Back to: Module: Helping Students Do Math
Slide 1: Hello, and welcome to this webinar on math and the Common Core with Daniel Showalter.
Slide 2: Just by paying attention to the news, social media sites, or gossip in the teacher’s lounge, you may have already heard of the Common Core State Standards or of Ohio’s New Learning Standards. But what are they? And what do they mean for you?
Slide 3: School administrators, teachers, and parents want their students (or children) to learn the most important math concepts so that they are prepared for the next steps in their lives. But the field of math is so big that it can be quite tricky for educators to decide which math topics should get taught in each grade level.
Slide 4: This is where standards come in. Every 10 years or so, national guidelines are published recommending what math students should be learning throughout their primary and secondary school years and how they should be learning it. In the past, these national guidelines have been quite general. Each state could then use these general guidelines as they wrote a more specific set of standards for students in their state. In many cases, the state standards were quite different from the national guidelines.
Slide 5: The Common Core State Standards were designed to follow a similar pattern in recommending which math topics and practices students should be learning. However, there were a couple important differences.
Slide 6: First, there was a strong effort between the states to come up with standards that would be adopted directly by a majority of the states. Second, the Common Core State Standards were intended to be much more detailed than previous national guidelines. The Common Core would detail the specific math topics and practices to be learned at each grade level.
Slide 7: In other words, under the Common Core, a sixth grade math class in rural Nebraska should be covering roughly the same topics as a sixth grade math class in center city New York or in suburban Beverly Hills.
Slide 8: Of course, not everyone believes that sixth grade students across the country should learn the same math. So, when the Common Core State Standards in Mathematics were released in 2010, several states decided not to adopt them or adopted them with modifications. Ohio adopted them completely and called them Ohio’s New Learning Standards.
Slide 9: So, what does all of this mean for you as a paraprofessional?
Slide 10: One thing you should be aware of is their importance in terms of testing. There are now tests designed to evaluate students according to the Common Core. The way in which students perform on these tests has implications for students, teachers, and school districts.
Slide 11: More importantly, you should be familiar with the basic principles of the Common Core so that you can support students and teachers as they pursue common goals in teaching and learning mathematics.
Slide 12: The Common Core is divided into two main parts: the Standards for Mathematical Content and the Standards for Mathematical Practice. Content and practice.
Slide 13: The content standards describe specific learning objectives in various topics in math such as geometry, measurement, and data for each grade level. The teacher uses these content standards to plan and design lessons.
Slide 14: The content standards are written as a final set of objectives that the students should reach by the completion of a given grade level. In most cases, students must progress through a series of intermediary steps before they reach a final objective.
Slide 15: These intermediary steps in the pathway toward the accomplishment of a content standard are called “learning progressions.” The extended Common Core details these learning progressions so that teachers and paraprofessionals can assess student progress toward meeting content standards. Let’s take a look at an actual learning progression.
Slide 16: One of the Numbers and Operations standards for Grade 2 is to compare three digit numbers using the symbol for less than, greater than, or equal to. A student should be able to look at these two numbers, 315 and 702, and be able to place the appropriate comparison symbol in between the numbers.
Slide 17: The extended Common Core provides a series of tasks that build up to the three-digit comparison. First, students should learn to compare one digit numbers using the words “more than”, “less than” or “the same as”. When they’ve mastered this, they compare two-digit numbers using the same words, and then three-digit numbers. Finally, they use symbols to compare three-digit numbers.
Slide 18: Learning progressions map out paths to help students reach the content standards. But just like there are many roads that lead to any given destination, there are many learning progressions that students could follow to reach the standards. An alternate learning progression on the path toward mastery of three-digit symbolic comparisons would be to master one-digit verbal comparisons, then one-digit symbolic comparisons, and then two-digit symbolic comparisons. The theory behind learning progressions is that students often learn best when the next learning objective is just slightly more advanced or more complicated than what they already know.
Slide 19: Whereas the content standards describe what math students should learn, the practice standards suggest how students should be able to interact with and use math. Teachers and paraprofessionals should work together to implement the Standards for Mathematical Practice. There are eight practice standards, but let’s omit #4 and #8 to focus on the six practice standards that are most relevant to paraprofessionals working with students.
Slide 20: Practice Standard #1 is to make sense of problems and persevere in solving them. Encourage students to spend time figuring out the problem, and then to ask themselves whether intermediary results and final results make sense. Spending this extra time on problems requires patience, which is why the second part of this standard mentions perseverance. Notice that this standard aligns well with Polya’s method.
Slide 21: Practice Standard #2 is to reason abstractly and quantitatively. Try to help students move back and forth between concrete objects and things such as numbers that cannot be seen. For example, the concrete situation of sharing a 12-slice pizza among three friends can be shifted to the math expression 12 divided by 3.
Slide 22: Practice Standard #3 is to make and critique arguments logically. Using mathematical terms, it is possible to make, defend, and critique claims. When you hear students making a claim that you know is not true, you can give them an opportunity to rethink the problem by showing a counterexample. For example, if students notice that (-2) + 3 = 1 and (-5) + 9 = 4, they might believe that the sum of a negative and a positive is always a positive. You could say, “What about (-2) + 1?”
Slide 23: Practice Standard #5 is to use appropriate tools strategically. “Tools” might include a calculator, the textbook, a spreadsheet, a ruler, or even a peer. When students get stuck on a problem, ask them what tools they have that could help them solve the problem.
Slide 24: Practice Standard #6 is to attend to precision. One of the reasons students get confused in math is because they have only vague concepts of the definitions and properties that they are learning about. When a student seems to be confused about a particular math term, encourage the student to look up the definition in the textbook.
Slide 25: Practice Standard #7 is to look for and make use of structure. Math is full of patterns, and, by helping students see these patterns, you can help make math easier and more enjoyable.
Slide 26: The main goal of the standards is to ensure that students will become fluent with the math they will encounter in all domains of life: careers, sports, financial matters, music, and nature. By supporting teachers’ implementation of the Common Core, paraprofessionals can help students effectively tap into the power and beauty of math!