EDIT I forgot a hunk of code. Inserted at right here.
  @Override
  public boolean onOptionsItemSelected(MenuItem item) {
    Log.w("Before switch", (String) item.getTitle());
    switch (item.getItemId()) {
      case R.id.menu_settings:
        Log.w("Before intent","\n");
        Intent intent = new Intent(this, SettingsActivity.class);
        startActivity(intent);
        Log.w("back from intent", "\n");
        preferences = getSharedPreferences(SETTINGS, MODE_PRIVATE);
        focusAtClue = preferences.getBoolean("focus",true);
        screenSaver = preferences.getBoolean("screen",true);
        Log.w("after intent", focusAtClue + " " + screenSaver);
        return true;
      default:
        Log.w("onOptItemSel","default");
        return super.onOptionsItemSelected(item);
    }
  }
}
The onCreate code here works to create the preferences, as shown in the pic. The xml in preferences.xml is inserted as a comment. It's also included below, intact.
The preferences are stored under the keys focus and screen. Right?
  @Override
  protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);
    preferences = getSharedPreferences(SETTINGS, MODE_PRIVATE);
    boolean firstUse = preferences.getBoolean(FIRST_USE, true);
    if (firstUse){
      Toast helloMessage = Toast.makeText(getApplicationContext(), "Hello First Time User",Toast.LENGTH_LONG);
      helloMessage.show();
      editor = preferences.edit();
      editor.putBoolean(FIRST_USE, false);
      editor.putBoolean  ("focus", false);
/*NOTE THE MATCHED STRING  vvvvv
      <CheckBoxPreference
              android:key="focus"   android:title="@string/focusAfterShow" android:summary="Always place the cursor" android:defaultValue="false"/> */
      editor.putBoolean  ("screen", false);
/*NOTE THE MATCHED STRING  vvvvvv
      <CheckBoxPreference
              android:key="screen"  android:title="@string/screenSaver" android:summary="Keep screen on" android:defaultValue="false" /> */
          editor.commit();
    }
    else {
    ///////////////////// problems here *******************
      SharedPreferences preferences = getSharedPreferences(SETTINGS, MODE_PRIVATE);
      focusAtClue = preferences.getBoolean("focus",focusAtClue);
      screenSaver = preferences.getBoolean("screen",screenSaver);
      Log.w("oncreate:", focusAtClue + " " + screenSaver);
    ///////////////////// problems 
    }
  }
preferences.xml:
<PreferenceScreen xmlns:android="http://schemas.android.com/apk/res/android">
    <PreferenceCategory
        android:title="Screen options">
        >
        <CheckBoxPreference
            android:key="focus"
            android:title="@string/focusAfterShow"
            android:summary="Always place the cursor at the 'clue' (sum) after tapping 'Show'."
            android:defaultValue="false"
            />
        <CheckBoxPreference
            android:key="screen"
            android:title="@string/screenSaver"
            android:summary="Keep screen on at all times while running this app."
            android:defaultValue="false"
            />
    </PreferenceCategory>
</PreferenceScreen>
After leaving the app for the home screen and then returning to it, there has been no change in prefs, as shown in the logcat.
Then I change the first pref by checking its box. The logcat shows that correctly. The code involved is in SettingsFragment.java:
package com.bffmedia.hour11app;
import android.content.SharedPreferences;
import android.content.SharedPreferences.OnSharedPreferenceChangeListener;
import android.os.Bundle;
import android.preference.PreferenceFragment;
import android.util.Log;
public class SettingsFragment extends PreferenceFragment implements OnSharedPreferenceChangeListener {
    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        addPreferencesFromResource(R.xml.preferences);
    }
  @Override
    public void onResume() {
        super.onResume();
        getPreferenceScreen().getSharedPreferences().registerOnSharedPreferenceChangeListener(this);
    }
  @Override
    public void onPause() {
        super.onPause();
        getPreferenceScreen().getSharedPreferences().unregisterOnSharedPreferenceChangeListener(this);
    }
    @Override
    public void onSharedPreferenceChanged(SharedPreferences sharedPreferences, String key) {    
       //SharedPreferences sharedPref = PreferenceManager.getDefaultSharedPreferences(getActivity());
       Log.w("onSharedPrefChgd", sharedPreferences.getBoolean("focus",false) + " " + sharedPreferences.getBoolean("screen",false));
       }
    }
Then I remove the app from the list of apps in memory and then run it from the apps icon.
onCreate says both values are FALSE, but only the first is.
Here's the logcat with only the lines that I wrote via Log.w. There are 3 groups to look at: creation of prefs and changing the first pref, which worked fine. And then the 2nd onCreate, where both values are said to be false, which is wrong--first is true--but the settings screen shows that I did check the first box.
I am clueless as to what I've done wrong.
05-16 13:25:20.290  18778-18778/com.bffmedia.hour11app W/Before switch? Settings
05-16 13:25:20.291  18778-18778/com.bffmedia.hour11app W/Before intent? [ 
05-16 13:25:20.292   438:0x1a07 I/ActivityManager ]
    START u0 {cmp=com.bffmedia.hour11app/.SettingsActivity} from pid 18778
05-16 13:25:20.449  18778-18778/com.bffmedia.hour11app W/back from intent? 
05-16 13:25:20.450 18778:0x495a W/after intent ]
    false false ***************************** CORRECT ************************
05-16 13:35:16.717  18778-18778/com.bffmedia.hour11app W/onSharedPrefChgd? 
     true false *********************************** CORRECT
05-16 13:37:21.185  20014-20014/com.bffmedia.hour11app W/Before switch? Settings
05-16 13:37:21.186  20014-20014/com.bffmedia.hour11app W/Before intent? [ 
05-16 13:37:21.188   438:0x2ef I/ActivityManager ]
    START u0 {cmp=com.bffmedia.hour11app/.SettingsActivity} from pid 20014
05-16 13:37:21.245  20014-20014/com.bffmedia.hour11app W/back from intent? [ 
05-16 13:37:21.245 20014:0x4e2e W/after intent ]
    false false *************************************** WHY? *******************************************
 

 
     
    