State Board of Education will consider an amendment to the Texas Essential Knowledge and Skills (TEKS) standards that would eliminate any references to mathematical process skills. Parents and activists in Texas have been upset with their inclusion in TEKS because it brings methodology that has been linked to Common Core (this pre-dates Common Core) into Texas standards.
The amendment reads:
Proposed Amendments to 19 TAC Chapter 111,Texas Essential Knowledge and Skills for Mathematics, Subchapter A,Elementary, Subchapter B, Middle School, and Subchapter C, High School (First Reading and Filing Authorization)
This item presents for first reading and filing authorization proposed amendments to 19 TAC Chapter 111, Texas Essential Knowledge and Skills for Mathematics, Subchapter A, Elementary, Subchapter B, Middle School, and Subchapter C, High School. The proposed amendments would remove references to mathematical process skills from knowledge and skills statements in the mathematics Texas Essential Knowledge and Skills (TEKS). Statutory authority for this action is the Texas Education Code (TEC), §§7.102(c)(4), 28.002, and 28.025.
The process standards, according to National Council of Teachers of Mathematics, include:
Problem Solving. Solving problems is not only a goal of learning mathematics but also a major means of doing so. It is an integral part of mathematics, not an isolated piece of the mathematics program. Students require frequent opportunities to formulate, grapple with, and solve com- plex problems that involve a significant amount of effort. They are to be encouraged to reflect on their thinking dur- ing the problem-solving process so that they can apply and adapt the strategies they develop to other problems and in other contexts. By solving mathematical problems, stu- dents acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations that serve them well outside the mathematics classroom.
Reasoning and Proof. Mathematical reasoning and proof offer powerful ways of developing and expressing insights about a wide range of phenomena. People who reason and think analytically tend to note patterns, structure, or reg- ularities in both real-world and mathematical situations. They ask if those patterns are accidental or if they occur for a reason. They make and investigate mathematical conjec- tures. They develop and evaluate mathematical arguments and proofs, which are formal ways of expressing particular kinds of reasoning and justification. By exploring phenom- ena, justifying results, and using mathematical conjectures in all content areas and—with different expectations of so- phistication—at all grade levels, students should see and expect that mathematics makes sense.
Communication. Mathematical communication is a way of sharing ideas and clarifying understanding. Through communication, ideas become objects of reflection, re- finement, discussion, and amendment. When students are challenged to communicate the results of their thinking to others orally or in writing, they learn to be clear, convinc- ing, and precise in their use of mathematical language.
Explanations should include mathematical arguments and rationales, not just procedural descriptions or summaries. Listening to others’ explanations gives students opportuni- ties to develop their own understandings. Conversations in which mathematical ideas are explored from multiple per- spectives help the participants sharpen their thinking and make connections.
Connections. Mathematics is not a collection of separate strands or standards, even though it is often partitioned and presented in this manner. Rather, mathematics is an inte- grated field of study. When students connect mathematical ideas, their understanding is deeper and more lasting, and they come to view mathematics as a coherent whole. They see mathematical connections in the rich interplay among mathematical topics, in contexts that relate mathematics to other subjects, and in their own interests and experience. Through instruction that emphasizes the interrelatedness of mathematical ideas, students learn not only mathemat- ics but also about the utility of mathematics.
Representations. Mathematical ideas can be represented in a variety of ways: pictures, concrete materials, tables, graphs, number and letter symbols, spreadsheet displays, and so on. The ways in which mathematical ideas are repre- sented is fundamental to how people understand and use those ideas. Many of the representations we now take for granted are the result of a process of cultural refinement that took place over many years. When students gain access to mathematical representations and the ideas they express and when they can create representations to capture math- ematical concepts or relationships, they acquire a set of tools that significantly expand their capacity to model and interpret physical, social, and mathematical phenomena.
Here is an example from the TEKS math standards for Kindergarteners.
First in the intro they write:
The process standards describe ways in which students are expected to engage in the content. 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. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. 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. 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. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, computer programs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Then we have some particular standards under knowledge and skills:
(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;
(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;
(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;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
This is for Kindergarten mind you.
Then we have algebraic thinking… for Kindergarteners….
(5) Algebraic reasoning. The student applies mathematical process standards to identify the pattern in the number word list. The student is expected to recite numbers up to at least 100 by ones and tens beginning with any given number.
If this amendment passes it should represent a welcome change in the TEKS standards.
HT: Donna Garner