joan is often confused when solving word problems. She is asked to solve the following: Fourteen ducks are floating on the lake. Seven fly away. How many are left? Joan draws a pond with fourteen ducks on it. She then draws seven more. She counts 21 ducks. Which method for solving is Joan using? A concrete model A semi concrete model An abstract model A semi abstract modelPatty Ratajczak is studying to become a teacher. As part of an experiment, Patty wants to understand how students view liquid volume. Patty has two water glasses. One glass is short and wide and the other glass is tall and thin, but each glass holds exactly eight ounces of liquid. Interviewing different first grade students individually, Patty fills the shorter glass with water. She then takes the water from the shorter glass and pours it into the taller glass. Patty asks each student which glass holds more water. Without exception, the students indicate that the tall, thin glass holds more water. This response indicates that the students in Patty's experiment are at which level of mathematical learning? Preoperational Concrete operational Operational Middle School