Helping Students Learn Lesson Design and Evaluation of Student Learning Copyright ©2014 by Lynda Aguirre

Copyright ©2014 by Lynda Aguirre Cardinality Cardinality is a concept that students must master before they can learn any kind of mathematics. They naturally develop this sense of what numbers are at around age 5. You can test them to see if they have achieved Cardinality like this: Test: Put some objects (let’s say 5) in front of them and ask them “how many objects are there?” 1) If they have achieved cardinality, they will say “5”, or they will count them and then say “5” 2) If they have not achieved cardinality, they will just count them. In simple terms, achieving cardinality means that they understand that the “5” is the total number of objects as well as the 5th object. If they don’t understand this concept, they can’t do addition like 2 + 3, because they don’t understand what the symbols “2” and “3” mean. Copyright ©2014 by Lynda Aguirre

Understanding True understanding occurs when we see how something is related or connected to other things we already know Teaching in a way that promotes understanding involves more than just sharing facts or methods. It must take the students attitudes and thought processes into consideration Copyright ©2014 by Lynda Aguirre

Copyright ©2014 by Lynda Aguirre Issues to consider The way a student thinks about their relationship with mathematics will determine whether they understand and retain the material in your lesson --Sex differences- Are Males assumed to be better at math than Females? Why? --Is Math Anxiety an issue? --What is the student’s societal attitude towards mathematics? Parents, peers and population --Individual Interview helps to pinpoint the way a student thinks about mathematical learning Copyright ©2014 by Lynda Aguirre

Copyright ©2014 by Lynda Aguirre Issues to consider The classroom environment, or social culture, can influence their ability to learn --What tools are available in the classroom? --Every student contributes their ideas without fear of ridicule --Tasks are accessible to all students --Ideas and methods are valued --Correctness resides in mathematical argument Copyright ©2014 by Lynda Aguirre

Copyright ©2014 by Lynda Aguirre Interview Questions When trying to determine a student’s learning strengths and weaknesses you can ask a series of Interview questions to narrow down your search How did you get your answer (I may have missed something) Why is your answer correct? Could you explain it another way? Can you make a drawing to show your answer is correct? What kinds of errors do you usually make? What do you do when you see an unfamiliar problem? What kinds of problems are you worst at? What can you do to get better at these? Copyright ©2014 by Lynda Aguirre

How do they justify their answers? 1) Externally based-textbook or authority is cited 2) Empirically based- use of perception or concrete objects to show their answer is correct Analysis-students use counting strategies or cite mathematical relations to justify their answers Copyright ©2014 by Lynda Aguirre

1)Nature of Learning Tasks Use everyday objects or situations they can relate to Use knowledge that they already have Give them some valid reason to learn the material Copyright ©2014 by Lynda Aguirre

Copyright ©2014 by Lynda Aguirre 2) Role of the Teacher Select tasks that will achieve the learning goals Share essential information Establish classroom culture Copyright ©2014 by Lynda Aguirre

3) Social Culture of the Classroom Ideas and input are encouraged and valued Students feel safe sharing their methods Mistakes are viewed as learning tools for everyone Alternative solutions are examined for validity Copyright ©2014 by Lynda Aguirre