The document discusses Common Core State Standards (CCSS) for mathematics, which have been adopted by 45 states and focus on conceptual understanding, procedural skills, and application. It introduces Cognitively Guided Instruction (CGI) as an approach for teaching mathematics through problem solving using real world problems. CGI builds conceptual understanding first before procedural skills and focuses on helping students understand connections in mathematics concepts from kindergarten through 12th grade.
3. ? Common Core State Standards (CCSS)
? A set of standards for reading, writing, and
mathematics
? Adopted currently by 45 states, the District of
Columbia, 4 territories, and the Department of
Defense Education Activity (DoDEA)
? Developed by state leaders, governors, and state
commissioners of education ¡NOT federally
governed
? Standards do NOT tell teachers how to teach
4. ? Cognitively Guided Instruction (CGI)
? Not ¡°NEW¡± math - Mathematics does not
change
? Fewer concepts per grade level-more depth
? Focus on conceptual understanding,
procedural skills and fluency, and
application
5. ?It¡¯s the same mathematics
?Build the concept first
?Not a list of disconnected topics, tricks,
procedures, or mnemonics
?Understand the connections
7. ?CGI is an approach for teaching
mathematics through problem solving
?Real world problems
?Has to be ¡°a problem¡±
8. ?Solve problems in context (stories) and
out of context (equations)
?A problem is posed within a story, the
students can remove the numbers,
decide what to do with them, solve, and
apply the answer back to the story
13. ?Look closely for a pattern or structure
within the mathematics
? 7 and 3 is the same as 3 and 7
? Categorize shapes by attributes
? 7 x 8 = (7 x 5) + (7 x 3)
? Symmetry
14. ?Notice if calculations are repeated
?Look for general methods and shortcuts
?Does my answer make sense?
#3: Common Core is a hot topic. Facebook, Instagram, Yahoo, the local news¡there is a ton of information about ¡°common core¡± flying around. What are the facts?
#4: The common core is simply a set of standards. We have always had standards/expectations of what is expected for students to learn by grade level. The common core standards- the minimum expected at each grade level in reading, writing, and math. NOT a curriculum. How a state, school district, school, teacher reaches the standards is up to them.Prior to CCSS the standards were developed state by state. 50+ different standards. Some highly rigorous/some much easierNOT developed by the federal government. NOT a curriculum. IS a consistent set of standards/expectations across the United States. Same expectations/same minimum regardless of where a child lives.
#5: Springdale School District is meeting the common core mathematics¡¯ standards through the use of CGI ¨Cmore on that later¡The mathematics we are teaching and guiding students to understanding of is the same mathematics that has been around for years and years. Mathematics does not change. We are working with the same properties of operations, the same base ten number system, the same measurement tools, the same concepts of geometry, the same equations. It took mathematicians centuries to come up with a ¡°standard algorithm¡± to explain how math works. We begin with understanding.The standards haven¡¯t even changed¡the sequence has been adjusted. There are fewer number of standards at each grade level. No repetition, but instead a foundation established in kindergarten with each following grade level adding another layer/another depth of understanding.1st Build/understand the concept 2nd procedural skills Fluency and application
#6: Yes, you are seeing your students doing some things that look different. Yes, you are seeing them begin earlier (kindergarten), fractions in 3rd grade. Yes, it¡¯s difficult to help at home when it looks different to you(we have an answer to that coming up¡).Through the years you will see the benefits.Major benefits to holding off on the procedural (carrying and borrowing) Once students have an understanding of the mathematics and how/why it works then the procedure is easy. But better than that; the mathematics knowledge is priceless!!We do get to the way many of us grew up ¡°learning¡±. Multi-digit addition and subtraction algorithm is 4th grade. Multi-digit multiplication algorithm is 5th grade. Long division algorithm (garage) is 6th grade. Cannot emphasize the benefits to this foundation for higher math (algebra, geometry, statistics, calculus)Students will still learn their facts. It actually begins in kindergarten.
#7: Along with grade level standards, every grade level is also expected to be developing the Standards for Mathematical Practice in their students. Of course this will look different at each grade level. As with the standards that begin as a foundation and grow; the SMPs will grow with the students¡¯ depth of understanding.
#8: CGI uses story problems, questioning, and discussion to lead to the mathematics. We want to pose problems that the students do not immediately know the answer to.
#9: In CGI we solve problems within stories (context) and we solve just equations. CCSS expects that students can see an equation and give it a context. Or when a problem is posed within a story, the students can remove the numbers, determine what to do with them, solve, and apply the answer back to the story.
#10: In CGI, this happens throughout the share time. Students prove their thinking mathematically both written and verbal. They compare strategies, and determine the better way to solve a problem.
#11: Students learn to apply what they already know to solve problems in everyday life.
#12: Students choose the best tool to solve a problem. They see the benefits of one tool over another.
#13: We see this during share time and/or partner talk.Students learn to discuss verbally and written. They label answers. We strive for accuracy and efficiency.
#17: Look for ¡°word problems¡± in real life. Some 4th grade examples might include:¡öAsk your child to compare numbers using phrases like ¡°times as much.¡± For example, if the family cat weighs 8 lbs. and the family dog weighs 56 lbs., how many times as much does the dog weigh?¡öAsk your child to help you compare fractional amounts ¡ª for example, if one recipe calls for 2?3 of a cup of oil, but another recipe calls for 3?4 of a cup of oil, which recipe calls for more oil? (In 5th grade, your child will learn ways to determine just how much more oil.)