This range has a glow bar ignitor system. The theory of operation for this system is shown in the first image below. Your range has a relay on the control board instead of a thermostat that closes to apply voltage to the circuit. Since the ignitor glows, this relay is apparently okay. If the ignitor continues to glow even though the burner shuts off, then a weak ignitor (part number 318177710) is the likely cause of this failure.
See if the broil burner works properly. If it does and the bake ignitor is constantly glowing, then you can
shut off the circuit breaker
for the range and switch the broil and bake ignitors. See if the bake burner works properly with the ignitor that was on the broiler burner installed. If it does, then replacing the bad ignitor should fix this problem.
Here is a direct Sears PartsDirect.com link for the ignitor:
A technician will sometimes use a clamp-on ammeter to check the amp draw through the yellow wire between the ignitor and the safety gas valve to check the ignitor. I provided a wiring diagram for this range in the second image below. A minimum of 2.9 amps is needed to open the safety gas valve. If the amp draw is too low, the safety gas valve will not open. You can check the amp draw through the yellow wire if you have a clamp-on ammeter. If you do not have an ammeter, you can use the routine described above to check for a failed ignitor.
If the ignitor is not glowing steady when the oven is set in the bake mode, then you could have a problem with the oven temperature sensor probe, the control board or a wiring failure in the circuit. To check the oven temperature sensor probe, you can measure the resistance of that component (with the circuit breaker shut off). The temperature/resistance chart for the sensor probe is shown in the third image below. The 4th image shows how to access this component. At room temperature, the sensor should measure around 1100 ohms. If not, I recommend that you plug the sensor back in and check the resistance through the entire sensor circuit from the control board. The 5th image shows how to access the control board in this type of range (with the circuit breaker shut off). If the resistance through the entire sensor circuit if okay, the you likely have a failure in the wiring or the control board if the ignitor is not glowing steady in the bake mode.
These tips should help you diagnose and repair this failure in your Kenmore range. If you need more assistance, reply with additional details.
If you do not feel confident repairing this problem yourself, then keep in mind that you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services